simulation and characterization of optical nanoantennas ... · acknowledgements i would like to...

IMPERIAL COLLEGE lONDON

Simulation and characterization of

optical nanoantennas for field

enhancement and waveguide coupling

Roberto Fernandez Garcıa

A thesis submitted in partial fulfillment for the

degree of Doctor of Philosophy

in the

Department of Physics

November 2013

Declaration of Authorship

I, Roberto Fernandez Garcıa declare that this thesis titled, ‘Simulation and characteri-

zation of optical nanoantennas for field enhancement and waveguide coupling’ and the

work presented in it are my own. I confirm that:

� This work was done wholly or mainly while in candidature for a research degree

at this University.

� Where any part of this thesis has previously been submitted for a degree or any

other qualification at this University or any other institution, this has been clearly

stated.

� Where I have consulted the published work of others, this is always clearly at-

tributed.

� Where I have quoted from the work of others, the source is always given. With

the exception of such quotations, this thesis is entirely my own work.

� I have acknowledged all main sources of help.

� Where the thesis is based on work done by myself jointly with others, I have made

clear exactly what was done by others and what I have contributed myself.

Signed:

The copyright of this thesis rests with the author and is made available under a Creative

Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to

copy, distribute or transmit the thesis on the condition that they attribute it, that they

do not use it for commercial purposes and that they do not alter, transform or build

upon it. For any reuse or redistribution, researchers must make clear to others the

licence terms of this work

IMPERIAL COLLEGE lONDON

Abstract

Department of Physics

Doctor of Philosophy

by Roberto Fernandez Garcıa

Optical antennas are nanostructures designed to efficiently convert free-propagating op-

tical radiation to localized energy and vice versa. They are based on localized surface

plasmon resonances (LSPRs) that generally exist in metal nanoparticles (NPs). The

excitation of LSPRs can lead to large near field enhancements and to an increase of the

near field effective area up to several times the physical cross section of the nanoparticle.

These properties can be used to increase the interaction of any object located in their

vicinity with free space radiation. In this thesis, we investigate experimentally and nu-

merically the interactions of nanoantennas with different systems like organic emitters,

graphene and dielectric waveguides.

we have numerically reviewed important experimental factors that generally control the

optical antennas properties. Substrates, metal sticking layers, geometries or dimen-

sions can significantly influence the maximum near field enhancement and the resonance

wavelength that optical antennas can provide for spectroscopies like Surface enhanced

Raman Scattering, (SERS) and Photoluminiscence, (PL). In particular, we experimen-

tally analyse the influence of the incorporation of a metallic reflecting layer. This provide

a straightforward way to increase the photoluminescence enhancement of nanoemitters

induced by optical nanotantennas.

Regarding SERS applications, we probe with surface-enhanced Raman scattering the

plasmonic properties of an isolated Au double disk nanostructure interfaced with sus-

pended graphene. By rotating the polarization of the excitation, we switch between the

dots acting as single plasmonic particles and a coupling regime, realizing a plasmonic

cavity. we observe a Raman intensity enhancement of the order of 103 resulting from

the near-field enhancement at the antenna cavity.

Acknowledgements

I would like to thank all the people who contributed to the work described in this thesis.

First, I thank my academic supervisor, Professor Stefan A. Maier, for accepting me into

his group. During my Phd, he contributed to a rewarding graduate school experience

by giving me intellectual freedom in my work, supporting my attendance at various

conferences and meetings, engaging me in new ideas, and demanding a high quality of

work in all my research activities. I am specially grateful to Dr. Yannick Sonnefraud

not only for giving me interesting ideas, sharing his knowledge and training me with

many different experiments, but also for his advise, supervision and patience during the

development of all my doctorate.

I also would like to thank all the members from the plasmonic group, at the Physics

department, for their help and advise. In particular, I thank Dr. Vincenzo Giannini, Dr.

Antonio Fernandez-Dominguez and Yan Francescato for being always willing to answer

and discuss any question. Without them, my job would have undoubtedly been more

difficult.

Every result described in this thesis was accomplished with the help and support of

several collaborators. Firstly, I want to thank Dr. Rahmani, Dr. Tyler R.Roschuk and

Antonios Oikonomou for carrying out the e-beam fabrication of the samples studied in

this thesis. Secondly, would like to thank Professor Nader Enghetha and Dr. Uday Chet-

tiar for their guidance and constructive discussions studying the possibilities of coupling

plasmonic nanoantennas and silicon waveguides.

Lastly, but not least, I thank all the researchers that took part in the collaborative

project, NANOSPEC leaded by Prof. Eleanor Campbell. My graduate experience ben-

efited greatly for collaborating with such an interdisciplinary group of people. I was

specially fortunate to collaborate extensively with Sebastian Heeg. I gained a lot from

his vast Raman scattering knowledge, motivation and scientific curiosity.

This thesis has been funded by the UK Engineering and Physical Sciences Research

Council (EPSRC) and Nano-Sci Era Nanospec.

Scientic publications of results presented in

this work

“Use of a reflecting-layer in optical antenna substrates for increase of photoluminescence

enhancement”. Optic Express Vol. 21, pp. 12552-12561, 2013

Roberto Fernandez-Garcia, Mohsen Rahmani, Minghui Hong, Stefan A. Maier, Yannick

Sonnefraud

“Polarized Plasmonic Enhancement by Au Nanostructures Probed through Raman Scat-

tering of Suspended Graphene”. Nanoletters Vol. 13, pp 301308, 2013

Sebastian Heeg, Roberto Fernandez-Garcia, Antonios Oikonomou, Fred Schedin, Rohit

Narula, Stefan A Maier, Aravind Vijayaraghavan, Stephanie Reich

“Enhancement of radiation from dielectric waveguides using resonant plasmonic core-

shells. Optic Express Vol. 20, pp. 16104-16112, 2012

Uday K. Chettiar, Roberto Fernandez-Garcia, Stefan A. Maier, Nader Engheta

“Controlling light localization and light-matter interactions with nanoplasmonics”. Small,

Vol.6, PP. 2498-2507, 2010

Vincenzo Giannini, Antonio Fernandez-Dominguez, Yannick Sonnefraud, Tyler Roschuk,

Roberto Fernandez-Garcia, Roberto and Stefan A.Maier

“Design considerations for near-field enhancement in optical antennas”. Contemporary

Physics 2013(Submitted)

Roberto Fernandez-Garcia, Yannick Sonnefraud, Antonio Fernandez-Dominguez, Vin-

cenzo Giannini, Stefan A.Maier

“Controlled optical coupling of carbon nanotubes into plasmonic cavities probed by sur-

face enhanced Raman scattering”. Nanoletters 2013(In preparation)

Sebastian Heeg, Antonios Oikonomou, Roberto Fernandez-Garcia, Christian Lehmann,

Stefan A.Maier, Aravind Vijayaraghavan, Stephanie Reich

Posters presented in this work

“Plasmonic Dimers for Controlling the Emission Polarization of Organic Emitters”. Pho-

ton12 Durhan,UK September 2012

“Enhancement of radiation from dielectric waveguides using resonant plasmonic core-

shells”. Photon12 Durhan,UK September 2012

“Simulation and characterization of optical nanoantennas for field enhancement and

waveguide coupling” Postgraduate Research Physics Symposium 2012 Imperial College

London, UK June 2012

Contents

Declaration of Authorship 1

Abstract 2

Acknowledgements 3

Scientic publications of results presented in this work 4

List of Figures 8

1 Introduction 11

1.1 Introduction to Surface Plasmons . . . . . . . . . . . . . . . . . . . . . . . 12

1.1.1 Fundamental optical properties . . . . . . . . . . . . . . . . . . . . 12

1.1.2 Optical response of metals and dielectrics . . . . . . . . . . . . . . 14

1.1.3 Localized surface plasmons . . . . . . . . . . . . . . . . . . . . . . 16

1.1.3.1 Nano-sphere interaction with an electro-magnetic wave . 17

1.2 Optical antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.2.1 Optical antennas cross section . . . . . . . . . . . . . . . . . . . . . 20

1.2.2 Antennas modes and field enhancement . . . . . . . . . . . . . . . 20

1.2.3 Applications of optical antennas . . . . . . . . . . . . . . . . . . . 25

1.2.4 Decay rate emission close to a nanoantenna . . . . . . . . . . . . . 28

1.3 References Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2 Methods 40

2.1 Experimental techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.1.1 Electron beam lithography(E-beam) . . . . . . . . . . . . . . . . . 40

2.1.2 Dark Field Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.2 Finite-difference time-domain (FDTD) method . . . . . . . . . . . . . . . 44

2.2.1 Lumerical FDTD Simulations . . . . . . . . . . . . . . . . . . . . . 48

2.2.1.1 How to avoid the divergence of the fields in the simulation 49

3 Design considerations for near-field enhancement in optical antennas 52

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2 Influence of the material . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.3 Influence of the dimensions and geometry on the plasmonic properties . . 56

Contents 7

3.4 Influence of substrate on the plasmonic properties . . . . . . . . . . . . . 60

3.5 Introduction of a reflective layer . . . . . . . . . . . . . . . . . . . . . . . 61

3.6 Influence of an adhesion layer . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.7 Antennas arrays and near field enhancement . . . . . . . . . . . . . . . . . 64

3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4 Use of a gold reflecting-layer in optical antenna substrates for increaseof photoluminescence enhancement 71

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.2 Experimental methods for Photoluminescence measurement . . . . . . . . 72

4.3 Effect of a gold reflecting-layer on the properties of gold dimmer antennas 75

4.4 Photoluminescence (PL) enhancement of the TPP emitters . . . . . . . . 77

4.5 Influencing the polarization of the emitted light by utilizing the asymme-try of dimer antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5 Polarized Plasmonic Enhancement probed through Raman Scatteringof Suspended Graphene 86

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.2 Description of the graphene-dimer interface . . . . . . . . . . . . . . . . . 88

5.3 Plasmonic resonances analysis of the structure . . . . . . . . . . . . . . . 89

5.4 Polarization dependence of Raman scattering on suspended graphene . . . 90

5.5 Strained Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.6 Polarization dependence on the near field enhancement . . . . . . . . . . . 92

5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6 Enhancement of radiation from dielectric waveguides using resonantplasmonic core-shells 99

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.3 Parameter scan of the total efficiency . . . . . . . . . . . . . . . . . . . . . 102

6.4 Core-shell directivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.5 Distance sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7 Conclusions 112

7.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

List of Figures

1.1 Components of the complex dielectric function for metals and dielectricsusing the Drude model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.2 Schematic diagrams illustrating a surface plasmon polariton and localizedsurface plasmon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.3 Sketch of a homogeneous sphere placed into an electrostatic field . . . . . 17

1.4 Normalized extinction, absorption and scattering cross sections for threedifferent Ag nanoparticles in vacuum . . . . . . . . . . . . . . . . . . . . . 21

1.5 Plasmonic resonances in a gold nanobar . . . . . . . . . . . . . . . . . . . 22

1.6 Extinction spectra calculated using plasmon hybridization theory for ahomodimmer and a heterodimmer . . . . . . . . . . . . . . . . . . . . . . 24

1.7 Normalized measurements of fluorescence decay rate of a dye near a res-onant nanoantenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.8 Schematic representation of molecules randomly placed around a goldbowtie antenna on a transparent substrate . . . . . . . . . . . . . . . . . . 31

2.1 Process to obtain a patterned resist mark by using electron beam writing 41

2.2 Techniques for transferring PMMA patterns onto the sample . . . . . . . 41

2.3 Configuration of standard dark field using a confocal microscope and po-larised side-illumination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.4 Sketch of the experimental setup used to obtain dark field spectra onnanoantenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.5 Distribution of electric and magnetic field components in the Yee grid . . 46

2.6 Space-time sampling of the Yee algorithm . . . . . . . . . . . . . . . . . . 46

2.7 Spherical gold particle simulation setup . . . . . . . . . . . . . . . . . . . 48

3.1 Real part and imaginary part of the permittivity of Ag, Au, Al and Cu . 54

3.2 Scattering and absorption cross sections of dimer antennas made of Ag,Au, Al and Cu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.3 Simulated near-field enhancement at the cavity center of dimer antennasmade of Ag, Au, Al and Cu . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.4 Evolution of the scattering cross section and near field enhancement withthe antenna gap distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.5 Evolution of the wavelengths of maximum far-field scattering and nearfield intensity distribution for dimmer antennas with different length . . . 57

3.6 Scattering cross section and near field enhancement distribution of plas-monic dimers with different geometries . . . . . . . . . . . . . . . . . . . . 59

3.7 Scattering cross section of a gold dimer antenna as a function of therefractive index of the substrate . . . . . . . . . . . . . . . . . . . . . . . . 60

List of Figures 9

3.8 3D integration of the near field enhancement at the resonance wavelengthfor each distance of separation between the antenna and the gold underlayer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.9 Quantum yield enhancement for a single emitter placed at the antennagap and oriented along the antenna axis for for each distance of separationbetween the antenna and the gold under layer . . . . . . . . . . . . . . . . 62

3.10 Scattering cross section and near field enhancement distribution of a goldplasmonic dimer with different adhesion layers . . . . . . . . . . . . . . . 63

3.11 Near-field enhancement at the gap of periodic arrays of gold dimers fordifferent pitches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.1 Spectral photoluminescence of TPP-doped PMMA films fabricated withdifferent PMMA/TPP weight concentration ratio . . . . . . . . . . . . . . 73

4.2 Experimental setup for TPP fluorescence measurement . . . . . . . . . . . 74

4.3 Effect of a gold underlayer on the antenna properties . . . . . . . . . . . . 75

4.4 Spectral overlap between the emission band of TPP and simulated NFresonances with and without gold underlayer . . . . . . . . . . . . . . . . 77

4.5 Influence of the polarization on the scattering of a gold dimer . . . . . . . 79

4.6 Spectral overlap between the emission bands of TPP and the simulatednear field resonances for both the X and Y polarizations . . . . . . . . . . 80

4.7 Study of the influence of the nanoantenna on the polarisation propertiesof the emitted PL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.1 AFM image of graphene placed on top of the double structure . . . . . . . 88

5.2 Experimental dark-field spectra and simulated scattering cross sections . . 90

5.3 Raman spectra on the double structure for λ = 532 nm and λ= 638 nm . 91

5.4 Raman line scan over the antenna structure . . . . . . . . . . . . . . . . . 93

5.5 Near-field enhancement distribution in the x-y and the x-z planes . . . . 94

6.1 Core-shell particle resonance under plane wave illumination,λres=592nm . 101

6.2 Schematic of the Si waveguide and the core-shell particle . . . . . . . . . . 102

6.3 Field intensity distribution of the mode polarised along the y axis at twodifferent waveguide cross section . . . . . . . . . . . . . . . . . . . . . . . 102

6.4 Maximum total efficiency in the 500 nm to 700 nm wavelength rangeas a function of the waveguide dimension and the waveguide-coreshellseparation for different values of collision frequency . . . . . . . . . . . . . 103

6.5 Reflectance, total efficiency and losses for various separations . . . . . . . 104

6.6 Reflectance, total efficiency and losses as for various collisions frequencies 105

6.7 Electric field distribution of the system constituted by a core-shell particleplaced at the output of the square waveguide . . . . . . . . . . . . . . . . 106

6.8 Far-field patterns of radiation from the system ystem constituted by acore-shell particle placed at the output of the square waveguide . . . . . . 106

6.9 Ratio of the forward radiated power to the total radiated power for variousseparations between the waveguide and the core-shell . . . . . . . . . . . . 107

6.10 Contour plots of the reflectance and total efficiency shown as function ofwavelength and separation . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

6.11 Reflectance as a function of separation of core-shell particle from thewaveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Chapter 1

Introduction

—————————————————————–

In chapter 1, it is given an introduction to LSPRs and optical antennas, discussing its

principal properties and most important applications. It will be followed by a brief

description of the experimental methods using in this thesis.

In chapter 3, we numerically analyse experimental parameters like substrate influence,

metal sticking layers, geometries or dimensions that influence the maximum near field

enhancement and the resonance wavelength that optical antennas can provide for spec-

troscopies like Surface enhanced Raman Scattering, (SERS) and Photoluminiscence,

(PL). In addition, a special emphasis is made on the influence of the antenna design on

the energy shift between near-field and far-field peak intensities. In chapter 4, we exper-

imentally analyse the influence of one of the parameters, the incorporation of a metallic

reflecting layer. This provides a straightforward way to increase the photoluminescence

enhancement of nanoemitters induced by optical nanotantennas. The nanoantennas are

placed above a gold film-silica bilayer, which produces a drastic increase of the scat-

tered radiation power and near field enhancement. We demonstrate this increase of

photoluminescence enhancement using an organic emitter of low quantum efficiency:

Tetraphenylporphyrin (TPP).

In chapter 5, we probe with surface-enhanced Raman scattering the plasmonic proper-

ties of an isolated Au double disk nanostructure interfaced with suspended graphene. In

addition, this thesis also explores the interaction between antennas and dielectric waveg-

uides based on Silicon-Carbide in chapter 6. We investigate numerically a method of

power extraction from a dielectric waveguide using a core-shell particle with a plasmonic

shell in proximity of the waveguide end.

Introduction. Optical antennas 12

1.1 Introduction to Surface Plasmons

In this section, a brief review of the optical properties of metals in comparison with

dielectrics is given in order to lay the foundations of plasmons. It will be followed by

a more detailed description of localized surface plasmons to introduce and explain how

an optical antenna works. Finally a general description of optical antennas and their

properties is provided as well as some of their potential applications related with this

PhD project.

1.1.1 Fundamental optical properties

Metals can be considered as an isotropic medium with a dielectric function, ε, permeabil-

ity µ and conductivity σ. It is possible to write the Maxwell equations in metals by using

the relationships between the electric field and these material quantities, D(r)=ε(r)E(r),

B = µH and J = σE where D is the electric displacement, J the current density and B

is the magnetic induction vector.

∇ ·H = 0 (1.1)

∇ ·E =ρ

ε(1.2)

∇×E + µ∂H

∂t= 0 (1.3)

∇×H + ε∂E

∂t= σE (1.4)

From these equations we can extract information on the material optical properties. 1.4

and 1.3 can be manipulated to eliminate H. If we consider monochromatic light and

propose a plane wave solution to Maxwell’s equations,

E = E0e−ik·x−iωt (1.5)

Then, the wave equations for a metal can be written:

∇2E + ω2µ(ε+ iσ

ω)E = 0 (1.6)

By defining a complex dielectric constant

ε = ε− iσ

ω(1.7)

a complex wave equation is obtained

∇2E + κ2E = 0 (1.8)

κ = ω

√µ(ε− iσ

c(1.9)

and n = n(1 − iκ) is the complex refractive index, where κ is called the extinction

coefficient. To analyse the consequences of a non-zero conductivity or the imaginary

part of the dielectric constant on a metal, we consider a plane wave propagating in the

z direction.

