near-field radiative transferhelper.ipam.ucla.edu/publications/msews4/msews4_11524.pdf · 2013. 11....

NEAR-FIELD RADIATIVE TRANSFER

For Energy Harvesting.... & Diagnostic+Manufacturing

MSEWS4: Energy Conservation and Waste Heat Recovery November 21, 2013

IPAM, UCLA, LA, CA, USA

M. Pınar Mengüç

Director, CEEE / EÇEM Center for Energy, Environment and Economy

& Head, Mechanical Engineering Ozyegin University

Istanbul, Turkey

Engineering Alumni Association Professor, Emeritus

Mechanical Engineering Department University of Kentucky

Lexington, KY, USA

Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey

OUTLINE OF PRESENTATION

The Big Picture

Overview of Far and Near-Field Radiative Transfer

Length Scales for Nano-regimes

Near Field Radiation

Near Field Radiation for Thermophotovoltaics (TPV) Applications

Analytical Analysis

Computational Analysis

Conclusions

CEEE/EÇEM


We are here…

Nano-Scale

Energy

Fundamentals Radiative

Transfer and

Thermal

Sciences

Energy

Applications

and

Efficiency in

Buildings

Multi-Disciplinary

Industrial

Applications

EEE Solutions

for Districts

and Cities

Quantitative

Sustainability for

Businesses Nature &

Climate

Change

CEEE/EÇEM FOCI

CLIMATE CHANGE? (IEA 2013)

CLIMATE CHANGE? (IEA 2013)

2 Degrees by 2050?

EVERY TON OF CO2 RELEASED TO THE ATMOSPHERE ...CORRESPONDS TO WASTED ENERGY ENDING UP SOMEWHERE! MINIMIZATION OF ENERGY USE HELPS DECREASING EMISSIONS OF CO2.

ENERGY LOSS

ONE-YEAR CO2 EMISSION TRENDS CHANGE (IEA 2013)

ENERGY RELATED CO2 EMISSIONS (IEA 2013)

BIG PICTURE: WORLD ENERGY USE IS ABOUT 15 TW. CO2 EMISSIONS ARE RELATED TO FOSSIL ENERGY USE. ONLY A FRACTION OF ENERGY GENERATED IS FROM RENEWABLES.

ENERGY MODALITIES

WORLD RENEWABLE ENERGY USE (IEA 2013)

Quantitative

Sustainability for

Businesses Nature &

Climate

Change

America’s Energy Future, 2012, National Acedemy of Sciences, USA

Energy Production Modalities

ENERGY MODALITIES

Quantitative

Sustainability for

Businesses Nature &

Climate

Change

America’s Energy Future, 2012, National Acedemy of Sciences, USA

REJECTED ENERGY

ENERGY MODALITIES

Wasted Energy should be used somehow!

ENERGY MODALITIES

• Energy Generation

• Energy Conservation/Efficiency

• Energy Harvesting

Energy Harvesting is to recover wasted energy from all sources to be used as auxiliarry energy source, for electricty generation or for storage. Carnot Efficiency:

ENERGY HARVESTING

HOT

COOL

Carnot Engine

Q-H

Q-L

Work

What to do with Q-L?

Aux Work

Q-L

h=W/Q

CONVERGENCE

Solve Energy Challenge via Advanced Engineering on Fundamental Physics

INSPIRATION: REACHING NANO-WORLD ... From 2005 ROCO!

2013 1999

Size of WATER VAPOR

1 m

1 mm

1 mm

1 nm

Humans

Car

Butterfly

1 km

STEAM ENGINE

Laptop

Wavelength of Visible Light

Micromachines

Width of DNA

Smallest feature in microelectronic chips

Proteins

Biological cell

Nucleus of a cell

Aircraft Carrier

Size of a Microprocessor

Nanostructures & Quantum Devices Decreasing

Length scale

Resolving power of the eye ~ 0.2 mm

Human hair ~ 60-120 mm wide

PERSPECTIVE ON LENGTH SCALES

Thermoelectric Devices (conduction/phonon based)

HOW TO RECOVER WASTE ENERGY?

