And

The Exciting Science of Light with Metamaterials

Vladimir M. Shalaev

Birck Nanotechnology Center

Outline

• Intro to metamaterials

• Nanophotonics enabled by Plasmonics and Metamaterials

• Toward Better Materials for MM and TO applications

• Negative-index metamaterials

• Transformation optics and cloaking

• Engineering PDOS & Sub-wavelength light confinement with Hyperbolic MMs

• Flat photonics with Metasurfaces: Generalized Snell’s Law, negative refraction, meta-lens, meta-hologram….

3

Natural Optical Materials

S

S

k

E

H

k

E

H

Negative Index

Materials

Common

Transparent

Dielectrics

Electrical Plasma(Metals at optical

wavelengths)

Magnetic Plasma(Not naturally occurring at

optical wavelengths)

Evanescent waves

Evanescent waves

k

k

1

1

Semiconductors

Crystals

Water

metals

Air E,H ~exp[in(ω/c)z] n = ±√(εμ)

4

What is a metamaterial?

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Metamaterial is an arrangement of artificial structural elements, designed to achieve

advantageous and unusual electromagnetic properties.

ta = meta = beyond (Greek)

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A natural material with its atoms A metamaterial with artificially structured

“atoms”

5

Photonic crystals vs. Optical metamaterials: connections and differences

0 1 aa<<.

Effective medium

description using

Maxwell equations with

, , n, Z

a~

Structure dominates.

Properties determined

by diffraction and

interference

a>>

Properties described

using geometrical optics

and ray tracing

Example:

Optical crystals

Metamaterials

Example:

Photonics crystals

Phased array radar

X-ray diffraction optics

Example:

Lens system

Shadows

6

Photonic crystals

... have lattice constants comparable to light

wavelengths: a ~

… can be artificial or natural

… have properties governed by the diffraction of

the periodic structures

… may exhibit a bandgap for photons

… typically are not well described using effective

parameters , , n, Z

… often behave like but they are not true

metamaterials

Electrical Metamaterials (Plasmonics): Route to Nanophotonics

Why Plasmonics/Electric MMs?

M. Brongersma, V. Shalaev, Science (2010)

Plasmonics will enable an improved synergy between electronic and photonic devices ̶ Plasmonics naturally interfaces with similar size electronic components ̶ Plasmonics naturally interfaces with similar operating speed photonic networks

Critical dimension active devices (nm)

Op

erat

ing

spee

d THz

GHz

MHz

kHz

10nm 100nm 1m 10m 1mm 100m

Semiconductor Electronics

Metallic Nanoplasmonics

Dielectric Photonics

The past

PHz

Silicon Integrated Nanophotonics

IBM Silicon Integrated NP Technology

IBM chip: BLUE optical waveguides and YELLOW copper wires

IBM 90nm Silicon Integrated Nanophotonics: Integrated photodetector (red feature) Modulator (blue feature) Silicon transistors (red sparks)

“After More Than a Decade of Research, Silicon Nanophotonics is Ready for Development of Commercial Applications.”

IBM Press release, December 10, 2012

ELECTRONIC-PHOTONIC INTEGRATION:

SUMMARY

Photonic circuit + High speed + High bandwidth - Component size is limited (>~ 100nm - 1 µm)

Modern communication systems Huge amount of data Ever increasing speed

Electronic circuit + Very compact (~ 10nm) - Operational speed is limited (RC-delay)

Electronic + Photonic circuit: NEED FOR NEW TECHNOLOGIES

Si NANOPHONICS (near-term)+ PLASMONICS/METAMATERIALS (~5 years)

Optical mode in waveguide > 0/2nCORE

Diffraction limit

www.mayang.com/textures/

[ Bow-tie antennas ]

Other Applications: Sensors

from LC-contour to nanophotonic circuits (Engheta – ‘metatronics’)

OE (2009); NJP (2008); Metamaterials (2008); APL (2008)

OPTICAL NANOANTENNAE

Optical Nanolaser Enabled by SPASER

Related prior theory: Stockman (SPASER)

