メタマテリアルによる熱輻射の制御に向けて高原淳一
大阪大学大学院基礎工学研究科
日本熱物性学会：研究会
2007年9月28日

目次
 背景と目的～高効率白熱電球へむけて マイクロキャビティアレイにおける熱輻射 擬似表面プラズモンと熱輻射 今後の展望と応用～メタマテリアルによる熱輻射制御
 まとめ
2

背景と目的～高効率白熱電球へむけて

3

From carbon to tungsten filament
1878
J.W. Swan
Carbon filament
lamp*Carbon filament
made from cotton
30W
Tungstendouble coil filament
100W

1879.10
T.A. Edison
Carbon filament
lamp*Single wire carbon
filament madefrom bamboo in Kyoto
30W*Commercially available incandescent lamps with carbon
filament for use of antique lamps.

1880.11
Bamboo filament
lamp

4Historic incandescent lamp replicas in my lab.

Edison’s patent

Swan lamp replica
Linear carbon filament
made from cotton

Edison lamp replica
Carbon filament made from real
bamboo in Yawata city, Kyoto

5

Luminous efficacy of various light sources
type

supplementation

Luminous efficacy（lm/W）

Incandescent lamp

100W-95W、2856K

16

Halogen lamp

With hotmirror, for home

19

Halogen lamp

With hotmirror, for studio

28

Fluorescent lamp (bulb)
Fluorescent lamp

58
White light 6500K

Metal haloid lamp

9680~140

Low pressure Na lamp

180W

180

High pressure Na lamp

400W

125~140

LEDToshiba in 2007

18-50
6

Low energy efficiency of incandescent lamp
Planck’s law

90% of total radiation

原因Efficiency of a lamp
Luminous efficacy (lm/W)=

Luminous flux
Input power

Normalized sensitivity of eyesenergy is infrared (IR)!

7wavelength (μm)

Emissivity of various materials
 blackbody ε=1
 Tungsten ε=0.1~0.4
 Typical ranges of emissivity
glassescarbonceramics
oxidized metals
unpolished metals
polished metals
0ε
0.2

0.4

0.6

0.8

1.0

Y.A. Cengel: Introduction to Thermodynamics and heat transfer (McGraw-Hill, 1997)8

Processes in thermal radiation
spontaneousemission
surface wave

stimulatedemission

surfacesurface phonon~wavelength
absorbtion

bremsstrahlung

Bulk phonon
free electron
thermally excited atoms
Microstructures on surface

Control of thermal radiations

9Micro-cavity Lamp
Analogy to microwave waveguide theory
Cutoff effect prohibits IR radiation

7000nm150nm
350nm
top view

Tungsten filament
Cross sectional view

J.F. Waymouth, J. Light & Vis. Env. 13, 2 (1989) 51.
U.S.Patent No.5079473（1992）.

10Principles of micro-cavity lamp
Waymouth’s assumptions
1) IR radiation is prohibited from microcavity due to cut-off2) IR radiates only from the top wall3) Radiation flux in top wall decreases to 20% to blackbody in cavity

150nm

Top wall Sw
350nm

7μm

Sc + Sw =1

Micro-cavity Sc

11

Radiation spectra of micro-cavity lamp
Energy flow: input power = radiative power
total radiation
radiation from cavity

Lx=Ly=380nm
Wall 160nm
Fraction of Sc: 0.5

radiation from wall

visibleIRVisible radiation increases

12Luminous efficacy [lm/W]

Improvement of luminous efficacy
by thermal spectral control

LED lamp

123Radiation power ratio

45
6visible / IR (times)

Luminous efficacy can be improved
close to fluorescence lamps.