Thermophotovoltaic Devices (Radiation/near-field radiation transfer based)

Nondimensional figure of merit:

ZT = σS2T/κ σ : the electrical conductivity S : the Seebeck coefficient T : the temperature κ : the thermal conductivity

Optical heat engine! (Figs from web sources!)

POWER GENERATION EFFICIENCY

Zebarjadi, et al. Energy Environ. Sci., 2012, 5, 5147-5162.

h=W/Q

THERMOELECTRIC DEVICES

Thermoelectric power generators are solid state devices which can directly convert heat into electricity. The device efficiency depends on the choice of material, configuration, and contacts. It requires new materials, dopants, and nanostructured geometries. MATERIAL PROBLEM!

Chen, et al., Progress in Natural Science: Materials International 2012;22(6):535–549

TPV CELL

Schematic of the thermophotovoltaic cell proposed by Fan group. The idealized absorption spectrum (solar spectrum in yellow) and emission spectrum (the dotted line: PV cell bandgap energy level) are shown. http://gcep.stanford.edu/research/factsheets/ultrahigh_thermosolar.html

Schematic of the industrial thermophotovoltaic cell.

http://gcep.stanford.edu/research/factsheets/ultrahigh_thermosolar.html

http://gcep.stanford.edu/research/factsheets/ultrahigh_thermosolar.html


THERMOPHOTOVOLTAIC DEVICES

Potential Applications of TPVs:

• Power sources for Micro-electromechanical devices (MEMS).

• Energy sources in transportation.

• Co-generation of electricity and heat.

• Remote electricity generators.

• Aerospace and military power suppliers.

• And..

Waste-Energy harvesting purposes.



•How can we improve the efficiency of TPV Devices? • Materials? • Design and Geometry?

TPV? Nano-TPV?

radiator

vacuum

T0 = 2000 K

Tcell(z)

thermal management system

tcell

dc

OBJECTIVE: RADIATE SELECTIVELY TO THE CELL ...

Nano Gaps!



Thermophotovoltaics (TPVs): energy-conversion systems generating an

electric current from the thermal photons radiated by a hot body.

TPVs

Far field TPVs

(Conventional TPVs) Near field TPVs

(Nano TPVs)

It is bounded by

Schockley-Queisser

limit.

Theory has shown

enhancement of power

transfer up to three orders of

magnitude.

DOI: 10.1038/srep01383


Near-field PV Ability to control plasmon damping √ High power density√ Ability to operate in the intermediate (600−1200K) emitter temperature range √ Emitter plasmon frequencies optimally matches to the bandgap √

Far-field PV Ability to control plasmon damping X High power density X ability to operate in the intermediate (600−1200K) emitter temperature range X Emitter plasmon frequencies optimally matchesto the bandgap X

Ilic, Ognjen et al. “Overcoming the Black Body Limit in Plasmonic and Graphene Near-field Thermophotovoltaic Systems.” Optics Express 20.S3 (2012): A366. © 2012 OSA