E = E0e−iκz = E0e

−inωcze−

zd (1.10)

The last exponential is the damping term, and d = cnωκ is the ”skin depth” of the metal.

n and κ can be written out in the forms of ε, µ and σ

n2 =c2

√µ2ε2 + (

ω)2 + µε] (1.11)

n2κ2 =c2

√µ2ε2 + (

ω)2 − µε] (1.12)

For typical metals, σω � ε, so n2κ2 w c2µσ

2ω and thus

µσω(1.13)

i.e the skin depth goes as 1σ . For near infrared frequencies the skin depth of gold is of the

order of 20 nm. This distance is small compared to the wavelength of the light, so there

is little interaction between the metal and the optical field, in this regime the gold can

be considered a perfect reflector. In the next section we see that this situation changes

as the frequency is increased to the visible regime at which the light wavelength decrease

and the electromagnetic field can penetrate more into the metal. Nanoparticles, whose

size is in the order of the skin depth in metals, provide a sub-wavelength confinement

that constitute the basis of surface plasmonics [1].

1.1.2 Optical response of metals and dielectrics

The conductivity, the dielectric constant and the magnetic permeability in metals are

properties dependent on the frequency of the incident light. The dielectric function of a

medium depends on the response of the electrons to an external electromagnetic field. In

a dielectric material, electrons are bound to the atoms, but in the case of metals, electrons

are free to move through the material. Since an applied optical field is oscillatory, we

will see that both cases can be described in terms of simple harmonic motion and are

known as the Lorentz and Drude models for dielectrics and metals respectively. The

equation for simple harmonic motion of an electron in a material can be written as:

mx+ bx+Kx = eE (1.14)

Where m and e are the electron mass and charge, b is the damping coefficient describing

the energy loss due to scattering; K is the spring constant describing the restoring force

induced by the electrostatic attraction between the the binding atoms and E the electric

field. Dielectric and metals can be described by equation 1.14. In a dielectric material,

electrons fill the valence energy bands and interband transitions with the required en-

ergies are permitted. The equation can describe the metals just by assuming K = 0.

In a free electron model, the electrons only partially fill the conduction band, allowing

just intraband transitions of low energies. The electron displacement x = x0e−iωt in the

presence of an external field E = E0e−iωt can be obtained by solving 1.14:

x =−eE0m

(ω20 − ω2)− γiω

(1.15)

where ω0 =√

Km corresponds to the resonant frequency of the bound electrons in a

dielectric material. The optical response of a material with a certain density NV of such

oscillators can be presented in terms of the induced polarization:

P = −exNV

=−e2NmV E0

(ω20 − ω2)− γiω

(1.16)

Figure 1.1: Graphs showing the components of the complex dielectric function (top)for (a) metals, modelled using the Drude equations and (b) dielectrics, modelled using

the Lorentz equations.

The dielectric constant corresponding to this polarization ε = ε1 + iε2 can be expressed

with the following solutions for both cases metal (Drude, ω0 = 0) and dielectric (Lorentz)

Pure Metal:

ε1 = 1−ω2p

ω2 + γ2ε2 =

ω2pγ

ω(ω2 + γ2)(1.17)

Dielectric:

ε1 = 1 +ω2p(ω

20 − ω2)

(ω20 − ω2)

2+ γ2ω2

ε2 =ω2pγω

(ω20 − ω2)

2+ γ2ω2

(1.18)

The plasma frequency is defined by ω2p = ne2

mε0, and γ = b

m describes the damping in

the system. By setting ω0 = 0, the dielectric solution is equivalent to the pure metal

solution. Hence, both cases can be described with the simple harmonic oscillator model

1.14. Figure 1.1 shows the complex values of the dielectric function obtained from

equation 1.15.

In perfect metals, the electrons are considered free (ω0 = 0), and the charge is balanced

by the rest of positive ions that make the system to have a zero net charge. Under

illumination,and the electrons will oscillate within the metal creating a charge distribu-

tion that induce a restoring electric field that tries to keep the charge neutrality. At a

certain frequency, when ε1 passes through zero Fig. 1.1(a), transverse electromagnetic

waves can not be sustained in the material, and only longitudinal waves are present.

This oscillation frequency is known as a plasma frequency, ωp. In a quantum mechan-

ical treatment of this problem the collective plasma oscillation is known as a plasmon,

Figure 1.2: Schematic diagrams illustrating (a) a surface plasmon polariton and (b) alocalized surface plasmon.(Modified with permission from the Annual Review of Phys-ical Chemistry, volume 58 2007, by Annual Reviews, http://www.annualreviews.org

a single entity that reflects the combined effect of many particles. Fig. 1.1(b) shows

the frequency response of a dielectric material. In this case, the binding of electrons

to atoms is responsible for the natural frequency of oscillation, ω0. We can show that

above ω0, the real and imaginary parts of the dielectric constant present the same trends

observed for metals, with ε1 going negative.

Dielectrics as well as metals, are highly reflective in this frequency regime. By using

the Lorentz and Drude expressions, it is possible to calculate the optical properties of

many materials; however, for many metals, such as silver and gold, the Drude model

breakdowns at high energy, and interband transitions have to be taken into account

at higher energies [3]. In the FDTD calculations performed in this thesis, the optical

properties of metals are modelled with a combination of Lorentz and Drude models that

are fitted to experimental dielectric data that includes the intra-band response.

1.1.3 Localized surface plasmons

Plasmons can couple to electromagnetic waves to form polaritons [3]. One of the excita-

tion modes are surface plasmon polaritons (SPP) which are electromagnetic excitations

that propagate along the interface between a dielectric (insulator) and a conductor. A

second fundamental excitation mode, more relevant for the purpose of this work, is the

localized surface plasmons (LSP). Figure 1.2 illustrates the two types of surface plas-

mons. Optical nanoantennas are based on localized plasmons in metal nanoparticles,

therefore a more detailed description of LSP is given in this section.

The curved surface of a nanostructure exerts an effective restoring force on the driven

electrons which leads to a resonance at a certain frequency (Fig. 1.2). This situation

Figure 1.3: Sketch of a homogeneous sphere placed into an electrostatic field

implies a field enhancement in the near-field of the particle. The resonance frequency

at which the field enhancement is maximal is the localized plasmon resonance.

Another consequence of the curved surface on sub-wavelength particles is that localized

plasmons can be excited by direct light illumination in contrast to propagating SPPs,

where phase-matching techniques have to be employed [3]. Gold and silver particles

with sub-wavelengths dimensions present resonances that fall into the visible region of

the electromagnetic spectrum. In the following sections, we will discuss the use of gold

or silver nanoparticles to obtain nanoantennas able to work in the visible spectrum.

1.1.3.1 Nano-sphere interaction with an electro-magnetic wave

The interaction of a spherical particle of diameter d with the electromagnetic field can

be analysed using the simple quasi-static approximation, λ � d i.e. the particle size

is much smaller than the wavelength of light in the surrounding medium. A simple

case, described in Fig. 1.3, is to consider a metallic sphere of radius a, illuminated

with an electromagnetic field E = E0x, and calculate the electric and magnetic fields

for the regions both inside and outside of the sphere using Maxwell’s equations. ε

and εm are the dielectric response functions of the particle and of the surrounding

medium respectively. By solving the Laplace equation for this potential, ∇2Φ = 0 and

applying Maxwell’s equations with the appropriate boundary conditions; equality of the

tangential components of the electric field and equality of the normal components of the

displacement field, the electric potentials inside and outside of the sphere can be written

as [5] ;

Φ1 = −E03εm

ε+ 2εmr cos θ (1.19)

Φ2 = −E0r cos θ + E0ε− εmε+ 2εm

a3 cos θ

r2(1.20)

φ2 physically describes the z-component of the external electric field superposed on

an electric dipole located in the middle of the sphere. It is possible to rewrite φ2 by

introducing the dipole moment p as [3, 6];

p = 4πε0εma3 ε− εmε+ 2εm

E (1.21)

Φ2 = −E0r cos θ +p.r

4πε0εmr3(1.22)

α = 4πa3 ε− εmε+ 2εm

(1.23)

where α is the polarizability defined by p = ε0εmαE. Equation 1.23 shows that the

polarizability experiences a resonant enhancement under the condition that | ε + 2εm |is a minimum, which means that for small variations of Im[ε],

Re[ε(ω)] = −2εm (1.24)

This relationship known as Frohlich condition defines the dipolar surface Plasmon mode

of the metal nanoparticle. Equation 1.24 expresses the dependence of the plasmon

resonance frequency with the dielectric properties of the surrounding medium, which

makes metal plasmonics nanoparticles ideal for optical sensing [7, 8]. Metal structures

interact partially with the electromagnetic energy carried by the incident light in two

ways; by dissipating it in heat within the NP or by re-irradiating it into the free space.

These two mechanisms express the well-known optical features in a material, absorption

and scattering. Both are determined by the particle geometry and the intrinsic dielectric

response of the metals. The scattering and absorption cross sections σscat and σabs can

be calculated via the Poynting vector determined from the magnetic and electric fields.

The results for a sphere are [3, 5, 6]

σabs = kIm[α] = 4πka3Im(ε− εmε+ 2εm

) (1.25)

σscat =k4

6π|α2| = 8π

3πk4a6| ε− εm

ε+ 2εm|2 (1.26)

The sum of absorption and scattering is called extinction. It is deduced from 1.25 and

1.26 that σabs scales with a3 whereas σscat scales with a6. Consequently, for large parti-

cles, extinction is dominated by scattering, whereas for small particles it is related with

absorption. Note that this derivation is only valid in the quasi-static limit (i.e. λ� a),

under this assumption the particle can be represented as a resonant electric dipole that

scatters and absorbs radiation. The scattering cross section of metal nanoparticles rep-

resent an effective area up to several times the physical cross section of the nanoparticle

[5]. We will refer to this important concept again in 1.2.1.

For particles of larger dimensions a more rigorous electrodynamics approach is consid-

ered. The derivation was developed by Gustav Mie [10] and the solution is basically a

power series expansion with higher order terms corresponding to the higher modes and

can be used for spheres of different sizes.

αSphere =1− 1

10(ε+ εd)x2 +O(x4)

(13 + εd

ε−εd )− 130(ε+ 10εd)x2 − i4π2ε

3λ30+O(x4)

V (1.27)

Equation 1.27 describes the polarizability of a sphere with volume V derived with the

Mie theory. When the particle size gets smaller, the higher order terms can be neglected

and Mie theory reduces to the solutions obtained in the quasi-static limit.

1.2 Optical antennas

An optical antenna is defined as a device designed to efficiently convert free-propagating

optical radiation to localized energy and vice versa [11]. They are generally based on

metal nanoparticles (NPs) and the interaction between light and metal NPs, which is

dominated by localized surface plasmon resonances (LSPRs) as previously discussed

(1.1). NPs play a very important role in the nano-optics field [12–14]. Optical antennas

squeeze light into nanometer dimensions producing large local enhancements of elec-

tromagnetic energy in the same way that their counterparts do in the radiowave and

microwave regimes.

Antennas are incredibly important in microwave and RF technology because of their

ability to efficiently transmit and receive electromagnetic signals in small devices. In

modern life they are used in a large diversity of systems, including radio and television

broadcasting, mobile phone communication, the wireless cards, and space exploration

[15]. The electronic circuitry in these systems consists of so-called lumped circuit ele-

ments, such as the familiar resistors, capacitors and inductors.

Alu and Engheta have developed an elegant quantitative framework to transplant all of

the RF circuit ideas to the optical frequency regime [15]. This concept may allow for

an optimization of nanoscale optical antennas for a wide variety of applications. More

recently, the same concept has been used to demonstrate the first optical nanoscale

circuits with fully three-dimensional lumped elements by N.Liu et al. [17].

1.2.1 Optical antennas cross section

As we have discussed in section 1.1.3.1, the excitation of LSPRs can lead to an increase

of the effective area up to several times the physical cross section of the nanoparticle

[5]. Fig. 1.4 shows how the effective cross section can be more than 10 times the actual

structure area at the resonance frequency, and also emphasizes the importance of the

geometry in LSPR excitations. This property can be used to increase the interaction

of any object located in their vicinity with free space radiation making possible that

metal NPs can be used for optical spectroscopy such as SERS, multiphoton absorption,

enhancement of fluorescence or other applications discussed in 1.2.3.

1.2.2 Antennas modes and field enhancement

An efficient antenna must not only have a large and spectrally tunable cross section,

but also induce high field enhancement in its vicinity. A simple plasmonic structure

combining these two characteristics is a metallic nanobar (see Fig. 1.5). The properties

of plasmonic resonances in this geometry are mainly controlled by the length of the

NP along the direction parallel to the polarization of the incident light. Therefore, this

structure provides us with a simple picture describing the fundamental physics behind

LSPRs. If we consider the nanobar particle as a Fabry-Perot plasmonic cavity (Fig.

1.5(a)), its length, L, must contain a half multiple of the effective wavelength of the

fields, λeff , within the metal at resonance, i.e.

L = nλeff

2(1.28)

where n=1,2... is an integer and λeff it is related to the wavelength λ of the external

incident field by the relation [18].

λeff = n1 + n2λ

λp(1.29)

where n1 and n2 are constants with dimensions of length that depend on the geometry

Figure 1.4: Normalized extinction σext, absorption σabs, and scattering σscat crosssections for three different Ag nanoparticles in vacuum. The extinction cross section isdefined as the sum of the scattering and absorption cross sections. (Reproduced with

permission [5])

and the dielectric properties of the background and the particle, and λp is the metal

plasma wavelength. Equation 1.29 reflects the momentum increase that the incoming

photons experience when interacting with the collective electron oscillations within the

metal NP. For λp the wavelength differences can be one order of magnitude smaller than

the free space wavelength [11].

The most intense plasmonic resonance (n=1) sustained by metallic nanobars satisfies the

relation L =λeff

2 (half wave resonance). For a fixed length, this condition determines

the LSPR with the lowest energy supported by the system. Fig. 1.5(a) shows the

extinction cross section and the electric field intensity for this resonance in the case of

a gold nanobar with dimensions 400x100x50 nm3 deposited on a glass substrate. It is

noticeable that the electric field surrounding the nanoparticle has the maximum at the

Figure 1.5: Plasmonic resonances in a gold nanobar. (a) Extinction cross section(blue line) of a gold nanobar with dimension 400x100x50 nm3 deposited on a glasssubstrate. Three different resonances are excited, one dipolar n=1 and two multipolar

n=2 and n=3. The respective near electric field enhancement |E|2|E0|2 is shown in a

logarithmic color-scale. (b) Electric field intensity enhancement |E|2|E0|2 for two antennas

with the same dimension (a) but with a gap 20 nm. Experimental hot spot map for asingle nanoantenna (c) and for a two coupled nanoantennas (d) by means of two-photon

luminescence measurements. (Reproduced with permission [5])

ends. In contrast, the electric field inside has a maximum at the middle and presents

two minima at the structure ends (see inset of Fig. 1.5(a)).

Correspondingly, the induced charges within the NP will present a dipolar distribution.

These arguments can be also applied to higher multipole resonances. In particular, note

that for higher multipole resonances,i.e. n=2 and n=3, one and two minima (nodes) are

presented respectively, in agreement with the Fabry-Perot cavity picture (see the near-

field map of Fig. 1.5(a)). Note that for n=2 the near field distribution is not symmetric,

this is just a consequence of the non-symmetric character of the incident field required to

excite this mode. The incident field in this case is applied at a low angle from the right

side of the structure. Another important characteristic of these resonances is the electric

field intensity enhancement which is extensively discussed in this thesis. The electric

field intensity enhancement can be bigger than 100 times the incident field intensity (red

color in the near field map of Fig. 1.5(a)).

The typical models of optical antennas are made from the interaction of a pair of metal

NPs. These type of antennas are particularly interesting for some of the work developed

in this thesis, the properties of a dipole nanoantenna are modified when we cut it at

its middle point, i.e. when a small gap is opened along its length L (see Fig. 1.5(b)).

Considering continuity conditions of the electric displacement at the gap interfaces,

and assuming as first approximation that within the gap the component of the electric

field parallel to L is uniform, the magnitude of the electric field can be taken as the

magnitude of the electric field proportional to the ratio between the dielectric constant

of the nanostructure and the background, where ENP stands for the electric field inside

the metallic NP and near the gap [5]).

Egap =εnpεbEnp (1.30)

For noble metal nanoantennas operating at visible and near-infrared wavelengths, this

means that intensity enhancements,|Egap|2|E0|2 (where E0 is the incident electric field), of

the order of 103 or higher can be obtained for gap widths of a few tens of nanometers,

as shown in Fig. 1.5(b)). If a light emitter is located within the gap of such antenna, it

will be excited very efficiently thanks due to the ability of the antenna to concentrate

the electromagnetic incident radiation within the gap. Dipolar LSPR are excited very

efficiently by free space radiation (plane waves). Therefore, light-matter interactions

occurring in deeply sub-wavelength structures are usually dominated by the electric

dipole moment induced in the nanoantenas by the incident fields.

The dipolar plasmonic resonances supported by metallic NPs which are the lowest in en-

ergy, are known as bright modes [5]. However, Maxwell’s equations additionally predict

the existence of higher multipole modes that are dipole-inactive and are hardly coupled

to light.

In contrast to dipole bright modes, these higher order resonances are usually denomi-

nated as dark modes. The only mechanisms that allow the excitation of these higher

order resonances by free radiation are retardation effects [19] caused by the slow re-

sponse of metallic plasma electrons to the external excitation. Retardation effects occur

when the structures present dimension comparable to the wavelength due to the phase

difference of the field from one side of the particle to the other. This means that higher

order modes can be only excited in metallic NPs big enough for these retardation effects

to be relevant. High multipole LSPRs only couple to incident fields whose symmetry

properties are different from the dipole mode supported by the nanostructure [20].

The difficulty of probing dark modes through optical methods has motivated the appear-

ance of several experimental works, in which these dark modes are studied by means

of electron energy loss spectroscopy techniques [21, 22]. A remarkable example of how

breaking symmetry on the coupled surface plasmon resonances can allow to observe dark

modes is presented in a recent work from L. S. Slaughter et al. [23].

Figure 1.6: Extinction spectra calculated using plasmon hybridization theory for (a)a homodimer β = R2

R1 = 1 of prolate spheroids with major and minor axes of 14 and

5.6 nm and (b) a heterodimer β = R2R1 = 1.2. dgap is the size of the gap and Lrod denotes

the length of one rod, the shorter one in the case of the heterodimer. Diagrams illustratethe interactions of the primitive dipoles for the (c) homodimer and (d) heterodimer.

They found that the normally dark antibonding dimer mode becomes visible when the

sizes of two nanorods are different. The calculated spectrum shows only one resonance,

the bonding dipolar mode (green) at 570 nm (2.19 eV). The dipolar antibonding mode

(red) remains dark, with an energy between the bonding dipolar and quadrupolar modes.