Zhang group: Plasmon Laser (Nature,2009) Room-T Plasmon Laser (Nat. Mat, 2010) “Spasing Laser” – Zheludev, Stockman M. T. Hill, et al; C. Z. Ning, et al (electr. pump) Spotlight on Plasmon Lasers (Perspective, Science, 2011)- X. Zhang, et al

Optical MOSFET (Stockman)

Noginov, Shalaev, Wiesner groups, Nature (2009)

Toward Better Materials for Plasmonic and MM Applications

(Boltasseva group, Purdue)

METALS TO LESS-METALS:

Doped semiconductors + Intermetallics (nitrides, borides, silicides, …)

New Plasmonic Materials

A. Boltasseva and H.A. Atwater, Science 331 (2011)

Alternative Plasmonic Materials

P. West, et al, Lasers & Photon. Rev. (2010) (Boltasseva group)

(see also work by the Noginov group)

Transparent Conductive Oxides

ε΄ becomes negative below 2μm

Metallic: Golden luster

Titanium Nitride

G.V. Naik et al., Optical Materials Express 2 p. 478 (2012)

http://www.mini-lathe.com/Feat_Mach/Turbocam

OSA press release March 27, 2012

‘Researchers Discover a New Path for Light Through Metal: Novel Plasmonic Material May Merge Photonic and Electronic Technologies’

Hard & tough: high speed drill-bits

Well-established processing

New Plasmonic Materials for HMMs

Performance of HMM devices: (A. Hoffman, Nature Materials 6(2007) 946–950)

FOM=Re{k}/Im{k}

Phys. Status Solidi RRL 4, 295 (2010) G..V. Naik and A. Boltasseva, Metamaterials 5(2011) 1-7

Negative Refraction in all-Semiconductor based HMM

G. Naik, et al, PNAS (2012)

Negative refraction in semiconductor-based metamaterials

• Semiconductors exhibit metallic

properties when heavily doped

• Aluminum doped zinc oxide (AZO)

exhibits metallic property in the

near-infrared

• Conventional metals replaced by

semiconductor-based ones such as

AZO can produce high

performance metamaterials

• The figure-of-merit of AZO/ZnO

metamaterial is 11: three orders

higher than metal-based designs

G. Naik, et al. PNAS (2012) (Boltasseva /Shalaev groups)

21

Sir Arthur Schuster Sir Horace Lamb

L. I. Mandel’stam

V. G. Veselago

Sir John Pendry

… energy can be carried forward at the group velocity

but in a direction that is anti-parallel to the phase

velocity…

Schuster, 1904

Negative refraction and backward propagation of

waves

Mandel’stam, 1945

Left-handed materials: the electrodynamics of substances

with simultaneously negative values of and

Veselago, 1968

Pendry, the one who whipped up the recent boom

of NIM researches

Perfect lens (2000)

EM cloaking (2006) Others: Sivukhin. Agranovich,…

22

if ,0n

• Refraction:

• Figure of merit: θ1

θ2

θ1 θ2

"/|'| nnF

εμn

εμn

2

0 ||' ||'

23

E

H

k

Dielectric

Metal

Nanostrip pair (TM)

< 0 (resonant)

Nanostrip pair (TE)

< 0 (non-resonant)

Fishnet

and < 0

S. Zhang, et al., PRL (2005)

24

O. Hess, Nature 455, 299 (2008)

Negative Refraction Effects

http://io9.com/5036183/secrets-of-the-metamaterials-that-will-make-you-invisible

Negative Refraction Effects

V. M. Shalaev, Transforming Light, Science, Oct. 17, 2008

27

Spatial profile of & tensors determines the distortion of coordinates

Seeking for profile of & to make light avoid particular region in space — optical cloaking

Fermat:

δ∫ndl = 0

n = √ε(r)μ(r)

“curving”

optical space

Distorted field line in distorted coordinate

Straight field line in Cartesian coordinate

Pendry et al., Science, 2006

Leonhard, Science, 2006

Greenleaf et al (2003)

L. S. Dolin, Izv. VUZ, 19614

28

Form-invariance of Maxwell’s equations

Coordinate transformation from x to coordinate x is described using the

Jacobian matrix G: ij i jg x x

( )