13マイクロキャビティアレイにおける熱輻射

14

History of thermal radiation control bymicrostructured surface
Deep 1D grating
P.J. Hesketh et al. Nature, 324 (1986) 549.
deep(45μm) grating on doped Si Proposal of micro-cavity lamp
J. F. Waymouth (1989)
Experiments in GE and Matsushita Electric (1992-1994)
 Applications to TPV cellMaruyama APL 79 (2001) 1393.
 Radiation control by surface phonon polariton
Spatial coherence: J.J.Greffet et al. Nature, 416 (2002) 61.
1D grating on SiC
 Photonic crystals (PC)
Tungsten rod pile PC: J.G. Fleming, Nature, 417 (2002) 52.
15

Deep microcavity array
Tungsten (W), Tantalum (Ta) substrate （t=0.5mm）
 W (T=3400゜C), Ta (T=3000゜C), doped Si cavity size: 3μm x 3μm x 3.7μm (36%)
 patterned area 3mm x 5mm
16Fabrication process
t=0.5mm
Polish W, Ta substrate
to form flat surface

PMMA remove

PMMA spin coating

Dry etching

E-beam lithography(5mm x 5mm area)

W and Ta have large hardness (W:7.5, Ta:6.5, SiO2: 7, diamond: 10).

17

Metallic microstructureswall width
2.5μm

Cavity size
5.5μm x 5.5μm

periodicity
8.0μm

depth
3.2μm

(Example) Ta substrate
18

Experimental setup

 heating → Electric current
 temperature → 470-630℃
 measurement → thermalradiation thermometer concave mirror (Au)： f = 452 mm
 FT-IR ( JASCO Inc.，FT-IR 660Plus ) DLATGS detector
 DC current source（ KENWOOD Electronics， PS10-210 ）19

Thermal radiation spectra flat and structured surfaces
 3 times enhancement@5.6μm Many peaks in relative emissivity

CO2F. Kusunoki, J. Takahara and T. Kobayashi, "Narrow-Band Thermal radiation with Low
Directivity by Resonant Modes inside Tungsten Microcavities", Japanese Journal of Appl. Phys.,
20Vol.43, No.8A, (2004) 5253.

EM field in open cavity
Open top

Boundary condition for perfect conductor wallTangential components Et=0 @ wall
Antinode @ open end of cavity
E x (r, t ) = E x (t ) cos(k x x )sin (k y y )sin (k z z )E y (r, t ) = E y (t )sin (k x x ) cos(k y y )sin (k z z )k x = n x π Lx , k y = n y π L y , k z = n z π 2 L z

E z (r, t ) = E z (t )sin (k x x )sin (k y y )cos(k z z )nx , n y = 0,1,2,3,...
nz = 0,1,3,5,...

Wavelength of eigenmodeλcavity (nx , n y , nz ) =Maruyama et al. APL, 79 (2001) 1393.

22⎛ nx ⎞ ⎛ n y ⎞ ⎛ nz ⎞⎜⎜ ⎟⎟ + ⎜ ⎟ + ⎜⎜⎟⎟⎟⎜⎝ Lx ⎠ ⎝ Ly ⎠ ⎝ 2 Lz ⎠2221

Single open cavity model
antinode
Boundary condition
perfect conductor wallE(boundary) =0nodeθδαnz=1,3,5… (Odd mode index)

Theory (resonance)

22Analogy ~Optical Woodwind Instruments
E-field in Optical cavity

openendLPressure in closed pipe

f= c/4L

f= v/4L

f= 3c/4L

f= 3v/4L

f= 5c/4L

f= 5v/4L

odd-numberharmonics

closedend

T.D. Rossing, F.R. Moore and P.W. Wheeler,
The Science of Sound (3rd ed.), (Addison Wesley, 2002).

clarinet23

Numerical simulation ~FDTD method
Finite Difference Time Domain (FDTD) method
 RSoft Design Group, Inc. FullWAVE
 Popular in antenna design, plasmonics, nanophotonics
Maxwell equations