In contrast, for the heterodimer (Fig. 1.6(b)), the antibonding dimer mode is now

visible on the blue side of the bonding peak. Fig. 1.6(b),(d) sketches a simple energy

diagram for the hybridized modes sustained by a dimer comprising two metallic rods.

The hybridization model [13] explains the observed red-shift of the rod resonance when

a dimmer antenna is created by placing the two metallic rods at a short distance, at

which their near field can interact (Fig. 1.6(c)).

In general, for deeply subwavelength systems, the energy levels are dictated by the

electrostatic interaction between the charges induced in the rods. Thus, the configuration

that maximizes the distances among charges of opposite sign corresponds to the lowest

energy. Everything discussed in this thesis is related only to the use of first order dipolar

resonances from symmetric dimmer antennas.

1.2.3 Applications of optical antennas

Research in the field of optical antennas includes a broad variety of possible applications

that take advantage of enhanced light-matter interaction. Most of the applications have

been extensively discussed in plasmonics and optical antennas reviews [1, 5, 9, 11, 26–

28]. Nanoantennas have found a vast number of applications. In this section we will

highlight the most popular topics related to optical nanoantennas.

Scanning near-field optical microscopy

Antennas have been proposed as imaging and spectroscopic probes. To that end, nanoan-

tennas need to be fabricated at the tip of a scanning probe. In this way, single-molecule

imaging has been achieved with bow-tie [29] and λ4 antennas [30]. Resolution down

to 25 nm can be obtained in the latter case. Single gold spheres have been attached

to dielectric tips in order to create well-controlled antenna probes. These probes were

used to image single molecules at a resolution smaller than the sphere diameter but

compatible with the expected extent of the localized field [31, 32]. Using these single

and also multiple-sphere nanoantennas on optical fiber near-field probes, single proteins

have been imaged at very high resolution in their native cell membranes [33, 34].

Spectroscopy Highly-sensitive spectroscopy represents another key area for nanoan-

tenna applications, where the antenna serves the purpose of enhancing the excitation

and the emission of the nano-object under investigation. In particular, Raman signals

can be largely enhanced following the surface-enhanced and tip-enhanced Raman scat-

tering [35, 36]. Raman scattering involves the absorption and emission of photons almost

identical in energy, and a nearby metal NPs can amplify both the incoming field and

the outgoing field.

The total Raman scattering enhancement can therefore be proportional to the fourth

power of the field enhancement. For this reason, typical enhancement factors obtained

are ≈ 106, and it is possible to obtain factors as large as ≈ 1010−1012. Such enhancement

enables the detection of single molecules [2]. In view of practical sensing applications,

an array of antennas fabricated by electron beam lithography (e-beam) has also been

transferred to the facet of an optical fiber, used for illumination and collection [38].

Optical lithography

The highly localized near field of a nanoantenna also finds a natural application in

optical lithography, where the fabrication of nanostructures has been accomplished via

nonlinear photopolymerization of a photoresist by exploiting both the largely confined

and enhanced fields in the gap of a bow-tie antenna and the nonlinearity of resist response

Optical tweezing with nanoantennas

Since highly localized optical near fields naturally possess strong gradients, their use as

localized trapping spots has been proposed already more than a decade ago [40]. More

recently, it has been demonstrated optical trapping in well-controlled hot spots in the

gap of nanoantennas, where the large antenna field enhancement allows trapping with

lower excitation power and higher efficiency and stability [41–43].

Antenna-based photovoltaics

Plasmonic photovoltaics is one of the most recent fields in nanophotonics at the moment

[28, 44]. Standard solar cells are combined with metallic nanostructures, which con-

centrate and guide light at the nanoscale, leading to a reduction of the semiconductor

thickness required, as well as enhancing the broadband absorption of the incident light,

which is one of the crucial challenges to modern solar cell technologies [44].

Optical antenna sensors

Since plasmonic nanoantenna systems display localized resonances that strongly depend

on the dielectric properties of the environment, they are very good candidates for sensing

applications down to extremely low concentrations. The demonstration of sensors based

on localized particle resonances opened new perspectives for plasmonic sensing, where

in principle much simpler transmission, reflection, or scattering measurements can be

performed. The local refractive index change in the surrounding medium of the antenna

translates into a shift of the particle’s resonance frequency. Sensing based on particle

arrays on a fiber facet [38] or on a substrate [45] has been demonstrated with sensitivities

down to the single-particle level [46, 47].

Coherent control with nanoantennas

Not all the applications of optical antennas are focused on the field enhancement as

well as on their resonances in the frequency-domain. There is also significant interest in

studying the temporal characteristics of the confined fields provided by plasmonics [1].

The broad spectral response associated with plasmons in metals, corresponds to dynam-

ics in the range of hundreds of attoseconds [48], which makes optical antennas useful

tools for ultrafast applications like nanoscale computing, time-resolved spectroscopy, or

selective chemical bonding [11]. In short, the rapid response of the free-electron gas in a

metal provides a means for controlling the dynamics of a system on the quantum level.

The temporal profile of the excitation pulse can be shaped by manipulating the spectral

phase and amplitude of the laser pulses used for excitation. In this way coherent spatio-

temporal control of localized near fields has been realized experimentally using antenna-

like gold nanostructures [49].

Lasing in nanoantennas

Surface plasmon amplification by stimulated emission of Radiation (SPASER), has been

originally proposed by Bergman and Stockmann [50]. In this context, metal nanoparti-

cles acting as optical antennas can play a role because of their large local field enhance-

ment and extremely reduced interaction volume. Very recently, subwavelength plasmon

lasers based on the original SPASER proposal have been demonstrated [51, 52]. Larger

enhancement and confinement, compared to single particles, can especially be encoun-

tered in the gap of two-wire or bow-tie nanoantennas. Along this line, laser operation for

bow-tie antennas coupled to semiconducting quantum dots or multiple quantum wells

has been theoretically addressed [53].

Nanoantennas and plasmonic circuits

Sub-difraction propagation in plasmonic waveguides offers the possibility of processing

electromagnetic signals combining the speed of photonics with the high degree of in-

tegration of modern microelectronics [54]. In this frame, optical antennas, working as

receiving and transmitting devices, represent an interface between sub-wavelength lo-

calized modes that propagate along transmission lines and free-space propagating waves

[55–58]. For example, wireless optical interconnects based on matched optical antennas

could be used as high-speed links in chip architectures [59].

In addition, an optical antenna structure that features electrical connections while pre-

serving its resonant optical properties has been demonstrated [60]. The proposed design

enables electro-optical effects to be investigated in plasmon-enhanced nanoscale devices

and could open new applications in quantum optics, nonlinear optics, optoelectronics,

and photovoltaics. In terms of interfacing electronics and plasmonics, the challenge re-

sides in efficiently converting electrical signals into plasmon waves and vice-versa. Very

Recently, it has been proved that plasmons can be generated starting from electrical

sources [61, 62] and reciprocally also electrical detection of plasmons has been realized

[63, 64]. In addition, electrical, mechanical, or optical tuning of nanoantennas by means

of anisotropic load materials [65], stretchable elastomeric films [66], or photoconductive

gap loads [67, 68] has been demonstrated.

Nanomedicine

The use of nonspherical metal particles [69, 70] for biomedical applications allows the

tuning of LSPR to the medical window (650-900 nm), where light penetrates much deeper

into living tissue, and the scattering to absorption ratio can be tuned [69]. The imaging

of biological samples and the detection of diseases such as cancer require biomarkers

and contrast agents. There is an interest in exploiting the large scattering cross sections

associated with LSPRs for bio-imaging and drug and gene delivery [71]; application

which rely on both their biostability and optical properties. Gold particles have also

been proposed as contrast agents for magnetic resonance imaging [72]. The absorptive

properties of metal NPs are also promising for medical imaging [73].

The main interest in the absorptive properties of metal NPs lies in the exploitation of

their resistive heating for medical treatment. A laser can be used to ablate tumors in

the presence of photoabsorbers. Using gold particles as the photoabsorbers maximizes

the light absorption due to the large cross section associated with their LSPR, which

leads to a reduction of the intensity of radiation required [74, 75].

Nanoantennas and emitters

The emission properties of nanoemitters can be drastically influenced by the high lo-

calised fields generated by nanoantennas [6]. In the right conditions, radiative decay

rates and quantum yields can be increased. By coupling plasmonic structures to these

emitters, a whole new range of materials might become viable for applications. An

example is the development of silicon-based emitters, which are of poor quality at the

moment, but are easy to process and are compatible with current technology. Indeed,

nanoplasmonics is set to open up a bright future for controlled light-matter interactions

at the nanoscale. The interaction of antennas and emitters will be discussed in more

detail in the following section, with the purpose of introducing important concepts for

chapter 4.

1.2.4 Decay rate emission close to a nanoantenna

As Purcell pointed out in 1946, the radiative properties of a given emitter (a fluorescent

molecule, for instance) are not intrinsic to it, but also depend on its environment. This

phenomenon is well known as the Purcell effect, [77] which several decades ago allowed

the control of stimulated-emission phenomena and opened the way to the development

of current laser technology. The Lorentz harmonic oscillator can be used to model

the decay rate of any fluorescent emitter, in spite of its classical character [78]. The

transition dipole moment induced in a weakly excited quantum emitter is modelled by

a classical electric dipole, µ, with the following equation of motion

dt2+ ω2

oµ + γodµ

m[µ∗ ·El]

(1.31)

where ωo and γo = 1τo

are the resonant frequency and the decay rate, respectively, of

the emitter in absence of any excitation. The term in the right hand side of 1.31 reflects

the interaction of the electric dipole with the local electric field El, projected along the

dipole axis and evaluated at the position of the emitter [5]. In the absence of any external

illumination, El corresponds to the electric field emitted by the dipole itself. This term

in 1.31 expresses the possibility of manipulating the radiative properties of quantum

emitters by placing them in the vicinity of metallic nanostructures. The excitation

of an isolated fluorescent molecule can be described by solving 1.31. The equation is

governed by the decay rate, γo, which describes the amplitude decay of the dipole in time.

There are two components that contribute to the overall decay: γro, which takes into

account the radiated electromagnetic energy, and γnro, which is related to non radiative

phenomena such as heat generated due to the excitation of rotational and vibrational

levels of the molecule. Considering both processes, radiative and non radiative, the

quantum yield of a emitter can be defined as

ηo =γroγo

γro + γnro(1.32)

which represents the probability of a photon emission by an excited fluorescent molecule.

The emission of light by a fluorescent molecule is altered by the presence of metallic

nanostructures in its vicinity. This effect modifies the quantum yield of the molecule

that can be written as

η =γrγ

γr + γnr + γnr0(1.33)

where γ = 1τ is the total decay rate and τ , the transition lifetime. We can identify three

different decay channels in the system now: the radiative rate, γr, the non-radiative

rate due to metal absorption losses in the environment, γnr, and γnro, the non-radiative

rate intrinsic to the emitter [78]. A deeper understanding of light-matter interactions is

possible by treating the molecular emitter as a quantum entity. By taking into account

the Fermi’s golden rule that describes the transition between two molecular energy states,

we can express the decay rate associated to the spontaneous emission process as

γr =2π

}2|Mif |2ρ(ω) (1.34)

where Mif is the transition matrix element between the initial molecular state |i >, and

the final state |f > (lower in energy), and ρ(ω) is the photonic local density of states

(LDOS) [5]. Note that the environment of an emitter can modify the emission properties

by changing the LDOS. For example, in free space and in the absence of any preferred

dipole direction and without any incident field, the transition matrix element averaged

over all directions is |Mif |2 = |µ|2}ω6ε0

[79], where µ = −e < i|r|f > is the dipole moment

associated with the electronic transition. The local photonic density of states in free

space is ρ(ω) = ω2

π2c3[5] and inserting this into 1.33, we obtain the radiative decay rate

of an isolated emitter

γr0 =|µ|2ω3

3πε0}c3(1.35)

If we consider an emitter located in the proximity of a nanoantenna, the density of states

ρ(ω) is strongly influenced by the antenna presence if the LSPR spectrally overlaps

with the emission frequency of the emitter. In this case, the excitation probability of

the resonance can be modelled through a Lorentzian function peaked at the plasmonic

resonance, λres considering just a single mode structure. As a consequence, the ratio

between the radiative rates of an emitter in the presence, γr, and in absence, γro, of the

nanoantenna can be calculated as

γrγro

4π2(λresQ

n3V) (1.36)

where Q and V are the quality factor and mode volume of the LSPR, respectively, and

n is the refractive index of the background medium [9]. Fig. 1.7 shows how the nanoan-

tenna clearly modifies the free decay rate (red circles) of the dye molecules close to

the nanoantenna which present a multi-exponential behaviour (black squares). We can

observe two different decay channels in the new decay behaviour: the slow decay approx-

imately corresponds to the molecules which are not coupled to the antenna LSPR, and

a fast decay of the ones coupled to the LSPR. This result illustrate the benefits of using

nanoantennas, built from metallic NPs, to manipulate and enhance the radiative decay

rate of any emitter, taking advantage of the narrow resonances and the subwavelength

modes supported by the metallic nanoantennas.

The intensity of fluorescent atoms or molecules in the vicinity of a nanoantenna is given

by the product of two different factors [5, 9]. On the one hand, the emitter quantum

yield, η, which measures radiative enhancement of the emitter once excited, and on the

other hand, the absorbed electromagnetic energy from the electric field under excitation,

which is proportional to |µ · E|2 (where µ is the transition dipole moment, and E, the

electric field evaluated at the emitter position. Thus, is possible to write the fluorescence

enhancement, S, induced by the nanoantenna as:

|µ · E|2

|µ · E0|2(1.37)

From equation 2.1, it is observed that the maximum fluorescence amplification is de-

termined by two factors; the quantum efficiency ηη0

and the local EM field. According

Figure 1.7: Normalized measurements of fluorescence decay rate of a dye (Atto680,Atto TecGmbH) near a resonant nanoantenna (diamonds, black) and away from thenanoantenna (open dots, red), with exponential decay fits (lines, black). Inset: SEMimage of the resonant gold nanoantenna, consisting of two 90x60x20 nm3 gold nanorodswith an antenna gap of 20 nm. (Reproduced with permission [6] Copyright 2007,

American Chemical Society)

Figure 1.8: (a) Schematic representation of molecules randomly placed around a goldbowtie antenna on a transparent substrate. (b) SEM image of a gold bowtie antenna.Scale bar = 100 nm. (c) Calculation of the local electric field intensity enhancement.(d) Enhancement factor, fF , from several nanoantennas as function of the gap size

to 1.33, the factor ηη0

would be positive as long as the radiative rate of the emitter is

increased with the antenna presence. To make this possible, the distance between the

antenna and the emitter should be optimized maximizing the field enhancement at the

emitter position, and minimizing the quenching related to non-radiative energy ther-

mally dissipated to the metallic surface. A clear example of this effect has been shown

by Kinkhabwala. et al. [36]. They have measured a fluorescence enhancement up to a

factor of 1,340 for molecules placed in the gap of a gold bowtie antenna (Fig. 1.8).

1.3 References Chapter 1

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Express, vol. 19, no. 22, p. 22029, 2011.

[2] H. Nalwa, “Handbook of thin film materials: Deposition and processing of thin

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Chapter 2

Methods

2.1 Experimental techniques

This part will focus on the description of the experimental techniques used during the

development of this Thesis. Electron beam lithography (E-beam) is used to fabricate

the nanoantennas which are in turn characterised by dark field spectroscopy to identify

their plasmon resonances. Once the antennas are characterised, we carry out fluorescence

measurements of organic dyes in interaction with the nanoantennas by using confocal

microscopy.

2.1.1 Electron beam lithography(E-beam)

Electron beam lithography appeared in the late 60s and consists of the electron irradia-

tion of a surface that is covered with a resist sensitive to electrons by means of a focused

electron beam. The energetic absorption in specific places causes the intramolecular

phenomena, like breaking of molecular bonds for instance, that defines the features in

the polymeric layer. Electron beam lithography provides a better resolution and accu-

racy than other types of lithography such as optical lithography where the resolution,

limited by the wavelength of the light and the optical diffraction phenomena, is about

180 nm [1]. Fine resolution (10-20 nm) is provided by the small size of the focused elec-

tron beam. Lithographic electron beam machines are similar to those used in scanning

electron microscopes (SEM). In these systems the electron beam is focused to the small-

est size possible for a given set of electron optics and operating conditions. Electron

beam lithography is carried out on electron-sensitive resist materials such as polymer

Poly(methyl methacrylate), PMMA. Solutions of the resist are spin-coated onto a sam-

ple and baked to leave a hardened thin-film on the surface of the sample. The e-beam

Methods. Experimental techniques 41

system is able to move a focused electron beam across the sample and selectively expose

a pattern in the resist. In the case of using a positive resist such as PMMA, the polymer

chain is broken into smaller molecular units in a process known as chain-scission. By

using a suitable developer solution, the fractured polymer chains from the exposed areas

are selectively dissolved, meanwhile the unexposed areas of resist remain insoluble in

the developer solution. Therefore a patterned resist mask is achieved using this method

for further processing.(Fig. 2.1)

Figure 2.1: Process to obtain a patterned resist mark by using electron beam writing

The resulting pattern in the resist can be transferred into the sample using either metal

deposition followed by lift-off or etching. Reactive ion etching (RIE) is generally pre-

ferred over wet chemical etching for e-beam lithography applications since it maintains

the small feature sizes produced in the resist (Fig. 2.2).

Figure 2.2: Techniques for transferring PMMA patterns onto the sample: a) Metallift-off, b) Reactive ion etching

The resist introduces certain requirements in terms of dose and pre and post exposure

processing that are necessary for adequate results and also its molecular structure limits

the resolution. The minimum feature size and maximal pattern density is considered

to be highly determined by the massive and charged nature of electrons that causes a

certain delocalization of the delivered radiation.

In fabrication, the methods to transfer the patterns to the substrate are crucial and

determinant. It is considered that features of a few tens of nanometers (10-20nm) can

be fabricated almost controllably and repeatedly by using EBL. One of the main goals of

this PHD is to experimentally investigate gold nanoantenas with very small gap distances

(20 nm) on glass substrates fabricated by using e-beam fabrication methods. In order to

fabricate nanoantennas, the influence of several parameters such as the electron beam

dose, the resist characteristics or the antennas thickness need to be considered. In

addition, a deposition of a sticking layer of Cr, Ti on the glass substrate is generally

necessary due to the low adherence between gold and glass. In chapter 3 we will discuss

numerically the effect of the adhesion layer in the nanoantenna properties.