FAR AND NEAR FIELD RADIATIVE TRANSFER

Near- Field Publications Statistics

Nano Thermophotovoltaic Published items in each year

Nano Thermophotovoltaic Citation in each year

Near-field thermal radiation Published items in each year

Near-field thermal radiation

Citation in each year

Near Field Radiation Transfer @ Ozyegin Univ, Istanbul

Nano-Scale RADIATIVE TRANSFER

MEASUREMENTS

M.Pınar Mengüç/OzU Hakan Ertürk/BU

David Kurt Webb/OzU

Nano-Scale DEVICE

FABRICATION

M.Pınar Mengüç/OZU Tuba OKUTUCU/METU

Zafer ARTVİN /METU

NEAR-FIELD RADIATIVE TRANSFER

DEVICES and APPLICATIONS

M.Pınar MENGÜÇ /OzU

FLUCTUATIONAL ELECTRODYNAMICS

Mathieu Francoeur/UTAH M.Pınar Mengüç/OzU

Azedeh Didari/OzU

NEAR FIELD RADIATON

TRANSFER CALCULATIONS

COMSOL Multiphysics

Tuba Okutucu/METU

Hakan Ertürk/BU

Gazi Huda/UK Farhad Kazemi Khosroshahi/BU

M.Pınar Mengüç/OzU

Azadeh Didari/OzU Vincent Loke

Kürşat Şendur/SU Ali Koşar/SU M.Pınar Mengüç/OzU

S. Eren Yalcın/OzU

Erdem Ogut/SU

PLASMONIC EFFECTS

FOR NANO-SCALE COOLING

Todd Hastings/UK

PLANCK’S BLACKBODY RADIATION: BROADBAND

0

0,2

0,4

0,6

0,8

1

0 2 4 6 8 10 12 14 16 18 20 22

En

erg

y/P

ea

k E

ne

rgy

Wavelength (mm)

5780 K

1600 K

300 K

(Francoeur, Mengüç)

T

“Throughout the

following discussion

it will be assumed

that the linear

dimensions of all

parts of space

considered, […], are

large compared with

the wavelengths of

the rays

considered.”

RADIATIVE TRANSFER

Infrared Energy to be harvested

PV range

+From Andy Keller


Maxwells’s Equations fully describe the propagation of electromagnetic waves in all types of media. Since the late 1800’s, emission of radiation and radiation transfer were sufficiently explained bt Kirchhoff’s and Planck’s Laws at the far-field. Far-field radiation transfer is all about the microscopic space-time fluctuation of charge carriers. Temperature of the emitting body determines the spectral nature of thermal radiation.

RADIATION TRANSFER: via electromagnetic waves

1T

2T

propagating waves

photons!

2T

RADIATIVE TRANSFER

RADIATIVE TRANSFER

Energy transfer by electromagnetic waves! Follows Planck’s Blackbody Law Long range ... No medium is required Scalable.... if the distance between objects more than wavelength of radiation

RADIATIVE TRANSFER

• What happens if the objects are closer than the wavelength?

• What if the objects have structures on them?

• What if there are new materials to be used?

• Can we model and measure them?

• Can we come out with a device?

NANO-GAP THERMOHOTOVOLTAIC (n-TPV) CELL

RADIATIVE TRANSFER

0

0,2

0,4

0,6

0,8

1

0 2 4 6 8 10

No

rmal

ized

En

erg

y

λ (μm)

5780 K

1600 K

About 400 K

About 3000 K Si Band Gap: 1.12 eV or 1.1 μm InSb Band Gap: 0.17 eV or 7.29 μm

InSb Indium Antimonide

PHOTONS RESULT i. at energy band voltage created ii. above energy band voltage + heat iii. below energy band heat


EVANESCENT WAVES: FRUSTRATED TIR

Evanescent waves on the surfaces (e.g., due to total internal reflection). Thermal near-fields and near-field spectral energy density are associated with the intrinsic electronic and vibrational excitations or extrinsic geometric resonances.

5.11 n

12 n

glass

air

cr 1

r

z

1 r

total internal reflection (TIR)

1n

air r

dipole oscillations

- + - - + -

+

+ [Jackson, 1999; Hecht, 2002]

z

+


NEAR-FIELD REGIME OF THERMAL RADIATION


What happens if a structure interacts with an evanescent wave?

Two regimes of radiative transfer:

• Far-field regime: energy transfer via only propagating electromagnetic waves

• Near-field regime: energy transfer via both evanescent and propagating EM waves

1 1

2

How to calculate and measure radiative energy transfer between two objects in close proximity to each other?

NEAR-FIELD RADIATION

1T2T

Wiend

+-

1T



Near field TPVs (Nano TPVs)

Near field TPVs (Nano TPVs) : By approaching a photovoltaic (PV) cell in

proximity of a thermal emitter, thermal energy can be extracted by photon tunneling

toward the cell…these devices are called Near-filed thermophotovoltaics (NTPVS).

