Near-field thermal radiation

Rémi Carminati

Laboratoire EM2CCNRS, Ecole Centrale Paris

France

remi.carminati@ecp.fr

Acknowledgments

• ACI and ANR projects (France)

• EU Integrated project

M. Laroche, F. Marquier, C. Arnold (coherent thermal emission)

J.P. Mulet (radiative transfer at small scale)

Y. Chen (LPN, Marcoussis, samples)

J.-J. Greffet(Paris)

J.J. Sáenz (Madrid)

C. Henkel (Potsdam)

K. Joulain (Poitiers)Y. De Wilde

(Paris)

Outline

• Blackbody radiation in the near fieldSpectral behavior - connection to LDOSSpatial coherence

• Coherent thermal emission by microstructured surfaces

• Thermal emission STM : measuring the LDOS of surface waves

• Radiative transfer at mesoscopic scale

T

20x103

15

10

5

0500x10

124003002001000

ω ( )Hz

=100 z μm

=1 z μm

= 100 z nm

15

10

5

0

L

Blackbody radiation

T

Radiative energy densityu(ω,T)

Planck’s function

Thermal emission by a heated body

T€

φemitted ∝ε ω,u,T( ) U ω,T( )

emissivity Planck’s function

• Incoherent summation of intensities

• Temperatures + emissivities : radiative transfer

Small is different

• Ray optics

• Incoherent summationof intensities (fluxes)

• Local radiative properties

• Opaque bodies(surface properties)

Classical theory Mesoscopic scale

L <<

L << lcoh

L << L << lcoh

L <<

WavesNear field (surface waves)

CoherenceInterferences

Non locality

Volume radiation

Near-fieldblackbody radiation

20x103

15

10

5

0500x10

124003002001000

ω ( )Hz

1.0

0.8

0.6

0.4

0.2

0.0

=100 z μm

=1 z μm

= 100 z nm

15

10

5

0

SiC, T = 300 K

z

• Energy density• Spectrum at T = 300 K• SiC surface

Shchegrov, Joulain, Carminati, Greffet, PRL 85, 1548 (2000)

Near-field thermal emission spectrum (SiC)

Physical origin of the near-field behavior

Blackbody radiation : UBB ω( ) =

ω2

π2c3

hωexphω/kBT( )−1

€

U r,ω( ) = ρ r,ω( ) hω1

exp hω /kBT( ) −1

Energy density LDOS Photon energy Bose-Einsteindistribution

Surface electromagnetic modes (surface polaritons)

• Surface modes modify the LDOS• Evanescent modes : near-field effect

ω peak

LDOS above an aluminum surface

d

• LDOS increases substantially in the near field• Plasmon resonance• Far-field value for d∞ and for ω∞

Joulain, Carminati, Mulet, Greffet, Phys. Rev. B 68, 245405 (2003)

20x103

15

10

5

0500x10

124003002001000

ω ( )Hz

=100 z μm

=1 z μm

= 100 z nm

15

10

5

0

€

ρ(z,ω) = 1

16π 2ω z3

Im ε ω( )[ ]

1+ ε ω( ) 2

Asymptotic expression of the LDOS

In the near field (z << ) :

Local density of states :

• Resonance for Reω = -1

• Quasi-static fields

Surface polaritons induce spatial coherence

Field spatial correlation

T

ρ=r−r'

Carminati, Greffet, PRL 82, 1660 (1999)

Metal (Au) with surface plasmon

Cristal (SiC) with surface phonon

Coherence length ~ decay length of the polariton

Example : 36 for SiC at = 11.36 μm

Blackbody radiation

Calculation of thermal fluctuating fields

T

E(r,t)

1) Linear response

€

E(r,ω) = iμo ω GE r, r ',ω( )∫ ⋅ j r ',ω( ) dr '

Rytov, Kravtsov and Tatarskii, Principles of Statistical Radiophysics (Springer, Berlin, 1989)

2) Spectral densities

€

W ijE r, ′ r ,ω( ) = E i r, t( )E j ′ r , t + τ( ) exp iωτ( )∫ dτ

€

E i r,ω( )E j∗ r ',ω'( ) = W ij

E r, ′ r ,ω( ) δ ω −ω'( )

3) Fluctuation-dissipation theorem

€

jk r,ω( ) jl∗ r,ω'( ) =

ω

πε0 Im ε ω( )[ ]

hω

exp hω kT( ) −1δkl δ r − r '( ) δ ω −ω'( )

Playing with surface modes :

Coherent thermal emission

Antenna versus standard thermal source

HF

Antenna

T

Thermal source

• Interferences produce directivity• Interferences if the fields are correlated along the antenna

Design of coherent thermal sources(surface phonon polaritons)

Ksw + 2πd

= 2πλ

sinθ SiC

Principle : grating coupling Ksw

Period : 6.25 μmHeight : 0.285 μmFill factor : 0.5

Blackbody Grating

Polarizer

KRS5 R = 600 mm

Experimental set-up

Heating(T contol)

Orientationcontrol

FTIRspectrometer

Greffet, Carminati, Joulain, Mulet, Mainguy, Chen, Nature 416, 61 (2002)

Green : theory T = 300 KRed : experimentT = 800 K = 0.22 μm

Angular emission pattern at = 11.36 μm

SiC

Infrared antenna

Emission pattern at different wavelengths

Marquier et al., Phys. Rev. B. 69, 155412 (2004)

Field spatial correlation

T

ρ=r−r'

Extraordinary spatial coherence on tungsten surfaces due to surface

plasmonsTungsten supports surface plasmons in the near infrared

Plasmoncontribution

Coherence length 600 at 4.5 μm !!!

