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

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

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

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

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

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

Near-field blackbody radiation

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)

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

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, 245405 (2003)

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

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 = 11.36 mm Blackbody radiation Field spatial correlation T Carminati, Greffet, PRL 82, 1660 (1999)

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)

Playing with surface modes : Coherent thermal emission

Antenna versus standard thermal source HF Interferences produce directivity Interferences if the fields are correlated along the antenna

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

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

Angular emission pattern at l = 11.36 mm q 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)

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

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

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

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, 123903 (2006)

Measurement of thermal near fields : Thermal Radiation STM

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

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)

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

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

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

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)

Radiative transfer at small scales

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

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)

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)

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

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)

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

Output electric power 50 3000 d TPV cell (T = 300K) T= 2000 K tungsten source quasi-monochromatic source near field :15.105 W/m2 near field : 2.5.106 W/m2 Pel (W. m-2) 50 Pel (W. m-2) 3000 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)

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, 063704 (2006)