Modeling NTPVS :

Analytical Techniques

Computational Techniques

Experimental Techniques

Lorenz-

Mie

Theory Finite Element

Method

Finite Difference Time

Domain Method (FDTD)

Discontinues Garlekin

Time Domain

Method(DGTD)

Discrete Dipole

Approximation

(DDA)

NEAR-FIELD RADIATION ANALYTICAL ANALYSIS


NEAR-FIELD RADIATION TRANSFER

Maxwell’s equations are valid to describe the propagation of electromagnetic waves at all scales (until the definitions of dielectric constant and magnetic permeability fails...down to a few nanometers). However, thermal emission is not accounted for in the formulation of MEs. Temperature of the medium can be entered to the MEs as a source term using the fluctuation-dissipation theorem (FDT). FDT incorporates the statistical properties of the current-density distribution.

Maxwell equations combined with fluctuational electrodynamics [Rytov, 1959; Francoeur and Mengüç, JQSRT, 2008; Francoeur et al., JQSRT, 2009]

)H(r,)B(r,)E(r, 0 m ii

),( rE)H(r, i

eρ ))E(r,)D(r, ˆ(

0))H(r,()B(r, 0 m

),( rJr

source of thermal radiation (stochastic current density)

Temperature of the medium correlated with Jr via the fluctuation-dissipation theorem

)(),()(

),(),( *rrrr

TJJ rvrr

isotropic media

locality of the dielectric constant mean energy of a Planck oscillator in thermal equilibrium



0))H(r,()B(r, 0 m


Radiative heat flux (time-average Poynting vector):

S(r,w) = 2Re iwmv d ¢VV

ò d ¢¢VV

ò

x(GyaE Gzb

H* -GzaEGyb

H*)

+y(GzaEGxb

H* -GxaE Gzb

H*)

+z(GxaE Gyb

H* -GyaE Gxb

H*)

é

ë

êêêê

ù

û

úúúú

Ja

r( ¢r ,w)Jb

r*( ¢¢r ,w)

ì

íïï

îïï

ü

ýïï

þïï

Fluctuation-dissipation theorem:

Ja

r ( ¢r ,w)Jb

r*( ¢¢r ,w) =wevp

Im er (w){ }Q(w,T )dabd( ¢r - ¢¢r )

absorption/dissipation of thermal

radiation

locality of the dielectric

function

isotropic

media

General expression for the radiative heat flux:

S(r,w) =2kv

2Q(w,T )

pRe i ¢¢er (w) d ¢V

V

ò

x(GyaE Gzb

H* -GzaEGyb

H*)

+y(GzaEGxb

H* -GxaE Gzb

H*)

+z(GxaE Gyb

H* -GyaE Gxb

H*)

é

ë

êêêê

ù

û

úúúú

ì

íïï

îïï

ü

ýïï

þïï

Near-field radiative heat flux between two thin films

TMTEdik

k

prop

abscz

v

eRR

TRTRdkk

Tq

,22

31

2

3

2

3

2

1

2

1

0

2

1,

21

11

4

),(

rr

TMTEdik

k

dkevan

abscz

v

cz

eRR

RRedkk

Tq

,22

31

312

2

1,

2

2

1

)Im()Im(),(

rr

r

z

SiC

vacuum

vacuum

t1

0

1

2

r1()

r2 = 1

r0 = 1

SiC3r3()

T3

t3

vacuum4 r4 = 1

z1

z2

z3

z4

T1

dc

Francoeur, Mengüç, Vaillon, J. Phys. D: Appl. Phys., 2010

NEAR-FIELD THERMAL RADIATION EMISSION

evan

abs

prop

absabs qqq ,,,

0))H(r,()B(r, 0 m


Total net flux between medium 1 and control volume Dzj in medium 3:

qDz j

abs =w 2

2p 2cv2

dw Q(w,T1)-Q(w,Tj )éë ùûw=0

¥

ò

´Re i ¢¢er1(w)bdb

¢¢g1b=0

¥

ò

g13ra

E (b, z j,w)g13qa

H* (b, z j,w)

-g13qa

E (b, z j,w)g13ra

H* (b, z j,w)

æ

è

çç

ö

ø

÷÷

-g13ra

E (b, z j+1,w)g13qa

H* (b, z j+1,w)

-g13qa

E (b, z j+1,w)g13ra

H* (b, z j+1,w)