2.1.2 Dark Field Microscopy

The dark field technique is used in combination with a confocal microscope [2] and it is

based on the dark field illumination. Light impedes on the sample at high angle and only

light scattered is collected to the objective lens (Fig. ??). The primary advantage to

this technique is that it provides high contrast images, but one of the major drawbacks

to using a dark field microscope is the low levels of light obtained in the final image.

Hence, an intense amount of light is required to the observation of nanoparticles.

Figure 2.3(d) shows the spectra of two different gold dimers composed of two oppos-

ing long arms separated by a 30 nm gap nanoantenna obtained using polarized side-

illumination (Fig. 2.3(b)). The arm length of the dimers are ∼100 nm and ∼70 nm for

a and b respectively. We can clearly see in Fig. 2.3(c) that the polarization determines

the amount of scattered light by the dimmer. In both set of antennas, only the scat-

tering is maximum when the illumination is polarised along the dimmer axis coupling

both particles, as we will discuss in the following sections. We can appreciate from the

spectra of Fig. 2.3(d) that the particle plasmon resonance is strongly determined by the

dimension of the particles. This important spectroscopy technique will be used during

the development of this thesis, because it provides a fundamental characterization tool

for describing the coupling effect on gold dimers controlled by the polarization of the

excitation light.

Figure 2.3: Configuration of standard dark field using a confocal microscope (a), andusing polarized side-illumination (b)(Image adapted from [3]). (c) Dark Field images oftwo arrays of gold dimers with different dimensions under polarized side-illumination.Scanning electron pictures (c top) with the real orientation in the sample. (d) Dark-field spectra of the dimers for the case when the polarization of the incident field liesalong the dimmer axis in both cases. The thickness of these particles was 40 nm and

the substrates silica glass. (The scale bar in the SEM figure is 100 nm.)

Figure 2.4 presents a schematic diagram of the Dark-Field experimental setup used to

characterise the antennas resonances in this thesis. The nanoparticles are illuminated

with a white-light source at a certain polarization angle, the scattered light is collected

by an objective microscope and coupled into an optical fiber that sent the transmitted

light to a beam splitter. From this point, 80% of the light is collected and directed to a

spectrometer which is equipped with a CCD detector to obtain the spectra in the visible

range (Fig. 2.3 (d)), the 20% left is focus into an APD detector. The APD function is

linked to the XY-Piezo scanner where the sample is placed. As the piezo scanner moves

the sample in X and Y direction, the APD detector measures the signal intensity that is

stored at each position making possible the generation of a confocal image that shows

2D-mapping of the scattered light from the sample.

Such an intensity mapping allow us to identify and select the particle that we are in-

terested in by repositioning the piezo stage to the specific position of a particle. On

the left side of Figure 2.4 is shown an example of 2D mapping of an array. Once we

have selected the particle to study, we need to measure three spectra to obtain the dark

Figure 2.4: Sketch of the experimental setup used to obtain dark field spectra onnanoantenna. The scattered light collected through the optical microscope is split intwo beams, one is directed to a spectrometer and the other beam hits an APD detectorwith the purpose of generating a 2D surface mapping of the scattered light intensity of

the surface by using a X,Y,Z-Piezo scanner.

field spectrum of the particle. Firstly, we measure the spectrum on the particle. Sec-

ondly, a spectrum of the background should be taken slightly away from the particle

position to be subtracted from the fist one. Finally, in order to eliminate the spectral

profile of the source light, we measure a spectrum on a very high reflecting material on

conditions similar than the previous one, with the purpose of using it as normalization

reference. In summary, the dark-field spectrum of the particle can be easily obtained

as DFpar =Ipar−IBack

IRef, where Ipar is the spectrum intensity on the particle, IBack on

the background and IRef refers to the spectrum on the reference sample. Note that the

three spectra should be taken in similar measurement conditions of integration time.

2.2 Finite-difference time-domain (FDTD) method

Since analytical solutions to Maxwell’s equations to describe complex structures do

not exist, numerical methods are required to predict the optical properties of metal

nanoparticles. The finite difference time domain (FDTD) method aims at solving the

time-dependent Maxwell equations. The origin of the method can be related to the

limitations of other techniques based on the frequency-domain used in defence and com-

munications technologies four decades ago. The FDTD method was presented as an

alternative with a different approach consist of obtaining the direct time domain so-

lutions of curl Maxwell equations on spatial lattices. The fundamentals of the FDTD

approach were established in 1966 by K. S. Yee [4], who designed the space grid and

time-stepping algorithm, which is the base of the method. A few years later on 1980,

A.Taflove employ FDTD models to describe the interaction of electromagnetic fields

with real metallic scatterers, and he introduced the term “Finite difference time do-

main” for the method [5]. The FDTD method has become one of the most extended

tools for studying EM fields and their interaction with material structures thanks to its

versatility with applications ranging from microwave communication devices, geological

and medical applications, or bio and nanophotonics [6, 7]. Some of the most relevant

features of the method are the following:

• By performing a single simulation in which a broadband pulse is used as the source,

FDTD method allows obtaining the response of the system over a wide range of frequen-

cies, thanks to the time-domain character of the method. This fact makes the FDTD

method very useful in applications where the resonant frequencies are not known or

broadband results are required.

• FDTD permits accurate modelling of a broad variety of dispersive and nonlinear media

allowing the analysis of a wide variety of EM phenomena arising in linear and nonlinear

dielectric and magnetic structures.

• In the FDTD method, all the EM field components are obtained directly. This fact

provides high stability to the calculations and make the technique very useful in appli-

cations like Plasmonics where all the components of the EM fields are relevant.

In the FDTD approach, both space and time are discretised. Space is segmented into

box-shaped cells, which are small compared to the wavelength and time is quantized into

small steps where each step represents the time required for the field to travel from one

cell to the next. Both space and time are linked through the Yee algorithm [4], which

represents robustly the curl Maxwell equations. Figure 2.5 shows how the components

of the electric and magnetic field vectors are located in the Yee algorithm. The electric

fields are located on the edges of the box and the magnetic fields are positioned on the

faces. They are placed in 3D space so that every component of E is surrounded by four

circulating H components and vice versa. This gives rise to a filling of the space by

interlinked contours of curl Maxwell equations.

Yee algorithm also links the E and H components in time, The electric and magnetic

fields are updated using a leapfrog scheme where first the electric fields, then the mag-

netic, are computed at each step in time. The electric field is calculated and stored at

a given time using the magnetic field data obtained in the preceding time step. Then,

new results for H component are obtained from the electric field just stored and the

Figure 2.5: Distribution of electric and magnetic field components in the Yee grid

previous magnetic field. This cycle, described in Fig. 2.6, is repeated until the loop in

time finishes.

Figure 2.6: Space-time sampling of the Yee algorithm showing the use of centraldifferences for the spatial derivatives and leapfrog stepping for the time derivatives

The following discretized expressions for the Faraday and Ampere-Maxwell equations

showing the mechanism that incorporate the Yee algorithm into the FDTD method,

∇×E = −µ(r)

c∂tH (2.1)

∇×H = −ε(r)c∂tE (2.2)

∆x, ∆y and ∆z are defined as the Yee mesh dimensions, and ∆t as the increment in

time. Each node of the spatial grid is labelled with three integers, i, j, k (see Fig. 2.5),

and we associate index n with each time step (see Fig. 2.6). Thus, it is possible to

denote any function of space and time, u, evaluated at a discrete point in the spatial

grid and at a discrete point in time as u(i∆x, j∆y, k∆z, n∆t) = u|i,j,kn. The discrete

versions of the spatial derivatives of this function, evaluated at a fixed time are;

∂x(i∆x, j∆y, k∆z, n∆t) =

u|i+1/2,j,kn − u|i−1/2,j,k

∆x+O[(∆x)2] (2.3)

∂y(i∆x, j∆y, k∆z, n∆t) =

u|i,j+1/2,kn − u|i,j−1/2,k

∆y+O[(∆y)2] (2.4)

∂z(i∆x, j∆y, k∆z, n∆t) =

u|i,j,k+1/2n − u|i,j,k−1/2

∆z+O[(∆z)2] (2.5)

Similarly, the time derivative of u, evaluated at a fixed space point i, j, k, has the form

∂t(i∆x, j∆y, k∆z, n∆t) =

u|i,j,kn − u|i,j,kn

∆t+O[(∆x)2] (2.6)

Note that taking increments of the form ∆2 is the most suitable choice in order to perform

the interleave of electric and magnetic field components characteristic of the Yee algo-

rithm. Finally, by using these derivatives expression, it is possible to write the discrete

version of 2.1 and 2.2 to obtain the electric and the magnetic field components in every

point. The FDTD is very memory and CPU-time consuming and consequently is not

suitable for large-scale problems. Such intensive memory and CPU time requirements

come from two reasons: 1) the spatial increment steps must be small enough in com-

parison with the wavelength (usually 10 to 20 steps per wavelength) in order to make

the numerical dispersion error negligible, and 2) the time step must be small enough to

satisfy the following stability condition (the Courant condition) [8]:

vmax∆t ≤ (1

∆x2 + ∆x2 + ∆z2)1/2 (2.7)

Here vmax is the maximum wave phase velocity within the model. The total simulation

time must be set according with this condition. This stability condition and the mesh

size accuracy determines the simulation time using this FDTD method.

2.2.1 Lumerical FDTD Simulations

In order to simulate scattering cross sections or the field enhancement induced by the

antennas based on metal nanostructures, we are using a commercial software, Lumer-

ical FDTD Solutions, Inc [15]. Structures to be simulated can have a wide variety of

electromagnetic material properties. Multiple sources as dipoles, plane waves or guide

modes may be added to the simulation as a pulses of light. It is possible to choose

to either set frequency/wavelength or set time-domain. By choosing to set the fre-

quency or wavelength ranges to define the sources, FDTD Solutions is able find the

optimum time domain settings that will cover the desired frequency/wavelength range

without compromising accuracy. The time extension and subsequent iteration results

in the electromagnetic field propagation in time. Typically in the simulation, the iter-

ation process is running until there are essentially no electromagnetic fields left in the

simulation region. Performing a simulation using Lumerical FDTD Solutions is straight-

forward. First, an FDTD Simulation Project file (with extension *.fsp) is created that

contains all the information about the physical structures, the sources and monitors,

and the details about the simulation parameters. This project file is saved and then the

simulation project is run. After running, the resulting data is added to the simulation

project file so that it may be analysed.

As it is required to find LSPR positions, for most simulations a total-field-scattered-

Figure 2.7: Spherical gold particle simulation setup: The Gold particle is in the cen-tre. Small arrows indicate the polarization direction; big arrow (pointing downwards)indicates the propagation direction of the incident light. Yellow box around the particle

is a group of monitors recording the total field

field (TFSF) source is used as it allows to separate the simulation in two regions, one in

which the total field is calculated, and the other where only the field scattered from the

input plane wave is computed. Two groups of monitors were used to calculate scatter-

ing, extinction and absorption rates. Both groups form a box around the particle, one

group of monitors was used to record the total field going into the gold particle, these

monitors were placed in the source area. The other group was used to record scattered

values thus forming a box further away from the particle. Figure 2.7 shows an example

of the simulation setup for a spherical gold particle where TFSF source is used.

Perfectly matching layer (PML) [10], a layer especially designed to absorb without re-

flection the electromagnetic waves, is used as boundary condition at the edges of the

simulation region. PML layers avoid unwanted reflections that otherwise would re-

turn to cause errors in the simulation. The simulation region should be defined by the

wavelength of the source in all the cases. In order to have accurate simulations, it is rec-

ommended to allow the longest wavelength to fit at least 2 times in the simulated region.

If we consider a source wavelength range from 450 nm to 800 nm, all the dimensions in

the simulation region should be ≥ 2x800 nm.

The cell size is the most important constraint in any FDTD simulation, since it deter-

mines the spatial and the spectral resolution on your simulation. As general rule ten

cells per wavelength is considered the limit for resolving the shortest wavelength con-

sidered in our spectral range. But the cell size will often be smaller than this in order

to resolve dimensions and features of the structure. For example, for a typical case of

a gold nanoatenna treated in this thesis, which is composed of two opposing long arms

separated by a 20 nm gap and with a thickness of 40 nm, a suitable mesh of 2 nm within

the particle would be small enough to allow us resolve the structure with accuracy on

the visible range. Lumerical FDTD allow us to specify really small mesh sizes (2 nm or

less) only on the considered structures and larger mesh sizes for larger particles or the

rest of empty space of the simulation volume at different regions. This possibility helps

us to optimise the simulation setup in order to decrease the total simulation time and

the memory necessary to storage all the fields data.

2.2.1.1 How to avoid the divergence of the fields in the simulation

We found very often an early termination of the simulation due to a divergence of the

calculated fields. This section discusses briefly some of the main reasons that make the

electromagnetic fields diverge and it gives some possible solutions to fix this problem.

Most diverging simulations are related either to the stability factor dt, or to the PML

boundary conditions.

Dt stability

Once physical structures and interfaces are included in the simulation, particularly when

dispersive materials are involved, sometimes it is necessary to set a time step smaller

than the step calculated from the mesh size based on the Courant stability criterion 2.7.

For certain physical structures and interfaces, a smaller time step is sometimes required

to avoid the divergence of the fields. One of the main reason causing the dt instability

is caused when the dielectric function of some dispersive materials is not properly fit

with the multicoefficent model used by the software to solve the Maxwell equations.

Multi-coefficient models that rely on a set of basis functions that describe Drude, De-

bye, or Lorentz models present some limitations to fit the dispersion profiles of certain

materials. In addition, using a large mesh aspect ratio higher than 5 is also a possible

reason of instability when dt is near the maximum theoretical limit.

PML considerations

In order to obtain the most accurate results, it is recommendable to extend the physical

structures through the PML boundary conditions, due to the fact that reflections from

the PMLs are minimized when structures are extended completely through the PML.

However, this can cause the simulation to diverge for some dispersive materials like met-

als. This problem can be solved by increasing the PML layers and decreasing the sigma

factor associated with the layer absorption without affecting the PML performance, or

by increasing the mesh size immediately before the PML. If none of this recommenda-

tions work, the only solution is to stop the material layer at the inside edge of the PML.

Bibliography

[1] E. L. Wolf, “Nanophysics and nanotechnology: an introduction to modern concepts

in nanoscience,” Weinheim: Wiley-VCH Verlag, vol. 69, 2004.

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no. 3, p. 427, 1999.

[3] D. Y. Lei, A. I. Fernndez-Domnguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund,

J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film

systems using dark-field spectroscopy,” ACS Nano, vol. 6, no. 2, pp. 1380–1386,

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[5] A. Taflove, “Application of the finite-difference time-domain method to sinusoidal

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– 379, 1996.

Chapter 3

Design considerations for

near-field enhancement in optical

antennas

Nanoantennas for visible and infrared radiation can strongly enhance the interaction of

light with matter by their ability to localize electromagnetic fields on nanometric scales

and enhance the scattering of light out of nanoemitters. In this chapter we discuss

the main parameters influencing the near-field enhancement provided by dimer-type

nanoantennas. To facilitate the design of structures we analyse the influence of the

substrate, adhesion layers, a reflecting metal underlayer and arrangements in gratings.

We highlight the factors which increase the damping of the plasmonic resonances or the

discrepancy between the far-field and the near-field resonances.

Design considerations for near-field enhancement in optical antennas 53

3.1 Introduction

In this chapter, we want to provide a compilation of relevant known properties of nanoan-

tennas, focussing on the parameters that experimentally would determine their proper-

ties, including considerations to bear in mind in the fabrication process to optimize the

antennas’ performances. Using Finite-difference time-domain (FDTD) numerical calcu-

lations, we discuss the influence on the field enhancement and scattering cross section

of the following factors: the type of metal, the adhesion layer, the substrate, and the

use of periodic arrays. In addition, a special emphasis will be made on the influence of

the antenna design on the energy shift between the far-field resonance and the near-field

maximum intensity around the antenna dimmer. This is of particular interest for ap-

plications that take advantage of the near field enhancement (Surface enhance Raman

scattering SERS, fluorescence enhancement)as the probing of the scattering properties

of optical antennas is easily accessible experimentally, whereas their near field charac-

teristics remain a challenge.

3.2 Influence of the material

In 1.1.2, it was discussed that a plasmonic behaviour is possible only for frequencies

lower than the plasma frequency. Metals with ωp in the UV range can sustain surface

plasmons in the visible and near-IR range. In this chapter, we focus on the four main

metals fulfilling this condition: silver, gold, copper and aluminium. Note however than

real metals present large losses in the visible and ultra-violet (UV) range because of

interband electronic transitions [1]. This leads to a deviation from the Drude model

mostly expressed by larger imaginary parts of the dielectric function in these wavelength

ranges. Note that these interband transitions are usually described through the addition

of Lorentz-like terms peaking at high frequencies to Eq. 1.17.

Figure 3.1 presents the real and imaginary parts of the permittivity for silver, gold,

copper and aluminium. On one hand, the real part ε′(ω) describes the strength of the

polarization induced by the external field. On the other hand, the imaginary part ε′′(ω)

describes the losses associated with the polarization process. Silver presents the lowest

loss in the visible range (400-700 nm), however its well known that degradation problems

generally make it less suitable for plasmonics applications. In contrast, gold is chemi-

cally very stable but shows higher losses below 550 nm associated with the occurrence

of electronic interband transitions. The dielectric properties of copper are comparable

with gold between 600 and 750 nm. If we consider its low cost compared with gold or

silver, copper could be a good alternative material to be used in optical antennas, is

Figure 3.1: (a) Real part ε′(ω) and (b) imaginary part ε′′(ω) of the permittivity ofAg, Au, Al and Cu obtained from [2].

Figure 3.2: (a) Scattering and (b) absorption cross sections of dimer antennas madeof Ag, Au, Al and Cu. Inset: Sketch of the nanoantennas composed of two opposing,70 nm long, 40 nm wide and 45 nm thick arms separated by a 30 nm gap. The antennas

are placed on top of a semi-infinite SiO2 substrate with dielectric constant εd=2.2

not a better choice mainly due to the fabrication problems associated with its oxidation

[3, 4].

Finally, aluminium presents large losses around 800 nm associated to interband transi-

tions at this wavelength, therefore it is not an ideal material for optical antennas in the

visible regime. However in the UV, away from the absorption band, aluminium is a very

promising plasmonic material [5]. Importantly, metals are not the only option: West et

al. [3] have reported a very detailed analysis of the advantages and disadvantages of us-

ing alternative plasmonic materials such as semiconductors or metallic alloys. Finally, a

recent report has shown that it is possible to maintain the plasmonic properties of silver

by passivating the surface of nanostructures with a monolayer of graphene, avoiding the

degradation induced by air sulfidation [6].

Figure 3.3: Simulated near-field enhancement at the cavity center of dimer antennasmade of Ag, Au, Al and Cu. The antennas’ dimensions are identical to those used in

Fig. 3.2.