( ) 0

E

H

HEt

EH Jt

Maxwell’s equation in x

1 1

;

( ) ; ( )

;

T T

T T

G G G G

G G

E G E H G H

GJJ

G G

Transformation of variables

Ward and Pendry, J. Mod.Opt. 43, 777 (1996)

Pendry et al., 2006

The bending of light due to the gradient in refractive index in a desert mirage

31

Kildishev, VMS (OL, 2008); Shalaev, Science 322, 384 (2008)

Optical Black Hole (Zhang group; Narimanov,Kildishev)

(b)

Fermat: δ∫ndl = 0 n = √ε(r)μ(r)

curving optical space

Planar hyperlens (Kildishev and VMS) (Schurig et al; Zhang group)

Light concentrator (also, Schurig et al)

Narimanov, Kildishev

32

Invisibility in Nature, Physics and Technology

• Natural camouflage

• Black hole

• …

Current technologies to achieve invisibility:

Stealth technique: Radar cross-section reductions by absorbing paint / non-metallic frame / shape effect…

F-117 “Nighthawk” Stealth Fighter

Optical camouflage: Projecting background image onto masked object.

Optical Camouflage, Tachi Lab, U. of Tokyo, Japan

The Invisible Man by H. G. Wells (1897)

“The invisible woman” in The Fantastic 4 by Lee & Kirby (1961)

Examples with scientific elements:

"... it was an idea ... to lower the refractive

index of a substance, solid or liquid, to

that of air — so far as all practical

purposes are concerned.” -- Chapter 19

"Certain First Principles"

"... she achieves these feats by bending all

wavelengths of light in the vicinity around

herself ... without causing any visible

distortion.” -- Introduction from Wikipedia

Pendry et al.; Leonhard, Science, 2006 (Earlier work: cloak of thermal conductivity by Greenleaf et al., 2003)

34

Nature Photonics (to be published)

Optical Cloaking with Metamaterials: Can Objects be Invisible in the Visible?

Cover article of Nature Photonics (April, 2007)

metal needles embedded in dielectric host

Unit cell:

Flexible control of r ;

Negligible perturbation in

Cai, et al., Nature Photonics, 1, 224 (2007)

Cloaking performance: Field mapping movies

Example: cloak @ 632.8nm with silver wires in silica

Cloak ON Cloak OFF

J. Li and J. B. Pendry , Phys. Rev. Lett., 2008

picture from discovery.com

Progress Towards True Invisibility on May.17, 2009, under Science www.codingfuture.com

Theory: J. Li, J. Pendry

GHz: Smith et al (Duke)

Optical: Zhang et al (Berkeley)

Lipson et al (Cornel)

39

Signal

Signal

Signal

Signal

Control C

Wave guide

Wave guide

Wave guide

Wave guide

(a)

(b)

(c)

(d)

Control C

Control C

Control C

Control A

Control A

Control A

Control A

Turn on Control A

Turn of fControl C

A B C

A B C

A B C

A B C

M. W. McCall and et al., Journal of Optics, 2011 Gaeta eta al, experiment

Star Trek transporter

Modern cosmology describes Universe as collection of spaces connected by black holes and wormholes. These spaces may have different topology and different number of dimensions.

Using transformation optics we can create “optical spaces” having non-trivial topology, which cannot normally fit into Euclidean 3D space:

Even metric signature of the “optical space” may differ from the (+ - - - ) signature of the Minkowski space. In hyperbolic materials (Smolyaninov, Narimanov – PRL, 2010):

2

2

2

2

2

2

1

2

22

2 1

yxztc

01 02

02

4

2

2

3

2

2

2

2

2

1

2

xxxx Flashes of light are observed during metric signature transitions : toy Big Bang physics

2T K-G

41

Hyperbolic Metamaterials: Engineering Photonic Density of States

& Subwavelength Light Confinement

S. Ishii, et al, Laser Photonics Rev., 1–7 (2013)

DOI 10.1002/lpor.201200095

Cover article

Hyperbolic Metamaterials (HMMs)