æ

è

çç

ö

ø

÷÷

é

ë

êêêêêêêê

ù

û

úúúúúúúú

ì

í

ïïïï

î

ïïïï

ü

ý

ïïïï

þ

ïïïï

NEAR-FIELD THERMAL RADIATION BETWEEN TWO-FILMS

z

r

vacuum

T1 = 300 K T3 = 0 K

d

SiCSiC

[Mengüç and Francoeur, Thermal Radiation Heat Transfer, Chapter 16, 2010]

about 96-97% of the flux concentrated around res

res = 1.786 × 1014 rad/s

= 10.55 mm

T > 0 K

SiC

vacuum r

+

-

+

+

+

+

-

- -

kx

transverse optical (TO) phonon

1013

1014

1015

10-14

10-12

10-10

10-8

10-6

far-fieldblackbodies

d = 1 mm

d = 100 nm

q

,13 [

Wm

-2(r

ad/s

)-1]

[rad/s]

d = 10 nm

T1 = 300 K

T3 = 0 K

res

surface phonon-polaritons (SPhPs) supported by polar crystals (SiC, cBN,…)

NEAR-FIELD THERMAL RADIATION BETWEEN TWO-FILMS

r

z

SiC

vacuum

vacuum

t1

0

1

2

r1()

r2 = 1

r0 = 1

SiC3r3()

T3

t3

vacuum4 r4 = 1

z1

z2

z3

z4

T1

dc

[Francoeur,Mengüc, Vaillon, J. Phys. D: Appl. Phys., 2010.

1.50x1014

1.60x1014

1.70x1014

1.80x1014

1.90x1014

10-17

10-15

10-13

10-11

10-9

10-7

10-5

LO

res

TO

dc = 500 nm

dc = 100 nm

dc = 50 nm

dc = 10 nm

q

,ab

stot [

Wm

-2(r

ad/s

)-1]

[rad/s]

dc = 1 nm

t1 = 10 nm

t3 = 10 nm

1.50x1014

1.60x1014

1.70x1014

1.80x1014

1.90x1014

10-14

10-13

10-12

10-11

10-10

10-9

t3 = 500 nm

t3 = 100 nm

t3 = 50 nm

t3 = 10 nm

LO

res

TO

q

,ab

stot

[Wm

-2(r

ad/s

)-1]

[rad/s]

dc = 100 nm

t1 = 10 nm

Francoeur , Mengüç, Vaillon, Physical Review B., Vol. 84, Issue: 7, Aug. 2011.

COEXISTENCE OF MULTIPLE NEAR-FIELD RADIATION REGIMES

TMTEdik

k

dk

k

dik

r

czv

cz

v

cz eRR

RRedkk

eRR

TRTR

dkk

T

Tdh

,2

2

31

31)Im(2

0

22

31

2

3

2

3

2

1

2

1

0

2

2

2

2 1

)Im()Im(

14

11

),(1

rr

rr

r

z

film 1

vacuum

vacuum0

1

2

r1()

r2 = 1

r0 = 1

film 33r3()

t3 << w

vacuum4 r4 = 1

z1

z2

z3

z4

T

dc << w

T + T

t1 << w

RADIATIVE HEAT TRANSFER COEFFICIENT: kr is the wavevector parallel to the surfaces of the layers, kzj is the z-component of the wavevector in medium j, and kv is the magnitude of the wavevector in vacuum. T and R are the transmission and reflection coefficients of layer j , respectively, in polarization state .



2

3

2

011

2

01

22

0131

231

2

3

2

01

01

1

2

01

01

0 0

2

22

)]21()(1)][21()(1[

)(41

14

)21()(1Im

)21()(1Im

),(1

DrDr

erDDDD

Dr

r

Dr

rde

T

Td

dh

TMTM

TM

TM

TM

TM

TM

c

r

hh

hh

hhhh

h

h

2

3

2

011

2

01

22

0131

231

2

3

2

01

01

1

2

01

01

0 0

2

22

)]21()(1)][21()(1[

)(41

14

)21()(1Im

)21()(1Im

),(1

DrDr

erDDDD

Dr

r

Dr

rde

T

Td

dh

TMTM

TM

TM

TM

TM

TM

c

r

hh

hh

hhhh

h

h

22

31

31

0 0

2

22

1

)Im()Im(),(1

h

h hh

eRR

RRde

T

Td

dh

TMTM

TMTM

c

r

Approximate the Radiative Heat Transfer Coefficient

Then, consider the asymptotic cases: e.g., For D much smaller than 1 (t<<d)

