near-field thermal radiation
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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
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