In Figure 3.2, we present numerical calculations of the scattering and absorption cross

sections of dimer antennas with different materials modelled through the Drude-Lorentz

fitting of the dielectric properties from Fig.3.1. The incident fields are polarized along

the axis of the antenna. The dimer antennas considered in this comparison are composed

of two opposing 70 nm long, 40 nm wide and 45 nm thick arms separated by a 30 nm gap.

Fabrication techniques such as focused ion beam milling and electron beam lithography

are widely used to fabricate such structures with the required precision. The advantage

of dimers compared to isolated nanoparticles lies in the drastic near-field enhancement

induced in the gap by the near field coupling of both particles [7].

All the results presented in this paper are calculated by using the commercial 3D full-

wave electromagnetic wave solver Lumerical FDTD Solutions. Fig.3.2(a) compares the

scattering power of antennas with identical dimensions and made of different metals,

highlighting the dependence of the wavelength resonance on the material characteris-

tics. We observe that silver presents the largest resonance strength for these specific

dimensions. The resonance wavelengths for Al (350 nm) and Ag (550 nm) are signif-

icantly shifted to high energies with respect to gold (630 nm). The same comparison

stands for the absorption cross sections, in Fig. 3.2(b): silver shows less absorption than

gold or copper at the resonant wavelength. In addition, one can observe absorption

at higher energies for all four metals, non attributed to the antenna dipolar resonance:

below 500 nm, 450 nm and 600 nm for Au, Ag and Cu respectively. This absorption

band is associated to interband transitions and occurs at lower energy for Al, leading to

the shoulder in the absorption cross section between 600 and 850 nm for that material.

Figure 3.3 continues the comparison by showing the near field enhancement at the gap of

the dimer antenna, where the electromagnetic field is predominately localized, when the

light is polarized along the antenna long axis. The ability of nanoantennas to generate

high localized fields is another crucial parameter to take into account in the design of

suitable devices. Near-field calculations show a tendency similar to the scattering cross

sections, although gold is the metal providing a higher localised field at the dimmer gap.

Therefore, gold is postulated as the best material for near-field enhancement applications

at wavelengths longer than 600 nm. In addition, the wavelength of maximum field

intensity is slightly red-shifted compared to the far field resonances. This effect will

be discussed in the following sections; 3.3 and 3.6. For the rest of the chapter, gold is

taken as the reference material used in the simulations of the antennas without loss of

generality in the conclusions.

3.3 Influence of the dimensions and geometry on the plas-

monic properties

The material is not the only factor governing the optical response of a nanoantenna:

shape and geometry also play a crucial role. In particular, the dimension of the particles

parallel to the incident electric field is one of the most determinant factors to control

the resonant frequency, the near-field enhancement or the scattering characteristics [8–

10]. Indeed, if we consider a single metal nanoparticle as a Fabry-Perot cavity [11], its

resonances will be given by its length; L = n2λeff where n is an integer number and λeff

the effective wavelength of the plasmon mode. The lowest LSPR supported by the metal

NP (n=1) is the most intense and the one that determines the energy of the resonance

for a dimer antenna composed by two identical NPs.

In order to understand intuitively the dependence of the resonance frequency with the

particle length, we can consider that the separation between the induced positive and

negative charges within the particle give rise the restoring force that creates the plas-

monic resonance. The larger the distance between the charges is, the smaller the restor-

ing force will be. In dimers, created by placing the two metallic particles at a distance

short enough so their near field can interact, the dimension of the gap between the LSPR

supported by each arm of the antenna also affects the antenna resonance [12].

In this case, a red-shift of the dimer LSPR is induced compared with the single particle

case. The hybridization model [12–14] explains this red-shift as a result of the electro-

static mixture of different energy levels associated with different charge distributions at

the isolated NPs. According to this intuitive formalism, the configuration that max-

imizes the distance between charges of opposite sign corresponds to the lowest dimer

Figure 3.4: (a) Evolution of the scattering cross section with the antenna gap distance.Inset: Evolution of the position of the scattering peak with the gap distance (b) Nearfield intensity at the gap and at the middle height of the particles (z = 22 nm) obtainedas a function of the incident frequency for different gap lengths. The particle length(100 nm), width (40 nm) and the thickness (45 nm) are fixed in all cases. The antennas

are sitting on a glass substrate (n=1.45).

Figure 3.5: (a) Evolution of the wavelengths of maximum far-field scattering andnear field intensity for dimmer antennas with different length. (b) Left column: X-Y Spatial distribution of the near field intensity around the antenna at the middleheight of the particles (z = 22 nm) obtained at the resonance wavelength for differentantenna arm lengths. Right column: spatial distribution of the wavelength resonanceshift, ∆λ = λpeak

nf − λpeakff in nm. (scale bar: 100 nm). The gold nanoantenna gap

(20 nm), the particle width (40 nm) and the thickness (45 nm) are fixed in the threecases corresponding to 100, 140 and 180 nm length antenna arms. The antennas are

sitting on a glass substrate (n=1.45).

resonance. Indeed Fig.3.4 shows that when the gap size is reduced, the scattering reso-

nance and the near field peaks (at the center of the gap) shift to lower energies, and the

near field intensity is increased. The near field enhancement increases exponentially with

the reduction of the gap: this illustrates the importance of obtaining small gaps, which

is one of the main fabrication challenges in the production of efficient nanoantennas [15].

Figure 3.5(a) show the evolution of the wavelengths of maximum far-field scattering

and near field intensity for the case of dimer antennas with different lengths, at a fixed

gap dimension. Note that the peak wavelength of near field intensity is evaluated at

the antenna gap. It is noticeable that modifying the antenna arm length by 40 nm

allows for a wide tunability range of approximately 200 nm. The spatial distribution

of the near-field enhancement shows a significant increase of the intensity at the gap as

the antenna arm length increases (Fig.3.5(b)). This can be understood as the result of

an effective increase of the coupling strength between the two antenna arms. As the

antenna arm increases, the gap has a smaller size relative to the resonant wavelength,

which results in a stronger coupling between the LSPRs supported by both arms.

An effect often overlooked is that the maximum near field intensity in the surroundings

of the antenna occurs at a wavelength different from that of maximum scattering[16–

19]. In the following, we will refer to this as the shift between near field and far field,

∆λ = λpeaknf −λ

peakff . This can be explained directly by the physics of a driven and damped

harmonic oscillator. Zuloaga et al.[16] showed that this shift depends directly on the

total damping of the system;intrinsic damping within the metal of the nanoparticle

and radiative damping of the localized plasmon. However, in the close vicinity of the

nanostructure, ∆λ depends on the position. This is shown in the right hand side column

of Fig.3.5(b) which presents the spatial distribution of ∆λ for antennas with arm length

of 100, 140 and 180 nm. In the zones where the enhancement is maximal, i.e. in the gap

and at the extremities of each arm of the dimer, a significant red shift is observed in all

three cases. Fig.3.5(b) shows that the shift in the gap increases with the antenna arm

length, up to a value of 30 nm for the 180 nm case in the near-infrared spectral regime.

If we consider that optical antennas are generally characterised by experimental tech-

niques in the far-field, such as dark-field spectroscopy or Fourier transform infrared

spectroscopy (FTIR), the energy shift between far and near-field must be considered in

the fabrication process. In particular, applications such as SERS can be very sensitive

to this effect as the mechanism influencing their efficiency is the near-field enhancement

and not the scattering properties of the antenna [17, 20].

Apart from the antenna length and the gap distance, the shape of the particle also in-

fluences significantly its LSPR [21]. Figure 3.6 highlights the influence of geometry on

the antenna properties. For the calculations, we consider dimers with different shapes:

bow-ties, rods, ellipsoids, disks and squares. Although the length of the particles paral-

lel to the incident field polarization and the dimer gap are fixed to 100 nm and 20 nm

respectively, the comparison shows a clear effect of the particle width and shape on the

energy and strength of the antenna LSPR. Ellipsoids were chosen with the semi-principal

axes matching the width and length of the rods to evaluate the effect of sharp edges.

Figure 3.6: (a) Scattering cross section of plasmonic dimers with different geometries.(b) Left column: near field intensity distribution around the antenna at the resonancewavelength for different dimers: bow-ties, ellipsoids, rods, disks and squares. Rightcolumn: spatial distribution of the far/near field resonance shift in nm. Scale bar:100 nm. The arm length in the horizontal direction is 100 nm in all cases. The goldnanoantenna gap and the thickness are set to 20 nm and 45 nm respectively, and the

antennas are lying on a glass substrate.

The ellipsoidal disks present a blue-shift of 40 nm in the scattering cross section with

respect to the rods (Fig.3.6(a)). Similarly, the disks resonant wavelength shows a more

significant blue-shift, 70 nm, compared to the squares. This is due to a effective diminu-

tion of the particle length in the polarization direction, that determines the resonance

energy as previously discussed. It is particularly important to consider this effect in the

design of the antennas, when fabrication constraints limit the production of sharp edges.

The scattering and the near-field enhancement comparison shows in Fig.3.6 a drastic re-

duction of the strength of the resonances for the geometries with high aspect ratio (disks

and squares) induced by the increase of the radiative plasmonic damping, as the particle

increase its width and the particle aspect ratio is increased [22, 23]. In addition, the

spatial distribution of the shift between near and far-field in Fig.3.6(b) shows a larger

magnitude at the gap region for these geometries.

In summary, nano-antennas with high aspect ratios like rods dimers present intense

plasmon resonances that provide high values of near field enhancement in the antenna

gap. Moreover, such antennas present a moderate near/far-field shift (≈10 nm in the

visible regime). On the other hand, for applications and devices that require the use of

nanoparticles with high aspect ratio such as disks or spheres, it is recommended to take

this shift into account in the fabrication process.

Figure 3.7: Scattering cross section of a gold dimer antenna as a function of therefractive index of the substrate. Si, GaAs, and Ge substrates were simulated fromexperimental dielectric data from Palik [24]. The dimer is made of two opposing rods

100 nm long, 40 nm wide, 45 nm thick and with a 20 nm gap.

3.4 Influence of substrate on the plasmonic properties

The Frolich condition discussed earlier (Eq. 1.24) illustrates the dependence of the

plasmon resonances of metal nanoparticles on the dielectric properties of the surrounding

medium. The resonance wavelength of plasmonic nanoparticles is gradually shifted to

longer wavelengths as the surrounding refractive index increases [25]. Similarly, it has

been experimentally demonstrated that the refractive index of the substrate affects the

plasmonic properties of the nanoantennas [26–28]. Figure 3.7 shows the evolution of the

scattering cross section of a gold antenna with the refractive index of the substrate.

Apart from a red-shift, increasing the refractive index causes a progressive increase in

damping of the resonance (broadening and reduction of intensity). Hence, using the

substrate with the lowest refractive index possible yields the best plasmonic properties.

The interaction of nanoantennas with semiconducting materials with high refraction

index such as Si, Ge or GaAs moves the antenna resonance into the near-infrared.

Applications requiring the use of nanoantennas with large index substrates have to bear

in mind the large red shift in the resonance that this induces. In such cases, introducing

a SiO2 gap of several hundreds of nanometers between the antenna and the substrate

can limit this effect [1].

Figure 3.8: (a) 3D integration of the near field enhancement. The inset shows thesample cross view. (b) Cross view of the near field intensity distribution of the antennaat the resonance wavelength for each distance of separation between the antenna andthe gold under layer. The nanoantennas are composed of two opposing arms with alength of 75 nm, width of 40 nm with, 40 nm thickness and separated by a 30 nm gap.

3.5 Introduction of a reflective layer

Recent studies have demonstrated that the addition of a metal underlay on a glass

substrate is a very effective means to increase even more the field enhancement and

the scattering cross section of metal nanoantennas. This phenomenon, explained by a

near-field coupling between the antenna and its mirror image in the metal layer [25],

has been used to improve SERS [26] or the directivity on optical antenna substrates

[27], allowing for single molecule detection [28]. The addition of a reflecting underlayer

provides additional ways of tuning optical antennas by changing the dielectric layer

thickness as well as increasing the near-field enhancement, achieving high quality factors

Figure 3.8(a) shows a simulation of the near-field enhancement as a function of the

excitation wavelength by spatially integrating the field intensity at every point in a

volume of 300×200×100 nm3 around the antenna, as a function of the SiO2 thickness.

This comparison shows a field enhancement factor amplified up to 5 times when the gold

underlayer is smaller than 25 nm, compared to the case without reflecting layer. The

near-field interaction between the antennas and the gold underlayer causes a significant

shift of the resonance to lower energies when the SiO2 separation decreases. This can be

explained by the hybridisation of the antenna dipole with its dipole image in the Au film,

which leads to a red shift when the gap is reduced and the interaction enlarged. [35]. The

cross views of the near field intensity distribution corresponding to the different SiO2

separations shown in Fig.3.8(b) illustrate the increase of the near field enhancement

Figure 3.9: Quantum yield enhancement, η/η0, for a single emitter of intrinsic effi-ciency η0 placed at the antenna gap and oriented along the antenna axis for for eachdistance of separation between the antenna and the gold under layer. The arm lengthin the horizontal direction is 100 nm in all cases. The gold nanoantenna gap and the

thickness are set to 20 nm and 45 nm respectively.

on the dimer gap as the SiO2 separation is reduced. In the same way, the radiative

properties of the antenna are drastically improved by the reflecting layer [1]. It is possible

to use a nanoantenna to modify the emission properties of a nanoemitter placed in its

vicinity. One of the two main effect the antenna can have is to modify their quantum

yield. The quantum yield is defined as the ratio between the radiative decay rate, ηr,

and the total decay rate of the molecule, ηT [5]. The calculation of the quantum yield

enhancement of the emission of a dye placed next to a nanoantenna is presented in

Fig.3.9. A dipole with an intrinsic quantum yield η0, positioned at the center of the gap

and oriented along the main axis of the dimer, experiences a maximum enhancement of

2 thanks to its optimal positioning with respect to the nanoantenna. When the reflector

layer is incorporated, this maximum enhancement increases to 6.

The maximum quantum yield enhancement occurs at a SiO2 separation of 50 nm, which

is different from the SiO2 separation of 15 nm at which the antenna provides the maxi-

mum near field enhancement. This difference is probably caused by the dipole orienta-

tion that is parallel to the reflector underlayer which, at a very small separation distance

(0-20 nm), results in a cancellation of the dipole radiation by its mirror image. Seok et

al. [25] demonstrated that the optimum SiO2 separation is achieved when the radiation

quality factor (Qrad) of optical antennas is matched to their absorption quality factor

(Qrad).

Figure 3.10: (a) Scattering cross section of a gold plasmonic dimer with differentadhesion layers. (b) Left column: x-y spatial near field intensity distribution aroundthe antenna at the resonance wavelength. Right column: spatial distribution of thenear/far-field shift in nm. The dielectric functions of Ti, Cr, and SiO2 are taken fromPalik [24]. The thickness of the adhesion layer is set to 4 nm. The dimer is made oftwo opposing rods 100 nm long, 40 nm wide, 45 nm thick and separated by a 20 nm

3.6 Influence of an adhesion layer

One of the main disadvantages of using gold nanoantennas on glass substrates is the poor

adhesion of gold to glass surfaces. This is due to the absence of an intermediate oxide

layer in the gold evaporation process [38]. Therefore the addition of a layer of another

material of several nanometers between the gold and the substrate surface is generally

used for most gold nanoantenna devices. Despite its thin character, the high sensitivity

of the LSPR to its environment makes the nanoantenna performance be influenced by

this adhesion layer. The presence of the adhesion layer leads to a red-shift of the plasmon

resonance and to a significant increase of its spectral width [39].

It has been demonstrated that this layer significantly deteriorates the properties of

plasmonic structures [40–43]. TiO2 is presented as the best material to use as adhesion

layer in terms of reducing the deterioration of the plasmonic properties [40, 44]. In Figure

3.10, we show the effect of an ultrathin adhesion layer of Cr and Ti on the plasmonic

resonance of a gold dimer on a glass substrate. The scattering intensity drops drastically

when adding the adhesion layer with a reduction of 55% for Ti and 65% for Cr. The

same reduction is observed in the near field enhancement on the dimer gap, shown in

Fig.3.10(b). Moreover, the additional damping introduced by the adhesion layer causes

a further energy shift between near/far field (30 nm for Cr) that must be considered

alongside with the sources of shift dependent on the nanoparticle dimensions discussed

in Fig.3.5(a) and Fig.3.5(b).

Figure 3.11: Near-field enhancement at the gap of periodic arrays of gold dimers fordifferent pitches. The sample plane view showed as inset illustrates the field enhance-ment localized at the antennas gap at the resonance frequency. Each nanoantenna iscomposed of two opposing 100 nm long, 40 nm wide, 40 nm thick arms separated by a

20 nm gap. The antennas are placed on glass.

In conclusion, these results illustrate the crucial role played by an adhesion layer in any

plasmonic application. An elegant solution around this problem, when gold is concerned,

is the use of a molecular linker which acts as sticking layer and does not introduce any

additional damping and maintiain, if not improves, the plasmonic properties of the

nanoantenna [45].

3.7 Antennas arrays and near field enhancement

The near-field enhancement can be further increased by organising the nanoantennas in

periodic arrays. The coupling between grating modes and localized surface plasmons

in nanoparticle arrays leads to narrow resonances in the near and far field that can be

specially suitable for sensing applications [46–48]. Such coupling has previously been

demonstrated in the optical regime and it can also be scaled to the THz regime with

the purpose of detecting changes in the refractive indices of fluids placed on the antenna

array [49].

Calculations predict that gold nanoparticle arrays can exhibit near-field enhancement

approximately one order of magnitude greater than those of single isolated gold nanopar-

ticles [20, 50, 51]. Figure 3.11 shows the near field enhancement at the antenna gap for

different periods. A narrow near-field resonance is observed at a periodic distance of

500 nm for the simulated case. The optimum periodic distance d occurs at the first

grating order and it can be easily estimated from the resonance of a single nanoantenna

λres and the refractive index of the antenna substrate nsubs, d = λresnsubs

3.8 Conclusions

We have numerically reviewed the factors that generally control the performances of

optical antennas. These include intrinsic factors such as the dielectric properties of the

metal used, or extrinsic factors such as the geometry, substrate or adhesion layer. The

maximum near field surrounding the antenna occurs at a wavelength different from that

of maximum scattering. In this work, we have emphasized that the near field-far field

shift on dimer antennas is highly influenced by many of the parameters discussed above.

In summary, the combination of nanoantenna gratings made of particles with high as-

pect ratio placed on low-refractive-index substrates like glass without damping adhesion

layer and the inclusion of a gold metal underlayer would improve drastically the qual-

ity factor of the plasmonic nanoantenna resonances, providing high values of near field

enhancement and scattering cross section. All these factors should be considered when

designing plasmonic nanoantennas for specific applications.