NEAR-FIELD THERMAL RADIATION EMISSION FROM A SINGLE FILM

z

r

vacuum

T1 = T T3 = T + T

d

SiCSiC

1 10 10010

0

101

102

103

104

105

106

far-field regime

blackbodies

Rad

iati

ve

hea

t tr

ansf

er

coef

fici

ent

hr [

Wm

-2K

-1]

Vacuum gap d [nm]

T = 300 K

near-field regime

(d -2 behavior)

d = 10 nm:

Near-field radiative transfer coefficient ~ 500 times

blackbodies

T

dq

hT

r

0

13,

0lim

1 10 100

100

101

102

103

104

105

106

t1 = 1 nm

t1 = 10 nm

t1 = 50 nm

bulk

Rad

iati

ve h

eat

tran

sfe

r

co

eff

icie

nt

hr [

Wm

-2K

-1]

Vacuum gap d [nm]

T = 300 K

1 10 100

101

102

103

104

105

106

t1 = 10 nm

d -3

Vacuum gap d [nm]

Rad

iati

ve

hea

t tr

ansf

er

coef

fici

ent

hr [

Wm

-2K

-1]

d -2

transition region

Coexistence of two near-field thermal radiation regimes due to surface phonon-polariton coupling within the emitter





r

z

film 1

vacuum

vacuum0

1

2

r1()

r2 = 1

r0 = 1

film 33r3()

t3 << w

vacuum4 r4 = 1

z1

z2

z3

z4

T

dc << w

T + T

t1 << w

NEAR-FIELD RADIATION COMPUTATIONAL ANALYSIS

FDTD (Finite Difference Time Domain Method) is a computational method

used to analyse electromagnetic wave propagation problems. It gives

solution to Maxwell’s equations. It is based on a computational grid.

• Two Silicon Carbide films, both supporting SPhP, each 10 nm thick, the

lower film has (T> 0 K) while the upper one (T=0 K ). They are separated

by vacuum gap of 100 nm thickness.

• Local Density of Electromagnetic States

(LDOS) is calculated. This allows

us to calculate thermal radiation

emission in the gap between

the SiC layers.

FDTD Analysis of Near Field Thermal Radiation Emission

Azadeh Didari, Mengüç, Ozyegin Univ, 2012


Computational Techniques : Finite Difference Time Domain Method (FDTD)

Finite Difference Time Domain Technique is a time domain technique

which has been chosen as our computational method of choice:

FDTD is a time domain based numerical method, hence it has the capability

to give us the solution of a very wide band frequency range within a

single run.

FDTD can model various arbitrary geometries having different shapes and

sizes whose analytical studies may not be available due to complexity of the

problem is possible

FDTD can incorporate the effects of reflection and radiation which are

commonly neglected by other methods

FDTD can model wave propagation in complex media, such as time-

varying, anisotropic, lossy, dispersive and non-linear media is possible.

The 1D-FDTD Equations

We start by Maxwell equations:

D, H, and E are vectors in three dimensions. We will start with 1D case using Dx and Hy and denoting the plane wave in z direction.

In order to apply the PML ABC we use the following equations:

Where σ and σ* are respectively the electric conductivity and the magnetic conductivity of the PML medium with 𝜎/𝜀0=σ*/µ0 In order to produce a smooth transition from air cells to the PML cells, the conductivity is gradually increased from zero at the vacuum-layer interface to a maximum value of σ* for each layer.σ(ρ)=σm (ρ/δ)2

FDTD Analysis of Near Field Thermal Radiation Emission

Azadeh Didari, Mengüç, Ozyegin Univ, 2012


How does FDTD work?