Maxwell equationsin FDTD algorithm~∂B~ =−
∇×E
∂t~
1
∂H~
= − ∇×E∂tμ~∂D~ =∇× H+ J~
∂t~
1σ~
∂E~
= ∇×H − E
∂t²²Time evolution of E and H
in Yee’s mesh in space24

FDTD calculation model
1

Reflectance R

Dispersion of metal
Pulse input

Time dependent field profile
Calculate spectral reflectance

Debye model
W, Ta negative dielectric（@IR）

boundary condition
1) PML (Perfectly Matched Layer:perfect absorber wall)
2) PBC (Periodic Boundary Condition)
25

Permittivity of Tungsten and Tantalum
1000

1040

05800

30-500400

ε1-520ε2-1000

ε2 (Im[ ε])W

ε1 (Re[ ε])0600-1010-1500
200

Negativedielectric-2000
02468-15-200.0

0100.5

Wavelength (μm)
100001.0

wavelength (μm)

1.510405800-500300ε1-1000-520ε2ε1600

ε2Ta02.0

400-10-1500

10200-15-200000246Wavelength (μm)

810-200.0

0.5

Palik: Handbook of Optical Constants of Solids (Academic Press)

1.0
Wavelength (μm)

1.502.026

EM field in the cavity
λ=2.6μm

λ=5.6μm

field inside the cavity

The open cavity model
is confirmed !

27

Reflectance

Reflectance of plane metal surface

Theoretical values are taken from
Palik: Handbook of Optical Constants of Solids (Academic Press)
28

simulated results
Calculation of reflectivity R from FDTD
α =1-R -T = 1-R
 Kirchhoff’s law (absorption=emissivity) α＝ε

relative emmisivity

Reflectancereflectance

We can simulate thermal emission by FDTD calculations.
J. Takahara, F. Kusunoki and T. Kobayashi, "Resonant Thermal Radiation from Tungsten
Surfaces With Rectangular Array of Square Holes", in IQEC '2005, JWH2-4, (2005).
29

擬似表面プラズモンと熱輻射

30

Thermal radiation spectra from small cavity
Smaller cavity

Cavity mode

AFM image

Differencein cavity resonant mode

Surface Plasmon Polariton?
31表面微細周期構造によって熱輻射が変化 開口部の割合により輻射スペクトルに質的変化

タングステン基板
表面のSEM像

共振器

SPP

F.Kusunoki et al.: Electron. Lett. Vol.39, No.1 (2003) 23.

32

2D optical wave
~surface plasmon polariton (SPP)

frequency ωsurface plasmon polariton (SPP)|εm| > ε >0Light line

TM wavewave vector kSPP

33

Coupling from SPP to radiation modeby 1D metallic grating
Coupling condition (1D)
Incidentlightk SPP = k xy + mK

kx: wavenumber, Λ:period, m: integer
Coupling wavelength⎞mΛ ⎛⎜ ε mλSPP = ⎜− sin θ ⎟⎟m ⎝ 1+ εm m⎠
34

SPP resonanceCavity mode

Relative Emissivity

directivity

Kusunoki et al.
Electron Lett. 39 (2003) 23.

difference inwavelength at θ=0

m=1
m=-1

m=-1
m=135

Dispersion relation of SPP

this study k0=kSPP

dispersion relation of SPP = light line?
36

Spoof surface plasmon in
microstructured perfect conductorSPP

Negative dielectric Spoof SPP

Perfect conductor
No surface wave

Perfect conductor
with periodic hall(a<<λ0)J.B. Pendry et. al., Science 305 (2004) 847.
37

good agreement with spoof SP theory38

今後の展望と応用～メタマテリアルによる熱輻射制御

39

技術的展望 技術的課題～タングステン微細構造の高温での耐久性

１０００℃以下での応用分野

40

Difficulty of Micro-cavity lamp101) Damage by dry etching process
2) Local T is higher than macro T3) Melting point modification in microstructure40530-520ε2ε10-1010-151) Microstructure melting2) W, Ta are not negative dielectric at visible
range-200.00.5

1.0

wavelength (μm)

1.502.0

Practical application

Micro-cavity lamp is difficult to realize atcurrent technology.