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Chapter 4

Use of a gold reflecting-layer in

optical antenna substrates for

increase of photoluminescence

enhancement

We report on a straightforward way to increase the photoluminescence enhancement of

nanoemitters induced by optical nanotantennas. The nanoantennas are placed above a

gold film-silica bilayer, which produces a drastic increase of the scattered radiation power

and near field enhancement. We demonstrate this increase via photoluminescence en-

hancement using an organic emitter of low quantum efficiency, Tetraphenylporphyrin

(TPP). An increase of the photoluminescence up to four times is observed compared to

antennas without the reflecting-layer. In addition, we study the possibility of influencing

the polarization of the light emitted by utilizing asymmetry of dimer antennas.

4.1 Introduction

As we have discussed in sec 1.2, the strong field enhancements provided by LSPRs

can be used to enhance optical spectroscopies such as SERS [2, 3] and multiphoton

absorption [4] or modify the spectral characteristics of nanoscale emitters (dyes, quantum

dots...) in the vicinity of the nanoparticles [5]. In the case of nanoemitters, fluorescence

enhancement can be obtained via three phenomena. On the one hand, an increase of

the emitter’s radiative decay rate can be induced by the interaction between the emitter

and nanoparticles resonant with the emission spectral profile [6]. On the other hand, the

nanoantenna can improve the transduction of the excitation light field from near field to

far field [6–12]. Finally, nanoantennas can exert directional control on the fluorescence

emission, allowing for a higher portion of the light to be emitted within the finite aperture

of the collection optics [13, 14].

In section 3.5, we have pointed out a very effective alternative to increase the field en-

hancement and the scattering cross section of metal nanoantennas via placing them on

a continuous thin dielectric film on a metal underlayer. However, none of the related

articles have investigated the possibility to use this concept to improve the radiative

properties of single dimmer nanoantennas, in terms of enhancement of the fluorescence

of organic nanoemitters. In this chapter, we investigate both theoretically and experi-

mentally a plasmonic resonant system consisting of gold dimer nanoantennas separated

by a thin dielectric layer of SiO2 from a gold metal underlayer. The nanoemitter cho-

sen for our study is meso-Tetraphenylporphyrin (TPP), an organic dye which presents

two well-separated emission peaks at 650 and 750 nm (as shown in Fig 4.1) [30]. We

demonstrate that the addition of the metal layer in the nanoantenna fabrication leads

to an increased scattering cross section and field enhancement. This is accompanied

by an increase of photoluminescence enhancement. The asymmetry of the dimer leads

to two LSPRs in different wavelength ranges along the two perpendicular polarisations.

Those two spectrally separated LSPRs enhance selectively the emission bands of TPP

depending on the polarisation.

4.2 Experimental methods for Photoluminescence measure-

Our study uses glass substrates covered by a 100 nm thick gold layer, further capped by

a continuous 25 nm SiO2 film (nd = 1.45). The nanoantennas were nanofabricated on

top of the SiO2 film, and are 40 nm-thick gold dimers composed of two opposing long

arms separated by a 30 nm gap, as illustrated in Fig 4.2(b). The process of fabrication

was made by Mohsen Rahmani and Minghui Hong from the Department of Electrical

and Computer Engineering at the National University of Singapore. The fabrication

technique used was electron beam lithography (Elonix 100KV EBL system) with the

process described in [31]. The antennas were fabricated in arrays at a separation of

4µm allowing to measure the optical response of a single antenna. The emitting layer is

produced by spin-coating a film of TPP-doped PMMA film on the sample, at a thickness

of approximately 40 nm. By comparing the measured spectral photoluminescence of films

with different concentration of TPP on the PMMA matrix we can estimate the optimum

weight concentration ratio PMMA/TPP that maximizes the TPP film fluorescence. We

have chosen this ratio to 75 according with the fluorescence comparison showed in Fig 4.1.

Note that for all the considered concentrations the film thickness is approximately fixed

in 90 nm eliminating the possible thickness dependence on the film spectral fluorescence.

These measurements were taken with a standard spectrofluoremeter (Horiba FluoroMax

Figure 4.1: Photoluminescence of TPP-doped PMMA films fabricated with differentPMMA/TPP weight concentration ratio. Inset: Evolution of the TPP photolumines-cence at 650 nm with the PMMA/TPP weight concentration ratio. The thickness of

the films is approximately 90 nm in all the cases

Since TPP possesses a low quantum yield (<20%)[30], it is an ideal candidate for pho-

toluminescence enhancement using plasmonic nanostructures [9].

Figure 4.2(a) presents a schematic diagram of the experimental setup. The excitation

laser is set at a wavelength of 405 nm to match the absorption band of TPP (Fig 4.2(c)).

A 40×, NA=0.6 microscope objective is used to focus the laser beam on the sample and

collect the emitted light from the sample. The fluorescent light is filtered in order to cut

Figure 4.2: (a) Experimental setup for TPP fluorescence measurement. The exci-tation laser at a wavelength of 405 nm is coupled into a 40× reflective objective thatfocuses the laser beam on the sample and collects the emitted light. The fluorescencelight is filtered using a dichroic mirror (DM) and a high pass filter (HP) at 420 nm inorder to cut off the incident light scattered from the sample. The beam can be eithersent to a spectrometer (SPEC) combined with a CCD camera, or to a pair of detectors.In the latter case, a 50 µm-pinhole PH selects the fluorescent light coming from thefocal spot only. Lens L2 collimates the light transmitted through PH, which is thendirected to a polarising beam splitter (PBS) that splits the two polarization compo-nents. Finally the light is focused on two APDs (avalanche photodiode) detectors thatcollect simultaneously both polarizations along x and y axes. (b) Schematic samplecross section. A film of TPP embedded in a PMMA matrix is deposited on top ofthe antennas at a thickness approximately equal to that of the antennas (40 nm). (c)Measured absorption and photoluminescence (PL) emission spectra from a film of TPP

into a PMMA host matrix.

off the incident light scattered from the sample. The fluorescent light can be sent to a

spectrometer or to a polarizing beam splitter that splits the two polarization components,

which are collected independently on two APDs (avalanche photodiode) detectors. The

scattering cross sections of the nanoantennas were measured on individual nanoantennas

using dark-field spectroscopy with a polarization-adjustable white-light illumination at

an incident angle θ = 60◦ with respect to the normal of the sample surface, as described

elsewhere [33]. Numerical simulations were performed to evaluate the scattering cross

sections of the antennas, as well as their near-field enhancement and the radiated power

of an emitter in the presence of the antennas. The simulations were performed using

the commercial 3D full-wave electromagnetic wave solver Lumerical FDTD Solutions, at

similar conditions to the measurements using the experimental sample geometries. The

optical constants were obtained by fitting the values found in [18] to a multi-coefficient

model.

800700600

Wavelength (nm)

800700600500

Wavelength (nm)

700600500

Wavelength (nm)

SiO2 (nm)

20 5030 7040 No Au

(a) (b)

Figure 4.3: Effect of a gold underlayer on the antenna properties. The nanoantennasare composed of two 75 nm long rods with a 30 nm gap on a glass substrate andsurrounded with air (n=1). (a) Comparison between the near field (NF) enhancement,integrated over a volume of 300 nm x 200 nm x 100 nm surrounding the antenna,of dimer antennas placed on a glass substrate with (black line) and without (red line)gold underlayer. For this comparison, the polarization is selected parallel to the antennaaxis, X-pol. Dotted red line: antenna with ≈ 95 nm long arms, without gold layer, tomatch the resonance at 655 nm. Inset: simulated power radiated by a dipole placedat the antenna gap for different values of SiO2 thickness. The dipole is placed at thecenter of the gap cavity with polarization parallel to the antenna main axis in order tomaximize the coupling. (b) Comparison between the simulated scattering cross section(continuous lines) and dark field scattering (dotted lines), for an incident polarisationalong the main axis of the antenna. Experimental and simulated data on black refers todimer antennas placed on a glass substrate and red data to dimmer antennas withoutgold underlayer. Inset: scanning electron microscope (SEM) image of one nanoantenna

being considered.

4.3 Effect of a gold reflecting-layer on the properties of

gold dimmer antennas

We firstly describe and characterize the antenna system used in our study. The nanoan-

tenna system is not yet covered with the dye-doped layer, and we choose a nanoantenna

composed of two opposing elongated disks 75 nm long arms with a 30 nm gap. Figure

4.3(a) shows a simulation of the near-field enhancement as a function of the excitation

wavelength by spatially integrating the field intensity at every point in the surround-

ing antenna volume with and without the reflecting layer. Since the confocal setup

probes a zone limited by diffraction, we choose to integrate the near-field intensity in

a volume comparable to the probing area of excitation (300 nm x 200 nm x 100 nm).

This allows us to estimate the average near-field enhancement on the TPP molecules,

which are randomly spatially distributed and oriented. The simulation was carried out

considering a broadband plane wave as illumination source and a SiO2 separation of

25 nm. This comparison shows a field enhancement factor being amplified up to 5 times

when the gold underlayer is used in these antennas. In addition, the resonance of the

nanoantenna shifts to lower energies when the SiO2 separation decreases, because of the

near-field interaction between the antennas and the gold underlayer. This is explained

by the hybridisation of the antenna dipole with its dipole image in the Au film leading

to a red shift when the interaction is stronger [35].

Moreover in Fig 4.3(a), we present the average enhancement corresponding to nanoan-

tenna without gold reflecting layer (dotted line), with the dimensions such that the

resonance position matches the position of the antenna with the reflective layer (long

arm of 95 nm instead of 75 nm). This allows us to estimate the maximum amplifica-

tion enhancement that the mirror layer introduces at a certain wavelength. In this case

(resonance at 655 nm) the factor is approximately 3.

To link this to the enhancement of the emission of a dye placed next to a nanoantenna,

the inset of Fig 4.3(a) presents the enhancement of the radiated power of a dipole ideally

coupled to the gold nanoantenna, i.e. positioned at the center of the gap and oriented

along the main axis of the dimer, influenced by the addition of the Au underlayer on the

antenna substrate. Here the nanoantennas are placed on top of a SiO2 layer at different

thickness. The enhancement of the power radiated by the dipole increases gradually as

the SiO2 separation layer gets smaller, achieving amplification factors of more than 100

times compared to the case without the gold underlayer. This comparison illustrates

the benefits of the underlayer on the radiation properties of dyes, albeit in the ideal

situation where the emitter is perfectly placed and oriented along the gap. This picture

is challenging to reproduce experimentally in our samples, TPP molecules are distributed

randomly around the nanoantenna and with random orientation. In addition, the red-

shift of the wavelength, previously discussed , allows us to select 25 nm as the SiO2

layer thickness for our samples to optimize the overlap between the near field antenna

resonance and the first emission peak of TPP at 640-680 nm. It is important to mention

that the predicted near field antenna resonance under plane wave illumination matches

the predicted antenna radiation resonance under the dipole excitation.

Figure 4.3(b) shows a comparison of the simulated scattering cross section (solid lines)

and the dark field scattering of the antennas (dotted lines) placed on a glass substrate

with (black) and without (red) gold underlayer. For these and all subsequent simulations,

the PMMA layer is not taken into account because the measurement of the scattering

cross sections of the antennas after deposition of the PMMA/TPP layer only exhibited a

minor shift of the resonances (≈10 nm). Spectra are normalised relatively to the intensity

of the resonance parallel to the dimmer axis for the case of using a gold underlayer. Far

field projections (not shown) of the light emitted by a dipole in the situation described

in Figure 4.3(a) show that the underlayer does not change the radiation profile: the

photoluminescence enhancement seen is not due to a beaming effect. For this reason, it is

not necessary to take into account the finite NA of the microscope objectives used in the

simulations. Hence we always estimate the scattering cross sections of the nanoantennas

by integrating over the full 4π space. We observe a good agreement between experiment

and simulation, both demonstrating that using a gold underlayer the scattering of the

antenna increases by a factor up to 4 in the current configuration.

nt I/I 0

6543210

Position (µm)

750700650600550

Wavelength (nm)

TPP emission NF resonance

SiO2|Au|SiO2

(a) (c)(b)

Figure 4.4: (a) Spectral overlap between the emission band of TPP and simulated NFresonances with and without gold underlayer, for the polarization parallel to the dimermain axis. (b) (resp. (c)) Photoluminescence intensity around single resonant antennasfor polarization of the detected light parallel to the antenna axis without (resp. with)the gold underlayer (scale bars 2 µm). Only light in the range 640-680 nm is collected,which corresponds to the first emission peak of TPP. The PL intensity I is normalizedto the intensity measured away from the nanoantennas, I0. Bottom: horizontal profilesas indicated on the images above. The antennas without the Au underlayer induceda 10% PL enhancement, while antennas with the gold underlayer reach up to 50% PL

enhancement.

4.4 Photoluminescence (PL) enhancement of the TPP emit-

We then evaluate the effect of the gold underlayer on the photoluminescence (PL) en-

hancement of the TPP emitters placed on the antenna vicinity. Figure 4.4(a) shows the

spectral overlap between the emission band of TPP and the simulated near-field reso-

nances for the polarization along the main axis of the dimer with and without the gold

underlayer. In both cases, the near-field resonances predominantly match the first emis-

sion peak at 640-680 nm. We thus filter the PL in this wavelength range to maximize

the intensity contrast (Fig 4.4(b)). The fluorescence comparison shows that antennas

without the Au under layer induces a 10% PL enhancement while the antennas with the

gold underlayer reach up to 50%, as highlighted on the profiles on Fig 4.4(b-d). This

result is in good agreement with the values predicted by the simulations as discussed

previously. The ratio of the enhancements is slightly higher than what is expected from

the near field integrations discussed in Fig 4.3(a), probably because the overlap between

the resonance of the nanoantenna and the emission peak of TPP is stronger in the case

with the reflective gold layer. Note while, the total maximum enhancement seen is

modest, this is due to the fact that the radiation collected is integrated over the whole

confocal volume, which contains many dyes, randomly positioned and oriented - only

the ones in the centre of the gap experience for optimum enhancement.

It has been reported that the fluorescence enhancement can be written as the product

of two factors related to different properties of LSPRs [5]. On the one hand, the near-

field enhancement | EEo| (where Eo is the free-space electric field that illuminates the

nanoantenna) is related to the capability of plasmons to concentrate electromagnetic

energy into sub-wavelength volumes and it is evaluated at the excitation frequency,

effectively increasing the absorption cross section of the nanoemitter. The other factor is

the quantum yield enhancement ηηo

, which is related to the modification of the photonic

density of states at the emitter position induced by the localized resonance and it is

determined by the emission frequency. These two factors can be simultaneously much

larger than unity, which leads to strong enhancements of the fluorescence intensity [36].

Considering that the emission and absorption of TPP are spectrally well separated (Fig

4.2(c)), and the excitation wavelength at 405 nm does not excite plasmon resonance

in our antennas, the observed PL increase should be mainly due to the direct emission

enhancement

4.5 Influencing the polarization of the emitted light by

utilizing the asymmetry of dimer antennas

Furthermore, we study the effect of polarization for the case of a dimmer antenna with

the reflecting underlayer. Figure 4.5 shows the two resonances sustained by a gold dimer

for both parallel and perpendicular polarizations with respect to the dimmer axis. For

this study, the dimer antennas used were chosen with a larger length in order to have the

main resonance along the X axis matching the low energy emission peak of TPP at 700-

740 nm. The resonance along the X axis is much more intense than the Y-axis resonance

due to the strong coupling between the particles as reflected also in the near-field profile

4.5(c). Dark field measurement and scattering simulation in Fig 4.5(a) clearly show the

difference in intensities and the spectral separation between both resonances.

900800700600

Wavelength (nm)

X pol. Y pol.

I/I0(a) (b)

Y pol.

X pol.

Figure 4.5: Influence of the polarization on the scattering of a gold dimer consistingof two elongated disks with the dimensions 105×60×40 nm3(long axis × short axis ×thickness) separated by a 30 nm gap. (a) Dark field spectra (solid lines) and simu-lation of the scattering cross section (dotted lines) of the nanoantenna for X and Ypolarizations In all cases the values are normalised to the value at the peak for the Xpolarisation. Inset: SEM image of the gold antenna considered (scale bar: 100 nm).(b) Near field intensity distribution of the antenna for illumination of polarization per-

pendicular (Y direction) and (c) parallel (X direction) to the antenna axis.

Figure 4.6(a) compares the emission band of TPP and the simulated near-field resonances

for an excitation along the main axis of the dimer (X-polarised) and perpendicular to it

(Y-polarised). There is a good overlap between the low energy peak at 700-740 nm and

the X-resonance and a partial overlap of the Y-resonance with the high energy peak at

640-680 nm.

In addition, a small contribution from the X-resonance tail overlaps with the high en-

ergy peak. The spectrum of PL of the TPP is acquired without specific filtering, on

the antennas and away from them. The results, as shown in Fig 4.6(b), show a PL

enhancement in all the emission ranges, which is more pronounced at the low energy

emission peak, with a 25% increase in the peak intensity. This is in agreement with

the overlap presented in Fig 4.6(a). The enhancement is 5% for the high energy peak,

attributed to the smaller contribution from both resonances in this spectral region at

640-680 nm. Figure 4.6(c) illustrates the PL enhancement difference for both peaks by

imaging three identical nanoantennas, either selecting only the first peak (top) or only

the second (bottom).

We finish our discussion by analysing the effect of both resonances independently and

experimentally test the overlap discussed in Fig 4.6(a). To do so, we collect indepen-

dently the two polarization components of the PL emitted, as described in Fig 4.2.

Figure 4.7(a) shows the PL enhancement in the X polarization. In this case, the low

energy peak is enhanced up to 80% whereas the high energy peak is enhanced up to

20%. The ratio between the two enhancements is in a reasonable agreement with the

predicted overlap between the near field resonance in the X-axis resonance and the two

Figure 4.6: (a) Spectral overlap between the emission bands of TPP (blue curve) andthe simulated near field resonances for the X and Y polarizations, black curve and redcurve respectively. The PL collected is filtered either in the area highlighted in blue(640-680 nm) or in green (700-740 nm). (b) TPP emission spectra collected from oneantenna (black curve) and on the plain TPP film (red) without a filter. (c) Filteredphotoluminescence intensity images around single resonant antennas: filtering for thefirst emission peak at 640-680 nm (top) and for the second emission peak at 700-740 nm(bottom). Note that here no particular polarisation is selected for the PL. Scale bars:

TPP emission peaks. Similarly, Fig 4.7(b) shows that for the polarization perpendicular

to the antenna axis, the TPP emission peak around 640-680 nm is more enhanced than

the low energy peak, which is again consistent with the magnitude of the field enhance-

ment provided by the nanoantenna for this polarisation. These observations support

that doubly resonant systems, like gold dimers, can be used to selectively influence the

polarization of emitted light in a specific wavelength range.