Using Yee cells as discrete units, Maxwell's equations are converted to a set of central

difference equations which are to be solved in each Yee unit cell according to the following

flowchart:

Yee Cell

Computational Techniques : Finite Difference Time Domain Method (FDTD)

Didari, Mengüç, 2013

FDTD Requirements :

• Boundary Conditions:

Mur’s first order ABC

Mei-Fang

superabsorption

Numerical Dispersion:

Cell size

Modelling of Near-field thermal radiation within nano-gaps via FDTD

λmin /10

Conventional Perfectly

Matched Layer(CPML)

Detailed modeling studies,

and accurate calculation of

near-field emission within

thin films are necessary in

order to calculate the local

density of electromagnetic

states (LDOS) which is a

key factor to obtain the

radiation heat flux in near

field thermal radiation

related problems.


The fluctuation-dissipation theorem is a general result of statistical thermodynamics that quantifies the

relation between the fluctuations in a system at thermal equilibrium and the response of the system to applied

perturbations

TM evanescent component of monochromatic Local density of Electromagnetic state (LDOS)

FDT: Fluctuation dissipation theorem

2 2

2 2

LOr

TO

i

i

0, , ,

rr rJ J T

r r r r

Drude-Lorentz Model

2 2 2 2 2 2

2

2

0

r E E E E H H

v XX XZ ZX ZZ YX YZ

V V

k dV G G G G dV G Gc

r

r

Modelling of Near-field thermal radiation within nano-gaps via FDTD… Fluctuation Dissipation Theorem (FDTD)…

FDT Maxwell’s Equations Required Info. to study

near-field thermal

radiation & LDOS


Medium specifications :

•Two Silicon Carbide films ,both supporting SPhP, each 10 nm thick, the lower film

has (T> 0 K) while the upper one (T=0 K ). They are initially separated by vacuum

gap of 100 nm thickness.

Modelling of Near-field thermal radiation within nano-gaps via FDTD…

Realistic model Considered model Future model


Modelling of Near-field thermal radiation within via FDTD…

Bulk metamaterial

Single film of metamaterial

Thin films of metamaterial


Methodology

A comparison has been made between Analytical results found

previously by Francoeur et al., and the FDTD calculations

developed. The results showed promising agreement between the

analytical and computational methods.


ΔT small enough

AMR techniques

Intersections!

r Inverse Fourier

Transform

An equivalent recursive expression in the time domain:

2 2 2 2

0 / / 4LO TO TOA 2 2 / 4TO / 2

1 2 2 12 cos sinn t n t n t nS e t S e S Ae t E D D D D D

Peak around :


1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9

x 1014

100

102

104

106

108

1010

[rad/s]

r( D

) [m

-3 (

rad

/s)-1

]

Analytical LDOS at D=50(nm) , dc=100(nm) , t

1=100(nm) , t

3=10(nm)

FDTD Analysis of LDOS



1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9

x 1014

100

102

104

106

108

[rad/s]

r( D

) [m

-3 (

rad

/s)-1

]

FDTD Analy sis of LDOS at D=250(nm) , d

c=500(nm) , t

1=500(nm) , t

3=500(nm)

FDTD Analy sis of LDOS at D=50(nm) , dc=100(nm) , t

1=100(nm) , t

3=100(nm)


1=1000(nm) , t

3=1000(nm)


1=100(nm) , t

3=10(nm)

Study of the effect of the gap size on LDOS profile…

An increase of three orders of

magnitude is observed when the

gap size is below 500 nm


What about arbitrary Geometries?

When it comes it arbitrary

geometries e.g. A tip and a

plate… Use

DDA-SI

Test FDTD for the same geometries and compare the

results with DDA-SI results.


RADIATION ABSORPTION AND SCATTERING

BETWEEN CLOSE PARTICLES AND SURFACES

Individual Absorptions

Integrated Poynting Vector

Geometries

Two Identical Spheres

Two Spheres with different sizes

Conical tip and a nanosphere

k

E, B

TWO PARTICLE INTERACTION

Donmezer, Okutucu, Mengüç

DDA-SI: TO ACCOUNT FOR SURFACE EFFECTS RIGOROUSLY

Discrete Dipole Approximation – Surface Interaction

Based on DDSURF, unreleased code by Schmehl et al.