T < 1000℃
IR radiation control
IR emitter41

科学的展望 将来展望～メタマテリアルと擬似表面プラズモン

メタマテリアルによる熱輻射制御
42

ε-μ diagram

SPP

Dielectric(D)Negative
Dielectric(ND)

negative
Index (NI) or
left-handedmaterials(LHM)

V. Veselago (1968).

Negative
Permeability(NP)43負屈折率媒質の実現
 TEMモードに対する負屈折率媒質（NIM）
SRR（Sprit Ring Resonator）

TW（Thin Wire）
E
E
H

D.R. Smith et. al.,PRL 84,
4148 (2000).

SRRとTWを用いたメタマテリアルによりNIMが実現
44

Centre de Physique 2007 / Physics center 2007
THERMAL RADIATION AT THE NANOSCALE:FORCES, HEAT TRANSFER, COHERENCE(TRN 07)
May 21-25, 2007, Les Houches, FranceOrganizers: Jean-Jacques Greffet (École Centrale Paris) and Daniel Bloch(Université Paris 13)
Scientific Commitee:
G. BARTON (Sussex U.), G. CHEN (MIT), I. DOROFEYEV (RAS, Nizhny
Novgorod), C. HENKEL (U. Potsdam), M. HOLTHAUS (U. Oldenburg), K.
KARRAI (LMU, Munich), J. OBRECHT (JILA, Boulder), B.N.J. PERSSON (IFF
Forschungszentrum J･lich), P. PITAEVSKII (U. Trento and Kapitza Institute,Moscow), S. REYNAUD (École Normale Supérieure, Paris), J. TAKAHARA (U.
Osaka), Z. ZHANG (Georgia Tech)

45

Lectures
S. BARNETT (Strathclyde U.), Radiation pressure and momentum transfer in dielectrics
C. HENKEL (U. Potsdam), Introduction to fluctuational electrodynamics, surface polaritons and coherence
M. RUBI (U. Barcelona), Nanothermodynamics
Seminars
M. ANTEZZA (U. Trento), Interaction between atoms and thermal radiation
D. BLOCH (U. Paris 13), Towards temperature effects in atom-surface van der Waals interaction
G. CHEN (MIT), Heat transfer at nanoscale
I. DOROFEYEV (RAS, Nizhny Novgorod), Energy and momentum transfer between microparticles and solids
J-J. GREFFET (École Centrale Paris), Coherent thermal emission
K. JOULAIN (ENSMA Poitiers), Radiative heat transfer in the near field
A. KITTEL (U. Oldenburg), Experimental study of the radiative heat transfer in the near field
K. KARRAI (U. Munich), Friction forces measurements in the near field
S. REYNAUD (ENS Paris), Casimir forces, a (re)view
U. MOHIDEEN (UC Riverside), Measurements on Casimir forces
K. MILTON (U. Oklahoma), Dependence of Casimir force on temperature
J. OBRECHT (JILA, Boulder), Recent experiments on temperature dependence of Casimir-Polder force
A. I. VOLOKITIN (Samara Tech. State U.), Radiative friction forces, a review of the theoretical models
J. TAKAHARA (Osaka U.), Modification of light emission by microstructured surfaces
E. VINOGRADOV (RAS), Vibrational polaritons in semiconductor films and surfaces
Y. DE WILDE (ESPCI Paris), Experimental measurements of thermal fields in the near field46

まとめ マイクロキャビティアレイの熱輻射 単一キャビティの共鳴モードによる輻射増大 キャビティアレイの擬似表面プラズモンにともなう共鳴増大 メタマテリアルによる熱輻射の制御の概念
Smaller cavity

Larger cavityOpen cavity mode

FDTD simulation

Spoof surface plasmon
47

Thank you!

48