4.6 Conclusions

We have demonstrated that the addition of a gold underlayer to the fabrication of

nanoantennas can improves their properties, by offering new possibilities of resonance

tuning by means of controlling the spacer thickness and increasing their scattered radi-

ation power and near-field enhancement. These in turn increase the photoluminescence

enhancement induced by the antenna on a low efficiency light emitter such as TPP. In

addition, this improvement enhances the intensity of the two resonances associated with

the perpendicular light polarizations existing in a gold dimer, allowing to measure their

influence in a specific wavelength of the dye emission. Such a system presents a way

to selectively influence the polarization of emitted light in organic dyes with multiple

Figure 4.7: Study of the influence of the nanoantenna on the polarisation propertiesof the PL emitted. (a) Top: PL intensity around single nanoantennas for polarizationof the detected light parallel to the nanoantenna axis, filtered at around 640-680 nmand 700-740 nm. Scale bars: 1µm. Bottom: horizontal profiles comparing the PL ofthe two emission peaks for X-polarised detected light. The TPP emission peak in the700-740 nm range is preferentially enhanced over the peak at 640-680 nm. The insetis an SEM image of the antenna considered, scale bar 100 nm. (b) PL intensity forpolarization of the detected light perpendicular to the antenna axis. The peak around

640-680 nm is preferentially enhanced in this case.

emission peaks.

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Chapter 5

Polarized Plasmonic

Enhancement probed through

Raman Scattering of Suspended

Graphene

The near field localisation in a dimer cavity between two Au nanodisks provides an

ideal platform to enhance the Raman scattering of graphene. A strained single layer

of graphene placed across the dimer cavity shows a Raman enhancement or the order

of 103. Spatially resolved Raman measurements demonstrated a near-field localization

one order of magnitude smaller than the wavelength of the excitation, which can be

activated by rotating the polarization of the excitation.

Polarized Plasmonic Enhancement probed through Raman Scattering of SuspendedGraphene 87

5.1 Introduction

The results of this chapter are immersed in the frame of ”NANOSPEC”, a collaborative

project, funded by NanoScience Europe whose partners are the University of Edinburgh,

The Free University of Berlin, The Hebrew University of Jerusalem and Imperial Col-

lege London. This project bring together expertises from different fields like carbon nan-

otubes, Raman spectroscopy or Plasmonics. My contribution to this project is related to

the optical characterization and the numerical simulation of the studied nanoantennas.

The central aim is to design and investigate the interface between plasmonic nanoanten-

nas and carbon nanomaterials like carbon nanotubes and graphene. The ultimate goal

of the project is to achieve simultaneous optical and electrical characterization of such

nanosystems [2].

Graphene is becoming a unique material in different fields like material sciences or con-

densed matter physics for its physical properties and numerous potential technological

applications [3]. Its remarkable conductivity at room temperature makes graphene a

solid candidate for the next generation of transistors and optoelectronic applications. [3–

5]. Recently, the wide-band photodetection capabilities of graphene has been drastically

enhanced combining it with plasmonic nanostructures [6–8]. Excitation of plasmons in

metals provide a great platform for SERS spectroscopy. The SERS phenomenon, which

is produced by the enhancement of the Raman emission of molecules in interaction

with rough metal surfaces or metal NPs[9], is also studied in graphene to explore its

unique properties as 2D material. Different types of nanoparticles such as arrays of gold

nanodisks [10] or closely packaged gold-nanopyramids [11] have been used to achieve

considerably high SERS enhancement factors on graphene.

Remarkably, nanoscale plasmonic cavities made of closely placed metallic nanoparticles

represent an new alternative to obtain high SERS enhancement factors approaching

those needed for single-molecule detection [12]. In this context, we use a nanoscale

cavity between two gold nanodisks to achieve a Raman enhancement of graphene up

to 103. By suspending graphene on top of the gold disk dimer and partially extending

it into the cavity, we are able to show that the enhanced Raman signal is originated

from suspended graphene under tensile strain. The gold dimer structure induces this

strain causing a localised elevation of the graphene. Raman enhancement measurement

shows a spatial confinement in an area below the diffraction limit, much smaller than

the wavelength of the excitation. A great advantage of using coupled gold nanoparticles

like disk dimers is that by rotating the polarization, the two disks can be selectively

coupled or uncoupled, acting as separate particles in the last case and causing a drop of

the enhancement factor by 20. The Raman measurements permits to identify strained or

unstrained graphene. We demonstrate that the use of Raman enhancement in strained

graphene can be used to characterize plasmonic enhancement in a disk dimer structure,

but the same concept could be applied to different plasmonics structures [1].

5.2 Description of the graphene-dimer interface

The plasmonic structure consist in a double disk structure with a height of 45 nm. An

adhesion layer of Cr (5 nm) is using between the substrate and the gold (Fig. 5.1(e)),

the disk diameter is ∼100 nm with an interparticle distance of ∼30 nm. The substrate

used is a 300nm thick SiO2 layer of 300 nm on top of pure Silicon. Figure 5.1(a)

Figure 5.1: (a) AFM image of graphene placed on top of the double structure. Thecoloured arrows indicate the y-position of the height profiles shown in (b). Each heightprofile is offset by 10 nm for clarity. c) 3D-AFM profile of the structure investigated.In (b) a comparable structure before graphene deposition is shown (d) Sketch of the

sample configuration(Adapted from [1])

shows the SEM image of the structure. Graphene is prepared by mechanical cleavage

and transferred on top of the structures [13]. Figure 5.1(a) shows the atomic force

microscope measurements of the topography of the graphene layer deposited on top of

the structure. The AFM topography analysis shows that the graphene layer is suspended

over the gap between the two particles and elevated from the surrounding substrate over

a length of around 150 nm in all directions. In fact, the 3D-AFM profile from Fig.

5.1(c),(d) confirms that graphene is suspended in the gap and between the edges of the

structures and the substrate. The arrows indicate different height profiles at different

topographic conditions shown in Figure 5.1(b). The green arrow shows the graphene

suspended at half the height of the antennas and the black arrow indicates graphene

completely adsorbed on the substrate. The red curve shows the topography crossing

at the center of the gap. It is noticeable that graphene is partially inserted inside the

cavity. Figure 5.1(d) shows the sample configuration that summarises the information

obtained for AFM analysis. The observed topography suggests that the graphene is

under tensile strain. In particular, we observe a strain in y-direction, as the graphene is

pulled around 4 nm into the gap between the particles.

5.3 Plasmonic resonances analysis of the structure

Polarized dark-field spectroscopy, as discussed in section 2.1.2, is used to measure the

scattering cross section of the double structure obtained before graphene deposition

showed in Fig. 5.2. The polarization Px of the illumination source is oriented along the

x-axis defined in Fig. 5.1(a). The plasmonic antennas were designed in order to obtain a

optimum overlap between the Px resonance and the excitation laser of 638 nm with the

purpose of maximizing the SERS enhancement for this polarization. By comparing the

simulation of both scattering cross sections, for Py and Px, we show a resonance blue-

shift of Py compared to Px, simulations were used by Lumerical FDTD (Sec 2.2.1). Note

that the graphene influence on the resonances was not considered in the simulations as it

was not measured any significant change in the resonance wavelength with and without

graphene layer on top of the structure.

The simulated scattering cross sections that described the far field resonances for both

polarizations can be explained by the near field interaction between the two particles. As

described in section 1.2, localized plasmon resonances of a single metallic particle depend

on its material, shape, and size. Using disks instead of rods as optical antennas allows us

to quantify the coupling between the two particles by rotating the excitation polarization.

In our case, Px polarization couples the particles whereas Py breaks the coupling and

both particles act independently. Geometrical deviations of the real particles, such as

imperfect edges, cause a blueshift of the experimental data compared to our simulation.

The wavelengths of the scattered light corresponding to the G and 2D peaks, which are

the dominant phonons observed in graphene Raman spectra, are indicated in Fig. 5.2 for

the two laser lines selected. Especially the energy of the 2D phonon Eph predominately

overlaps with the line width Γ of the plasmon. Therefore, it is possible to distinguish

between the regimes of enhanced absorption (red) and enhanced emission (green) and

Figure 5.2: Experimental polarized dark-field spectra for Px (circles) and simulatedscattering cross sections for Px (solid) and Py(dashed). The excitation wavelengthsemployed in the Raman experiments are indicated as vertical lines, together with the

corresponding wavelengths of the G and 2D modes of graphene.(Modified from [1])

expect the SERS enhancement factor to scale with |ELocE |

2 for both cases. This can be

distinguished from the general case where SERS enhancement scales with the fourth

power of field enhancement, which is generally observed in SERS when absorption and

emission are simultaneously enhanced [15, 16].

5.4 Polarization dependence of Raman scattering on sus-

pended graphene

Figure 5.3 shows the Raman spectra taken on the structures for two different excitation

wavelengths 532 nm (green plots, a-b) and 638 nm (red, c-d) and for both polarizations

Px (a,c) and Py (b,d). All spectra are normalized to the 2D peak height on SiO2. The

position and the full width at half-maximum (fwhm) of the G peak (∼ 1580/11 cm−1)

and the 2D peak (∼ 2670/25 cm−1)on SiO2, extracted from Fig. 5.3(a), confirm the

presence of single layer graphene [17]. In addition, the peak height ratio 2D/G of 2.8

for an excitation of 532 nm and an oxide layer thickness of 300 nm also supports the

existence of single-layer graphene [18, 19].

Figure 5.3: Raman spectra on the double structure for (a) λ = 532 nm and Px, (b)λ = 532 nm and Py, (c) λ= 638 nm and Px ,(d) λ= 638 nm and Py. The spectraare normalized to the 2D peak height measured on SiO2 next to the structure for the

corresponding excitation and polarization (Reproduced from [1])

In order to evaluate the SERS enhancement, we focus only on the 2D peak. Indeed,

the G peak is not suitable: gold nanostructures exhibit a luminescence that predomi-

nantly overlaps in energy with the G peak, causing noisier spectra [20]. Regarding the

enhancement of the absorption, these results show that the observed signal intensities

are in good qualitative agreement with the scattering cross sections shown in Figure 5.2.

For an excitation wavelength of 638 nm, clearly overlapping the experimental plasmonic

resonances, the highest 2D intensity occurs for Px. By rotating the polarization to Py,

which means lower scattering cross section and a reduction of the localised field due

to the lack of coupling between the particles, we observe a 2D enhancement much less

pronounced than for Px.

Interestingly, when the excitation wavelength is 532 nm and the scattered light energy

overlaps the plasmonic resonance, we do not observe a notable enhancement with either

polarization. This apparent lack of enhanced emission is certainly of interest regarding

the mechanism of cavity induced SERS of graphene, it may be explained by the random

character of the polarization of the emitted Raman light. In this case, the enhancement

of the emitted light on the gap cavity would be restricted only to the Px polarised light

but this question is not considered in the scope of this work as it requires a much deeper

study of the Raman properties of graphene.

5.5 Strained Graphene

In graphene, a frequency downshift is expected from the graphene-metal interface dis-

cussed in section 5.2. Figure 5.3 confirms this downshift and shows that it is more

significant in the 2D peak. This is due to a higher sensitivity to strain than the G peak,

in agreement with the literature [21, 22]. In Figure 5.3(a), the 2D peak observed on top

of the structures is slightly shifted compared to the spectrum on SiO2. Its width also

increases significantly. We do not observe a downshift of the G peak within the resolu-

tion of our spectrometer but a small increase of the fwhm is noticeable. The broadening

itself is the result of the spatial variations of the strain configurations around the struc-

ture. The broadened G and 2D peaks and the downshifted 2D peak on the structures

represents the sum of all locations in the laser focus. We can observe a drastic change

in the position and width of the peaks when the plasmonic enhancement plays a role.

In Figure 5.3(c), the 2D peak arises from local hot spots where the enhanced near-field

from the particles interacts with strained graphene. The same mechanism applies to the

G peak. We can conclude from the analysis of the Raman signal intensities that the

enhanced Raman peaks arise from areas under strain, indicating that the enhancement is

localized around the particles and as we will analyse in the next section that enhancement

depends on the polarization. A complete analysis of the influence of strained graphene

on Raman scattering is given in [1].

5.6 Polarization dependence on the near field enhance-

As we have discussed, the near field enhancement determines the SERS enhancement.

In our configuration, this is directly dependent on the polarization that controls the

near-field coupling. Px triggers the strong localization field in the cavity. Figure 5.4(a)

shows a Raman line scan over the structure along X-direction with a step size of 100 nm

for a wavelength excitation of 632 nm under Px polarization. The intensity is normalized

to the integrated 2D intensity on SiO2 away from the structure and is plotted versus

the spatial distance of the laser focus relative to the antenna center. The profile is a

convolution between the laser spot, which has a fwhm of ∼570 nm and the distribution

of the localized Field enhancement. A Gaussian fit allow us to obtain an intensity

enhancement factor of 12.8 with a fwhm of 610 nm for Px. In Fig. 5.3(b), the same

Gaussian fit for Py gives a maximal enhancement factor of 3.2 and a fwhm of 840 nm,

the smaller intensity enhancement and spatial localization at this polarization agrees

with the fact that the particles approximately act as two isolated objects.

Figure 5.4: Raman line scan over the antenna structure where the sum of all 2Dpeak components is plotted versus the spatial position of the laser focus for Px (a) andPy (b) with λ = 638 nm with (step size of 100 nm). The corresponding Gaussian fits

including fwhm are shown (Reproduced from [1])

Figure 5.5(a) shows the simulated near-field enhancement | EE0|2 at a height of 40 nm for

Px at the laser Raman wavelength 638 nm. Although the gold particles height is 45 nm,

40 nm was selected as z coordinate to quantify the near-field enhancement in X-Y plane,

considering the fact that the graphene is suspended and inserted in the cavity particle for

approximately 5 nm [Fig. 5.1(b)]. As expected, the near-field coupling of the particles

localise and drastically enhance the field in the gap area. A near-field cross section in the

(x,z) plane, shown in Fig. 5.5(b), complete the field distribution on the cavity volume,

it illustrates how the field enhancement increases along the z axis obtaining a maximal

intensity value nearly at the substrate. Fig. 5.5(c) presents a spatial profile of the near-

field enhancement at z = 40 nm and y = 0, we consider the field enhancement at the

gap, where the cavity is indicated by the gray square. It should be remarked that the

high values of field enhancement at the edges do not really represent the reality as the

edges are considered ideal in the simulations whereas the real structures are imperfect.

Due to that, the best approximation of the near field enhancement is taken at the cavity.

The near-field for Py, shown in Fig. 5.5(d), extends predominantly in the y-direction for

each of the particles and no cavity enhancement is present due to the lack of coupling.

The simulation predicts two spatially separated scattering centers, which leads to a

significant broadening of the intensity profile as it is shown in Fig. 5.4(b).

In order to obtain a real estimation of the overall Raman enhancement, we need to con-

sider that the laser spot is much larger than the cavity area where the field is localised.

Therefore the observed factor enhancement of 12.8 for Px in Fig. 5.4(c) has to be nor-

malised. In Fig. 5.5(a)(d), the dashed line delimitates the area relevant considered to

estimate the enhancement. For Px, it includes 90 percent of the calculated integrated

near-field intensity within the cavity [1]. Considering the ratio between this area and

the area of the laser spot in the normalization, we obtain an overall enhancement of

Figure 5.5: Near-field enhancement | EE0|2 for Px is shown in the (x,y) plane at z

= 40 nm (a) and in the (x,z) plane at y = 0 (b). The area considered contributingto the enhancement is indicated by the dashed line in (a). The corresponding datafor Py is shown in (d,e). Cross sections of the nearfield enhancement relevant for theenhancement factor are given in (c) for Px and (f) for Px.These plots are simulated at

λ=638 nm. (reproduced from [1])

4× 103. Similarly, the integrated enhancement factor for Py is 2.2× 102. By comparing

the experimental enhancement factors for Px and Px it is possible to estimate the con-

tribution from the outer particle edges compared to the cavity enhancement. Figures

5.5(a) and (d) show that the near-field profile at the outer particle edges for Px approx-

imately matches the near-field for Py in shape and magnitude. Therefore, if we consider

that half of the near-field enhancement for Py is equivalent to the near field enhance-

ment of the outer particle edges for Px, we can evaluate the contribution of the outer

particle edges of around 12% (6% per cent each edge) of the cavity enhancement. This

approximation looks consistent with the localization observed in the intensity profile for

Px, and confirms that the observed enhancement predominantly arises from the cavity.

Other publications have reported SERS enhancement in graphene where the near field

localization area is estimated in different ways. The observed enhancement factor is

inversely proportional to the estimated area of near-field localization. Due to that,

our results of enhancement are not easily comparable with the values in the literature.

For instance, in [10] an experimental enhancement factor of 35 is observed for periodic

gold nanodisks placed on top of graphene. Wang et al. [23] measure graphene placed

on top of closely spaced gold nanopyramids, observing an enhancement factor of the

order of 104 in the experiment. They obtain and enhancement of 107 by assigning the

enhancement to a narrow area of 5×5 nm, which could be considered not completely

realistic as the particles are closely packed. In both cases, the particles are placed too

close compared with the laser spot not allowing an evaluation of the real enhancement

provided by a single structure. In this direction this work is the first SERS study on an

isolated plasmonic dimer structure with graphene.

5.7 Conclusions

In conclusion, SERS enhancement in graphene can be used to analyse the plasmonic

coupling between particles. The plasmonic enhancement, originated in the cavity be-

tween the particles, is of the order of 103. This enhancement is originated only by the

increase of the absorption induced by the plasmonic resonances. In the cavity, graphene

can be seen as a 2D-Raman integrator of the local near field The enhanced signal arises

from an area much smaller than the wavelength of the excitation and probes suspended

graphene under strain.

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Chapter 6

Enhancement of radiation from

dielectric waveguides using

resonant plasmonic core-shells

We present parametric studies of a method for enhancing radiation from a dielectric

waveguide through the use of resonant core-shells nanoparticles. These core-shells par-

ticles act as a compact impedance matching element between the guided modes of the

waveguide and the radiation modes in free space. Furthermore, we also show that we

can sense the distance between the waveguide end and the core-shell by monitoring the

reflectance of the waveguide mode. Core-shell decoupled radiation from dielectric waveg-

uides could hence be used for highly integrated optical coupling elements or nanometric

distance sensors.

6.1 Introduction

Nanoparticles based on concentric structures with cores made of ordinary dielectrics

and shells of plasmonic materials, or vice versa, have been widely studied as plasmonic

antennas with resonant frequencies tuned by the ratio of radii of the core and shell

in a wide frequency range [2–5]. Concurrently, there has been significant progress in

the area of silicon photonics and integrated optics [6–8]. Silicon photonics can provide

an alternative for interconnects in electronics and also enables on-chip integration of

optical and electronic functions. Optical waveguides can be combined with plasmonics

elements such as antennas, metallic nanoparticle chains [9] or plasmon waveguides [10–

12] in order to provide new possibilities for subwavelength integrated photonic circuits for

telecommunications and optical logic applications. One of the problems in using silicon

waveguides is achieving efficient coupling of the waveguide mode to radiation modes

in a small footprint and with good directivity. Using methods like grating coupling or

gradually reducing the waveguide cross section requires a sizeable area.