Prototype MATLAB implementation can be ported to C and Fortran if speed is required

MATLAB has a very efficient numerical linear system solver (gmres)

R. Schmehl, B. M. Nebeker and E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two-dimensional fast Fourier transform technique”, J. Opt. Soc. Am. A. 14(11), 3026-3036 (1997).

V. L. Y. Loke and M. P. Mengüç. “Surface waves and afm probe-particle near-field coupling: Discrete dipole approximation with surface interaction”. to appear in J. Opt. Soc. Am. A, 2010.

Loke, Mengüç, 2010

DDA-SI SYSTEM OF EQUATIONS

SI

,

1

N

jk k inc j

k

A P E jinc

N

k

kjkjk ,

1

EPRA

The interaction matrix now comprises the direct and reflected terms


DECOMPOSING THE SPHERICAL WAVE

i

r

kre 0J kr r zik z

e

Spherical Cylindrical Planar

rr

rr dkeRkJ

k

ke jz zkTETM

zref

kri,

210

0

i

ir

(1)

0

1

2H kr ror

A. Sommerfled, “ ¨Uber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Physik 28, 665–737 (1909). Loke, Mengüç, 2010

M. A.Taubenblatt and T. K.Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method”, J. Opt. Soc. Am. A, 10(5), (1993).

Testing the implementation


TM incident TE incident

λ = 632nm

DDI-SI: TM VS TE COUPLING


AFM PROBE SHAFT LENGTH

TM incident, λ = 632nm

• Field intensity of the 32 dipoles in the nanoparticle


LATERAL DİSPLACEMENT

TM incident, λ = 632nm


Wavelength


DDA-SI is a useful tool for studying near-field coupling for systems comprising nano-objects on or in the vicinity of a subtrate

It currently does not account for emission

We can calculate optical forces

Half-space T-matrix for system can be formulated

Arbitriraly complex configurations are limited by available memory

Irregular local area for substrate possible

Conclusion


NUMERICAL MODELING OF

AFM-BASED

MANUFACTURING

• Spherical simulation domain

• Symmetric plane

• Field defined analytically everywhere, except PML

• Setup checked with known solutions, and tested for convergence

Huda, Hastings, Menguc et al. IEEE JSTQE Nanoplasmonics 2013

Nano-Scale Patterning via AFM: (Gazi Huda)

11/21/2013

As tip is brought closer to

particle:

• Absorption enhances.

• Resonant wavelengths get

red shifted.

• Quantum effects were not

taken into account.

x

y

z

k Huda, Hastings, Menguc et al. Opt. Express 2011

Effect of the Tip on Particle Absorption (TM)

Preliminary results: Effect of Tip on Particle Absorption w.r.t. Lateral Separation (TM & TE)

82

• highest absorption when particle 5 nm

right of tip.

• Secondary peak might be because of

the interference between the particle

and tip.

k

x

y

z

Huda, Hastings, Mengüç, 2012

At total internal reflection illumination • The field is strongly localized and enhanced under a nanoscale tip • The absorption is enhanced under a Si tip • The absorption is suppressed under a Au tip.

Huda et al. IEEE JSTQE Nanoplasmonics 2013

Absorption modification caused by a tip

Effect of tip on different particle size

11/21/2013

10 15 20 25 30 35 40 45 500

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Diameter of the Au nano particle (nm)

Ab

sorp

tio

n e

ffic

ien

cy o

f A

uN

P

TM with tip

TM without tip

TE with tip

TE without tip

Efficiency=Cross section/geometrical cross sectional area Greatest enhancement is when radius of particle is smaller than the tip

Gazi M. Huda Master’s Thesis 114 University of Kentucky

Effect of tip on different particle size


THE STORY: NANO- & CASCADED PV & TPV

At Ozyegin University

FP-7-PEOPLE-IRG-2008 (Grant No: 239382) TUBITAK 1001 Grant (No: 109M170)

At the University of Kentucky:

US National Science Foundation (NSF-CMMI-0403703)

Kentucky Science and Engineering Foundation (KSEF-1718-RDE-011) US Department of Energy (DE-FG02-07ER46375)

ACKNOWLEDGMENTS

www.ozyegin.edu.tr/energy

[email protected]

http://www.ozyegin.edu.tr/energy

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