1. Near-field thermal radiation
Rémi Carminati
Laboratoire EM2C
CNRS, Ecole Centrale Paris
France

2. ACI and ANR projects (France) EU Integrated project
Acknowledgments
K. Joulain
(Poitiers)
C. Henkel
(Potsdam)
Y. De Wilde
(Paris)
J.-J. Greffet
(Paris)
J.J. Sáenz
(Madrid)
M. Laroche, F. Marquier, C. Arnold (coherent thermal emission)
J.P. Mulet (radiative transfer at small scale)
Y. Chen (LPN, Marcoussis, samples)
ACI and ANR projects (France)
EU Integrated project

3. Outline
Blackbody radiation in the near field Spectral behavior - connection to LDOS Spatial coherence
Coherent thermal emission by microstructured surfaces
Thermal emission STM : measuring the LDOS of surface waves
Radiative transfer at mesoscopic scale T L

4. Radiative energy density
Blackbody radiation T
Planck’s function
Radiative energy density
u(w,T)

5. T Thermal emission by a heated body emissivity Planck’s function
Incoherent summation of intensities
Temperatures + emissivities : radiative transfer

6. Small is different Classical theory Mesoscopic scale Ray optics
Incoherent summation of intensities (fluxes)
Local radiative properties
Opaque bodies (surface properties)
L << l
L << lcoh
L << l L << lcoh
L << d
Waves Near field (surface waves) Coherence Interferences Non locality Volume radiation

7. Near-field blackbody radiation

8. Near-field thermal emission spectrum (SiC)
Energy density
Spectrum at T = 300 K
SiC surface z
SiC, T = 300 K
Shchegrov, Joulain, Carminati, Greffet, PRL 85, 1548 (2000)

9. Physical origin of the near-field behavior
Energy density
LDOS
Photon energy
Bose-Einstein
distribution
Blackbody radiation :
Surface electromagnetic modes (surface polaritons)
Surface modes modify the LDOS
Evanescent modes : near-field effect
w peak

10. LDOS above an aluminum surface
LDOS increases substantially in the near field
Plasmon resonance
Far-field value for d∞ and for w∞
Joulain, Carminati, Mulet, Greffet, Phys. Rev. B 68, (2003)

11. Asymptotic expression of the LDOS
In the near field (z << l) :
Local density of states :
Resonance for Re[e(w)] = -1
Quasi-static fields

12. Surface polaritons induce spatial coherence Field spatial correlation
Metal (Au) with surface plasmon
Cristal (SiC) with surface phonon
Coherence length ~ decay length of the polariton
Example : 36 l for SiC at l = mm
Blackbody radiation
Field spatial correlation T
Carminati, Greffet, PRL 82, 1660 (1999)

13. Calculation of thermal fluctuating fields
E(r,t) T
Linear response
2) Spectral densities
3) Fluctuation-dissipation theorem
Rytov, Kravtsov and Tatarskii, Principles of Statistical Radiophysics (Springer, Berlin, 1989)

14. Playing with surface modes : Coherent thermal emission

15. Antenna versus standard thermal sourceHF
Interferences produce directivity
Interferences if the fields are correlated along the antenna

16. Design of coherent thermal sources (surface phonon polaritons)q l
Principle : grating coupling
Ksw
SiC
Period : 6.25 mm
Height : mm Fill factor : 0.5

17. Experimental set-up Orientation control Heating (T contol) Blackbody
Grating
FTIR
spectrometer
Polarizer
KRS5
R = 600 mm

18. Angular emission pattern at l = 11.36 mmq
Infrared antenna l
Green : theory
T = 300 K
Red : experiment
T = 800 K
Dl = 0.22 mm
SiC
Greffet, Carminati, Joulain, Mulet, Mainguy, Chen, Nature 416, 61 (2002)

19. Emission pattern at different wavelengths
Marquier et al., Phys. Rev. B. 69, (2004)

20. Extraordinary spatial coherence
on tungsten surfaces due to surface plasmons
Tungsten supports surface plasmons in the near infrared
Plasmon
contribution
Coherence length 600 l at 4.5 mm !!!
Field spatial correlation T

