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Near-field thermal radiation

Near-field thermal radiation. Rémi Carminati Laboratoire EM2C CNRS, Ecole Centrale Paris France. remi.carminati@ecp.fr. Acknowledgments. K. Joulain (Poitiers). C. Henkel (Potsdam). Y. De Wilde (Paris). J.-J. Greffet (Paris). J.J. Sáenz (Madrid).

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Near-field thermal radiation

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  1. Near-field thermal radiation Rémi Carminati Laboratoire EM2C CNRS, Ecole Centrale Paris France remi.carminati@ecp.fr

  2. 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 T L • 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

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

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

  6. L << l L << lcoh L << lL << lcoh L << d WavesNear field (surface waves)CoherenceInterferencesNon localityVolume radiation Small is different Classical theory Mesoscopic scale • Ray optics • Incoherent summationof intensities (fluxes) • Local radiative properties • Opaque bodies(surface properties)

  7. Near-fieldblackbody 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 Blackbody radiation : w peak Surface electromagnetic modes (surface polaritons) • Surface modes modify the LDOS • Evanescent modes : near-field effect Bose-Einstein distribution Energy density Photon energy LDOS

  10. LDOS above an aluminum surface d • 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, 245405 (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 Metal (Au) with surface plasmon Cristal (SiC) with surface phonon Coherence length ~ decay length of the polariton Example : 36 l for SiC at l = 11.36 mm Blackbody radiation Field spatial correlation T Carminati, Greffet, PRL 82, 1660 (1999)

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

  14. Playing with surface modes : Coherent thermal emission

  15. Antenna versus standard thermal source Antenna Thermal source T HF • Interferences produce directivity • Interferences if the fields are correlated along the antenna

  16. Period : 6.25 mm Height : 0.285 mmFill factor : 0.5 Design of coherent thermal sources(surface phonon polaritons) q l Ksw Principle : grating coupling SiC

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

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

  19. Emission pattern at different wavelengths Marquier et al., Phys. Rev. B. 69, 155412 (2004)

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

  21. Highly-directional near-infrared tungsten source Emission pattern Theory Measured emissivityat = 4.53 m Experiment Dq = 0.9° ≈ CO2 laser Lcoh = 154 l (0.7 mm) Laroche et al., Opt. Lett. 30, 2623 (2005) a = 3 mm, h = 0.125 mm Fill factor 0.5

  22. Emissivity Observation angle Surface waves on photonic-crystal slabs Angular thermal emission pattern atl = 1.55 mm Ge Dq = 0.6° Lcoh = 40 l (60 mm) Laroche, Carminati, Greffet, PRL 96, 123903 (2006)

  23. Measurement of thermal near fields :Thermal Radiation STM

  24. HgCdTe Thermal radiation STM (experiments) De Wilde et al., ESPCI (Paris) (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. Tunneling current Matrix element Example : Tersoff and Hamman theory (1983) First interpretation of the STM signal Bardeen’s formalism in the context of STM Nature 363, 524 (1993)

  28. SNOM signal : Generalized Bardeen’s formalism 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, 245405 (2003)

  30. Radiative transfer at small scales

  31. Radiative heat transfer through a small vacuum gap T1 f 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. hR 1/L2 Ballistic conduction in air Classical value Radiative heat-transfer coefficient SiC - SiC, T = 300 K SiC L SiC 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/d3in 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. TPV cell PV cell T= 300 K T= 300 K Application : near-field thermophotovoltaics Near-field thermophotovoltaics Photovoltaics Thermophotovoltaics thermal source T= 2000 K T= 6000K thermal source T= 2000 K d << rad TPV cell T= 300 K

  37. Output electric power T= 2000 K d TPV cell (T = 300K) tungsten source quasi-monochromatic source near field :15.105 W/m2 near field : 2.5.106 W/m2 Pel (W. m-2) 50 3000 Pel (W. m-2) far field :3.104 W/m2 BB 2000 K far field : 1.4.103 W/m2 BB 2000 K d (m) d (m) Laroche, Carminati, Greffet, J. Appl. Phys. 100, 063704 (2006)

  38.  (%) d (m)  (%) d (m) Efficiency of a near-field TPV system T= 2000 K d TPV cell (T = 300K) quasi-monochromatic source tungsten source 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, 063704 (2006)

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