Highly-directional near-infrared tungsten source

Laroche et al., Opt. Lett. 30, 2623 (2005)

Emission pattern

Theory

Experiment

Measured emissivity at = 4.53 μm

= 0.9°≈ CO2 laser

Lcoh = 154 (0.7 mm)

a = 3 μm, h = 0.125 μmFill factor 0.5

Ge

Angular thermal emission pattern at = 1.55 μm

Em

issi

vity

Observation angle

Laroche, Carminati, Greffet, PRL 96, 123903 (2006)

= 0.6°Lcoh = 40 (60 μm)

Surface waves on photonic-crystal slabs

Measurement of thermal near fields :

Thermal Radiation STM

HgCdTe

Thermal radiation STM (experiments)

De Wilde et al., ESPCI (Paris)

(no filter)

Imaging surface plasmons on gold

• Interferences of thermally excited plasmons (spatial coherence !)

• Number of fringes depends on the width of the stripe (cavity)

De Wilde et al., Nature 444, 740 (2006)

(filter, = 10.9 μm)

Probing the LDOS of surface plasmons(filter, = 10.9 μm)

De Wilde et al., Nature 444, 740 (2006)

Bardeen’s formalism in the context of STM

Tunneling current

I =

2πeh

f Ep( )−f Es +eV( )[ ]p,s∑ Mps2 δ Ep −Es( )

Matrix element Mps =

h2

2mΨp

∗∂Ψs

∂z−Ψs

∗∂Ψp

∂z

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ ∫ dS

Example : Tersoff and Hamman theory (1983)

I ∝ Ψs rp( )2δ Es −EF( )

p,s∑ ≡ρ rp,EF( )

First interpretation of the STM signal

Nature 363, 524 (1993)

Generalized Bardeen’s formalism

Carminati and Saenz, Phys. Rev. Lett. 84, 5156 (2000)

Mps =1

8π2 iγ Kp( )Ψp ⋅

∂Ψs

∂z−Ψs ⋅

∂Ψp

∂z

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥ ∫ dS

Sω( )=2π2ε0cγ2 Kp( ) Mps

2SNOM signal :

€

S ω( )∝ ρ EM rp ,ω( )

Carminati and Saenz, Phys. Rev. Lett. 84, 5156 (2000)

Joulain, Carminati, Mulet, Greffet, Phys. Rev. B 68, 245405 (2003)

Analogy between SNOM and STM

• A SNOM measuring thermally emitted fields would probe the LDOS

• Exact LDOS if point detection (+ polarization average)

Radiative transfer at small scales

Radiative heat transfer through a small vacuum gap

L

T2 > T1

T1

€

φ=hR T2 − T1( )Radiative flux (W.m-2)

Classical heat transfer (far field) : hR 5 W.m-2.K-1

Monochromatic heat-transfer coefficient AsGa - Au

= 6.2 μm, T = 300 K

Au

AsGa

Classical value

Wave effects

Near field(evanescent waves)

100

Mulet et al., Opt. Lett. 26, 480 (2001)

L

SiC

SiC

L

hR 1/L2

Radiative heat-transfer coefficient

SiC - SiC, T = 300 K

Ballistic conduction in air

Mulet et al., Microsc. Thermophys. Eng. 6, 209 (2002)

Classical value

Spectral behaviorL = 10 nm , T = 300 K

Quasi-monochromatic radiative heat transfer !

SiC

SiC

L

Near-field radiative heating of a nanoparticle

10-6

10-4

10-2

100

102

10-8 10-7 10-6 10-5 10-4

d in m

Far field value

1/d3

10-20

10-18

10-16

10-14

10-12

2.52.01.51014 ω .in rad s-1

ω1 ω2

abc

10-3010-2010-10

1015101410131012ω .in rad s-1

ef

Td

Sphere radius r = 5 nm

SiC

• The absorption increases as 1/d3 in the near field

• 8 orders of magnitude between d=10 μm and d=10 nm

Mulet et al., Appl. Phys. Lett. 78, 2931 (2001)

thermal source

T= 2000 K

TPV cell

T= 300 K

d << rad

thermal source

T= 2000 K

TPV cell

T= 300 K

PV cell

T= 300 K

Photovoltaics Thermophotovoltaics Near-fieldthermophotovoltaics

T= 6000K

Application : near-field thermophotovoltaics

tungsten source quasi-monochromatic source

d (m)

50

far field :3.104 W/m2

near field :15.105 W/m2

Pe

l (W

. m

- 2)

d (m)

near field : 2.5.106 W/m2

far field : 1.4.103 W/m2

3000

Pe

l (W

. m

- 2)

BB 2000 KBB 2000 K

Output electric power

Laroche, Carminati, Greffet, J. Appl. Phys. 100, 063704 (2006)

T= 2000 K

TPV cell (T = 300K)

d

€

η =Pel

Pradη (%

)

d (m) d (m)η

(%)

near field : 27%

far field : 21 %

near field : 35%

far field : 8 %

tungsten source quasi-monochromatic source

BB 2000 K BB 2000 K

Laroche, Carminati, Greffet, J. Appl. Phys. 100, 063704 (2006)

Efficiency of a near-field TPV system

T= 2000 K

TPV cell (T = 300K)

d