In this chapter, we investigate numerically a method of power extraction from a dielectric

waveguide using a core-shell particle with a plasmonic shell in proximity of the waveguide

end. The simulations were performed using two commercial 3D full-wave electromag-

netic wave solvers, CST Microwave studio [14] and Lumerical FDTD 2.2. Both methods

are based on a finite-integration technique (FIT) with the main difference that CST uses

a frequency-domain method and Lumerical FDTD uses a time-domain method for the

calculation. Using two different software allow us to reproduce and test some of the

results obtained under two different approaches of calculation. we have performed para-

metric studies to demonstrate that, under proper conditions, a core-shell particle placed

near the output of the waveguide results in an improvement in the impedance matching

between the dielectric waveguide and the free space, when the core-shell particle under-

goes resonance. Additionally, we observe that the reflected energy in the waveguide is

strongly dependent on the distance between the particle and the waveguide output. This

permits us to sense the distance between the particle and the waveguide by monitoring

the reflected energy.

6.2 Geometry

The schematic of the structure is shown in Fig. 6.2. We use a silicon carbide (SiC)

waveguide (instead of a silicon waveguide since our operating wavelength is set to visible

wavelengths and silicon is highly absorbing at these wavelengths). The cross section

of the SiC waveguide was set to a square cross section with a series of sizes in our

parametric study. The outer radius of the core-shell was set to 50 nm and the radius of

the silica (SiO2) core was taken to be 42 nm. The material of the shell was set to silver

(Ag). The dimensions of the core-shell are such that the core-shell particle is resonant

at a wavelength of 592 nm under a plane wave illumination (Fig. 6.1). Dimensions have

Figure 6.1: Core-shell particle resonance under plane wave illumination,λres=592nm

been taken from [13], where Li et al. optimized numerically a Yagi-Uda optical antenna

made of similar core-shell particles.

The separation, d, between the core-shell and the waveguide output face is varied to

perform a parametric study and to obtain the conditions for the best response, i.e.

lowest reflected energy in the waveguide. The separation represents the length of the

air gap between the waveguide and the core-shell. The relative permittivity of SiO2

was taken to be 2.25. The permittivity of SiC was set to the tabulated experimental

permittivity for beta-SiC [16, 17] which also took into account the dispersion in SiC.

The relative permittivity of Ag was modelled using the Drude model, eq 1.17 i.e. ε(ω) =

ε∞−ω2p

ω(ω+iΓ0)) with realistic losses obtained from experimental data in the literature [18].

The parameter values are as follows, ε∞ = 5.0, ωp=9.2159eV (fp = 2.228 1015 Hz), Γ0

= 0.0212 eV, (fΓ = 5.12 1012 Hz). With the specified dimensions the waveguide has two

orthogonal, hybrid and degenerate modes, one of which was excited in the simulations.

The excited modes electric field was polarized along the y axis, while the degenerate

modes electric field was polarized along the z axis. The waveguide supported only

these two modes at wavelengths shorter than 600 nm as long as the cross section of the

waveguide was 200 nm x 200 nm or below.

Figure 6.2: Schematic of the Si waveguide and the core-shell particle

6.3 Parameter scan of the total efficiency

In order to perform a rigorous study of the behavior of the waveguide and core-shell

system, we did a parameter scan of several parameters. The dimension of the core-shell,

permittivity of the core and plasma frequency of the shell material largely determine

the resonance wavelength. Since we are not focusing on the tunability of the resonance

wavelength, we keep these parameters constant. The cross section of the waveguide

determines the nature of the modes propagating inside the waveguide including its con-

finement and dispersion. In our parametric study, we vary the waveguide cross-section

from 150 nm x 150 nm to 200 nm x 200 nm in steps of 10 nm. The cross section is

always kept square. Figure 6.3 shows the excited mode with y-polarization for two dif-

ferent cross sections, 150 nm and 200 nm. For w=200 nm, the confinement is noticeably

higher. The separation (d) controls the amount of coupling between the waveguide and

Figure 6.3: Field intensity distribution of the mode polarised along the y axis at twodifferent waveguide cross section,150 nm(left) and 200 nm (right)

the core-shell. As the separation is increased, the performance of the waveguide should

approach that of an isolated waveguide without any core-shell near its output face.

In the parameter scan, we set the separation to a range of values between 5 nm and

500 nm. Finally, the collision frequency of the shell material (γ) determines the damping

of the core-shell resonance. In the parameter study, we vary the collision frequency as

a multiple of the collision frequency of silver, i.e. the ratio γγ0

is varied between 0.25

and 1.5 in steps of 0.25. The simulated results were processed to obtain the reflection

coefficient for the waveguide mode (S11), the total radiated power in all directions as

a fraction of the total input power, also known as total efficiency [19] in the context of

antennas, and the losses due to the absorption in the plasmonic shell. Note that the

total efficiency accounts for power radiated in all directions. Later in the section, we

will look deeper into the power radiated in the forward direction.

Figure 6.4 shows the surface plot for the maximum value of the total efficiency within

the wavelength range of 500 nm to 700 nm. The exact wavelength at which the total

efficiency reaches its maximum value depends on the parameter values as shown in

further plots. The surface plot is shown for four different values of collision frequency.

Figure 6.4: Maximum total efficiency in the 500 nm to 700 nm wavelength range as afunction of the waveguide dimension and the waveguide-coreshell separation for differentvalues of collision frequency. Γ0 represents the collision frequency of silver.(Reproduced

from [1])

From these plots we can see that there is a strong enhancement in the total efficiency

when the waveguide-coreshell separation is around 70 nm. The relative enhancement at

this optimum separation is stronger when the waveguide cross section is bigger, i.e. the

waveguide modes are more confined within the waveguide. With a smaller waveguide

cross section, the modes are less confined and spread out into the surrounding space as

Fig. 6.3 shows. Consequently, the smaller cross section waveguides have a fairly large

total efficiency even in the absence of the core-shell particles.

The enhancement in total efficiency is further increased if the collision frequency is

reduced. This is expected since a lower collision frequency implies a stronger resonance

in the core-shell particle, which results in a stronger radiation of energy by the core-

shell. Figure 6.5 shows the plots of the reflectance, total efficiency and loss for various

Figure 6.5: (a) Reflectance of the waveguide mode. (b) Fraction of the input powerthat is radiated into free space (Total efficiency). (c) Fraction of losses due to absorp-tion in Ag. All the magnitudes are presented as fractions of the total input power.The different curves correspond to different separation between the waveguide and thesurface of the core-shell, i.e. d. In all the cases, the waveguide cross section is set to200 nm x 200 nm and the collision frequency of the shell material is set to Γ0, the

collision frequency of silver(Reproduced from [1])

separations (d) when the waveguide cross section is set to 200 nm x 200 nm and the

collision frequency is set to Γ0. From these plots, it is clear that the presence of the

core-shell enhances the radiation into free space for a range of separations between

the core-shell and the waveguide. Also not surprisingly, the strongest enhancement

occurs close to the wavelength of resonance for the core-shell particle under plane wave

illumination, i.e. 592 nm (Fig. 6.1).

Although the wavelength of maximum enhancement is red shifted compared to the

resonance wavelength of the core-shell under plane wave excitation. This is due to the

influence of the waveguide in the near field of the particle. This red-shift increases

at small values of d, as the interaction between the core-shell and the waveguide get

stronger. As pointed out in Fig. 6.4, the strongest effect occurs when the separation is

set to 70 nm. At this separation, we see an enhancement in the radiated energy by a

factor of 1.17 at a wavelength of 620 nm compared to the case when there is no core-

shell at the waveguide output. More detailed studies of the effect of a change in collision

frequency for the same cross section and a 70 nm separation are shown in Fig. 6.6.

Figure 6.6: (a) Reflectance of the waveguide mode. (b) Fraction of the input powerthat is radiated into free space (Total efficiency). (c) Losses due to absorption in Ag.The different curves correspond to different values of Γ in the plasmonic shell. Γ0

represents the collision frequency of silver. In all the cases the waveguide cross sectionis set to 200 nm x 200 nm and the separation, d, is set to 70 nm.(Reproduced from [1]

As expected, the peak total efficiency rises as the collision frequency is reduced. The

minimum in the reflectance plot is fairly low for all values of collision frequency. This

implies that the increase in total efficiency is largely caused due to a reduction in the

losses.

6.4 Core-shell directivity

In order to observe the presence of the resonance in the core-shell particle, we plotted

the electric field at two different wavelengths, 620 nm and 565 nm, corresponding to the

maximum and the minimum total efficiency respectively for the case of d = 70 nm. The

field plots are shown in Fig. 6.7. We can clearly see that the local electric field around

the core-shell shows strong resonance at wavelength of 620 nm whereas the response is

Figure 6.7: Plot of the absolute value of the electric field for separation of d = 70 nmand waveguide cross section of 200 nm x 200 nm. (a) Wavelength = 620 nm, (b)

Wavelength = 565 nm.(Reproduced from [1])

more subdued around 565 nm, resulting in a stronger reflection. This in turn leads to

a more pronounced standing wave pattern inside the waveguide. On the other hand,

due to the resonance at 620 nm the core-shell acquires a strong dipole moment. The

resulting dipole strongly radiates energy into the free space.

In order to understand the manner in which the energy is radiated out into the free

space, we look at the farfield plots at these two wavelengths for a waveguide-coreshell

separation of 70 nm. The plots are shown in Fig. 6.8.

Figure 6.8: Far-field patterns of radiation from the waveguide for separation of d =70 nm and waveguide cross section of 200 nm x 200 nm. (a) Wavelength = 620 nm, (b)

Wavelength = 565 nm. The color represents the directivity.(Reproduced from [1])

At 620 nm the presence of the resonant core-shell particle results in a forward directed

lobe in the radiation pattern. Note that the dipole created by the core-shell is oriented

along the y axis, due to the polarization of the exciting waveguide mode, leading to

preferential radiation in the xz plane. The pattern is superimposed on the radiation

pattern of the waveguide giving rise to the resulting far field plot. The radiation in the x

direction is suppressed by the presence of the waveguide, but there is some enhancement

in the directivity in the backward direction at certain angles to the x axis where the

radiation is not hindered by the waveguide. On the other hand, at 565 nm the core-shell

acts more like an opaque object that suppresses the main radiation lobe of the waveguide

and splits it into two small lobes in the xy plane, making an angle of roughly 40 with

the x axis.

In Fig. 6.5 and Fig. 6.6, we looked at the total radiated power without any regard to

the direction of radiation. Ideally, we would like to maximize radiation in the forward

direction. In order to get a quantitative idea of how much energy is radiated in the

forward direction, we calculated the ratio of the power radiated in the forward half

space (Pr,front) to the total radiated power (Pr,total) as shown in the Fig. 6.9.

Figure 6.9: Ratio of the forward radiated power to the total radiated power for variousseparations between the waveguide and the core-shell (a),and various collision frequencyin the plasmonic shell material (b). In both cases the waveguide cross section is set to200 nm x 200 nm. In (a) the collision frequency of the shell material is set to Γ0. and

in (b) the separation, d, is set to 70 nm.(Reproduced from [1]

At longer wavelengths, we observe that the presence of the core-shell particle does not

cause a significant change in the fraction of energy that is radiated in the forward direc-

tion. Even though the core-shell increases the total radiated power around a wavelength

of 620 nm, the enhancement is essentially caused through dipolar radiation, which is

isotropic in the plane perpendicular to the dipole moment, i.e. the xz plane. Hence,

around the resonance wavelength, the forward radiated power is suppressed compared

to the total radiated power.

On increasing the separation, the ratio approaches the results without the core-shell,

i.e. the ratio at shorter wavelengths increases while the ratio at the longer wavelengths

tends to stay the same. Changing the collision frequency while keeping the waveguide

dimension and the separation fixed, has a small influence in the ratio, because this

change only implies an isotropic change in the radiated power.

6.5 Distance sensing

From Fig. 6.5 we can see that the reflectance is particularly sensitive to the separation

between the waveguide and the core-shell. This dependence can be exploited to indi-

rectly measure the distance between the waveguide and the core-shell by monitoring the

reflectance of the incident mode in the waveguide. To explore this possibility we simu-

lated the reflectance for a series of separation between the waveguide and the core-shell

for a range of wavelengths. The waveguide cross section was set to 200 nm 200 nm and

the collision frequency was set to Γ0 for this study. The result is presented in Fig. 6.10

in the form of a contour plot. The reflectance shows a peak at a wavelength of around

575 nm and a separation of around 100 nm. This condition corresponds to the state of

maximum impedance mismatch with this waveguide and core-shell.

Figure 6.10: (a) Reflectance and (b) Total Efficiency shown as contour plots as func-tion of wavelength and separation (d)

On the right half of the contour plot, we can see the parameter space where the re-

flectance is lower and the transmittance is high. Around the wavelength of 615 nm the

region of low reflectance is sensitive to the distance d, but if we consider longer or shorter

wavelengths the reflectance is not too sensitive to the distance.

Figure 6.11: Reflectance as a function of separation of core-shell particle from thewaveguide

In order to sense the distance by monitoring the reflectance, we need the reflectance to

be highly sensitive to the distance d and hence, we should preferably be working around

wavelengths where the contour lines are somewhat horizontal and closely packed. Such

wavelengths are located around the wavelength with minimum reflectance (615 nm).

As an example, we show the reflectance as a function of separation for wavelengths of

615 nm and 630 nm in Fig. 6.11. The plot is essentially a cross section of the contour

plot shown in Fig. 6.1(a). We can see that the reflectance shows a change of almost

35% over a range of 70 nm for a wavelength of 615 nm. The change is lower as we move

away from 615 nm, as seen for a wavelength of 630 nm in Fig. 6.11(b). This provides

an ample margin to ensure detectability via simple reflectance monitoring. An obvious

problem with this approach is that the reflectance is multi valued and can provide the

same reflectance for more than one value of d. Nevertheless, we could use the slope of

the reflectance versus d plot to resolve this ambiguity.

6.6 Conclusions

Using numerical simulations, we have conducted parametric studies and have shown that

through the use of resonant core-shell particles with a plasmonic shell, we are able to

provide a means of improving the impedance matching between a dielectric waveguide

and free space. Moreover the radiation characteristics of the waveguide and core-shell

system are sensitive to the separation between the two. This may also allow us to control

the placement of the core-shell particle by monitoring the reflectance in the waveguide.

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Chapter 7

Conclusions

we have numerically reviewed the influence of important factors that generally control

the optical antennas properties such as the resonance energy, the near field enhancement

or the scattering performances of optical antennas. The metal, the dimensions of the

particles composing the dimmers, as well as the refraction index of substrates allow us

to tune the resonance frequency of the antenna. In addition, we have emphasized that

the shift between the near field and far field peaks is highly influenced by some of the

factors that can induce damping, such us the increase of the arm length, the substrate

or the adhesion layer. In particular, we have discussed that the addition of a reflecting

underlayer provides additional ways of tuning optical antennas by changing the dielectric

layer thickness as well as increasing the near-field enhancement.

The influence of the reflective layer is demonstrated in the enhancement of photolumines-

cence in organic dyes. An increase of the photoluminescence up to four times is observed

in a low efficient organic dye as TPP, compared to antennas without the reflecting-layer.

In addition, this improvement enhances the intensity of the two resonances associated

with the perpendicular light polarizations existing in a gold dimer, allowing to measure

their influence in a specific wavelength of the dye emission. Such a doubly resonant sys-

tem presents a way to selectively influence the polarization of emitted light in organic

dyes with multiple emission peaks. We have seen, that the polarization dependence of

dimmers allow us to trigger not only the induced Photoluminescence enhancement in

dyes, but also the Raman scattering enhancement in graphene.

In order to perform SERS studies in suspended graphene, we have selected disks dimmers

in order to quantify the coupling between the two particles by rotating the excitation

polarization. The analysis of the Raman signal intensities indicates that the enhanced

Raman peaks arise from areas under strain. The Raman enhancement depends on

the polarization that controls the near-field coupling between the two disks. Near-field

Outlook. Conclusions 113

enhancement simulations for Px and Py demonstrated that Px triggers the strong local-

ization field in the cavity. we obtain an overall Raman signal enhancement of 4× 103.

In addition, we have conducted parametric studies to show that through the use of

resonant core-shell particles with a plasmonic shell we are able to provide a means of

improving the impedance matching between a dielectric waveguide and free space. Sim-

ulations of the reflectance for a series of separation of distances show the reflectance

particularly sensitive to the separation between the waveguide and the core-shell. Re-

flectance shows a change of almost 35% over a range of 70 nm for a wavelength of

615 nm which provides an ample margin to ensure detectability via simple reflectance

monitoring.

7.1 Future work

In this thesis, we have highlighted many important parameters that determine the per-

formance of optical antennas. Using grating antennas or low refraction substrates with

a reflecting-underlayer are easy ways of implementing the efficiency in any future device

involving optical antennas. As we have seen, the described polarization dependence of

dimmers allow us to trigger the Raman scattering and the induced Photoluminescence

enhancement in dyes. This property can be used to design new doubly resonant systems

activated by the polarization of the incident light. For example, using cross resonant

antennas composing of two gold opposing dimmer antennas with different arm length

or made of different metals would provide two different energy resonances that can be

selectively excited by controlling light polarization. Ideally, the emission of a single

emitter with two emission peaks placed at the dimmers gap could be controlled by the

incident polarization light.

In that direction, the experimental challenge resides in how to achieve the best coupling

between a quantum emitter and an optical antenna system. So far it has been achieved

mainly by positioning of nanoantennas on scanning tips on top of emitters, by AFM

nanopositioning, and by self-assembly of antenna and emitter. Future advances in these

techniques would allow us to set an ideal interface between a molecule and the nanoan-

tenna gap. In particular, we are in the progress of studying the optical properties of a

single carbon nanotube under the influence of a dimmer antenna by performing polar-

ized SERS experiments. Once the nanotube-antenna interface is set, combined electrical

and optical measurements could lead to a further physical study on carbon nanotubes.

In such case, single photon light based on a carbon nanotube emitting devices could be

explored and demonstrated.

Outlook. Conclusions 114

To conclude, it is still necessary to efficiently convert electrical signals into plasmons and

viceversa with the goal of interfacing electronics and nanoantennas. In that direction,

one of the biggest challenges to be addressed in the following years resides in the design

and fabrication of efficient electrically pumped antennas in the optical regime.

simulation and characterization of optical nanoantennas ... · acknowledgements i would like to...

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