21. Highly-directional near-infrared tungsten source
Laroche et al., Opt. Lett. 30, 2623 (2005)
Emission pattern
Theory
Experiment
a = 3 mm, h = mm
Fill factor 0.5
Measured emissivity at  = 4.53 m
Dq = 0.9°
≈ CO2 laser
Lcoh = 154 l
(0.7 mm)

22. Angular thermal emission pattern at l = 1.55 mm
Surface waves on photonic-crystal slabs
Angular thermal emission pattern at l = 1.55 mm
Emissivity
Observation angle Ge
Dq = 0.6°
Lcoh = 40 l (60 mm)
Laroche, Carminati, Greffet, PRL 96, (2006)

23. Measurement of thermal near fields : Thermal Radiation STM

24. Thermal radiation STM (experiments)
De Wilde et al., ESPCI (Paris)
HgCdTe
(no filter)

25. Imaging surface plasmons on gold
(filter,  = 10.9 m)
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)

26. Probing the LDOS of surface plasmons
(filter,  = 10.9 m)
De Wilde et al., Nature 444, 740 (2006)

27. Bardeen’s formalism in the context of STM
Nature 363, 524 (1993)
Tunneling current
Matrix element
Example : Tersoff and Hamman theory (1983)
First interpretation of the STM signal

28. Generalized Bardeen’s formalism
SNOM signal :
Carminati and Saenz, Phys. Rev. Lett. 84, 5156 (2000)

29. Analogy between SNOM and STM
A SNOM measuring thermally emitted fields would probe the LDOS
Exact LDOS if point detection (+ polarization average)
Carminati and Saenz, Phys. Rev. Lett. 84, 5156 (2000)
Joulain, Carminati, Mulet, Greffet, Phys. Rev. B 68, (2003)

30. Radiative transfer at small scales

31. f Radiative heat transfer through a small vacuum gap T1 L T2 > T1
Radiative flux (W.m-2)
Classical heat transfer (far field) : hR  5 W.m-2.K-1

32. Monochromatic heat-transfer coefficient AsGa - Au
l = 6.2 mm, T = 300 K
Near field
(evanescent waves) Au L
Classical value
AsGa
Wave effects
l/100 l
Mulet et al., Opt. Lett. 26, 480 (2001)

33. Radiative heat-transfer coefficient
SiC - SiC, T = 300 K
hR  1/L2
SiC
Ballistic conduction in air L
SiC
Classical value
Mulet et al., Microsc. Thermophys. Eng. 6, 209 (2002)

34. Spectral behavior L = 10 nm , T = 300 K
SiC L
SiC
Quasi-monochromatic radiative heat transfer !

35. Near-field radiative heating of a nanoparticle
SiC
 1/d3 d T
Sphere radius r = 5 nm
The absorption increases as 1/d3 in the near field
8 orders of magnitude between d=10 mm and d=10 nm
Mulet et al., Appl. Phys. Lett. 78, 2931 (2001)

36. Application : near-field thermophotovoltaics
thermal source
T= 2000 K
T= 6000K
thermal source
T= 2000 K
d << rad
PV cell
T= 300 K
TPV cell
T= 300 K
TPV cell
T= 300 K

37. Output electric power 50 3000 d TPV cell (T = 300K) T= 2000 K
tungsten source
quasi-monochromatic source
near field : W/m2
near field : W/m2
Pel (W. m-2)
50
Pel (W. m-2)
3000
far field :3.104 W/m2
BB 2000 K
far field : W/m2
BB 2000 K
d (m)
d (m)
Laroche, Carminati, Greffet, J. Appl. Phys. 100, (2006)

38. Efficiency of a near-field TPV system
T= 2000 K d
TPV cell (T = 300K)
quasi-monochromatic source
tungsten source
 (%)
d (m)
d (m)
 (%)
near field : 35%
near field : 27%
far field : 21 %
far field : 8 %
BB 2000 K
BB 2000 K
Laroche, Carminati, Greffet, J. Appl. Phys. 100, (2006)