A metamaterial has hyperbolic dispersion relation

22 2 2x y z

k k k

c

hyperbolic dispersion

Jacob, et al., Opt. Express, 2006

22 2 2x y z

k k k

c

x

y

z

22 2 2

x y zk k k

c

normal dispersion

Transverse Negative (TN) Transverse Positive (TP)

x

y z

PHOTONIC DENSITY OF STATES (PDOS)

Iso-frequency surface at ω

Iso-frequency surface at ω+δω

QED IN THE ’HYPERSPACE’

• Rate of SE, can be understood as property of atom-environment system

• Environment (cavity, PhC, nanowire) enhances density of states

(Dipole matrix element)2

Environment strongly alters the rate of SE through the available PDOS!

Fermi’s Golden Rule:

Available density of states for emitted light

Coupling of emitter to field (depends on the mode volume)

: Ford and Weber (1984)

QED: Hughes group (2009)

Calculation Methods:

EMISSION POWER SPECTRUM

Diffraction from double slits

– FWHM = 45 nm at = 465 nm

Diffraction inside Hyperbolic Media

• Hyperbolic metamaterial (HMM) – Ag/SiO2 lamellar HMM

– High-k waves are supported

– Propagation of high-k waves is confined

eff

x

eff

z

2.78 0.22

6.31 0.15

i

i

S

=465 nm

=465 nm

(15 nm Ag/15 nm SiO2)3

S. Thongrattanasiri and V. A. Podolskiy, Opt. Lett. (2009) Satoshi Ishii et al, in preparation

Subwavelength Interference (Experiment)

Ag/SiO2 HMM sample SiO2 sample

• For Ag/SiO2 HMM sample: FWHM = 83 nm (< ) • For SiO2 sample: FWHM = 542 nm (~ )

1. Sample fabrication

Deposition and FIB

2. Photolithography

Photoresist exposure, develop

3. AFM scan

=465 nm

Flat Photonics with Metasurfaces: Generalized Snell’s Law,

Negative Refraction, and much more....

Birck Nanotechnology Center

Principle of Least Action

Maupertuis felt that “Nature is thrifty in all its actions”, and applied the principle broadly

Pierre Louis Maupertuis (1698-1759)

Leonhard Euler (1707-1783)

Louis de Broglie (1892-1987)

Principle of least action → The momenta difference between blue and red path is zero

Generalized Snell’s Law (Capasso Group)

For refraction

For reflection

see also S. Larouche and D.R. Smith, OL v. 37, 2391 (2012)

A

B

ni

Ф Ф+dФdr

θt

θr

nt

In essence, momentum conservation!

Generalized Snell’s Law

N. Yu, et al. Science, 2011 (Capasso Group)

Demonstrated at 8 µm wavelength

Broadband light bending with plasmonic nanoantennas

ΛΛ/8

xyz

200

1920

240

1760

220

1600

200

1440

180

unit: nm

X. Ni, et al. Science-Express, Dec. 22, 2011 (Shalaev & Boltasseva groups) Science v. 335, 427 (2012)

Incident Angle Sweep – Refraction

λ = 1500 nm

λ = 1500 nm

Incident Angle Sweep – Reflection

θi = 30⁰

Broadband!

Broadband Negative Refraction

Ultra-thin planar meta-lenses: design

• Au film (30 nm) by electron beam evaporation

• Babinet antennas fabrication by focused ion beam (FIB)

r

X. Ni etal (2012)

Ultra-thin planar meta-lenses: experiment

sample

x-polarizer

y-polarizer

Ar/Kr laser (676 nm / 530 nm / 476 nm)

Z = 0 μm

Z = 7 μm

Z = 10 μm

Focal length: 2.5 μm Focal length: 4 μm Focal length: 7 μm

wavelength 676 nm

Take home messages

• Nanophotonics enabled by Plasmonics and Metamaterials

• Toward Better Materials for MM and TO applications

• Negative-index metamaterials

• Transformation optics and cloaking

• Engineering PDOS & Sub-wavelength light confinement with Hyperbolic MMs

• Flat photonics with Metasurfaces: Generalized Snell’s Law, negative refraction, meta-lens, meta-hologram….