Radiative Heat Transfer at the Nanoscale

1. Radiative Heat Transfer at the Nanoscale Jean-Jacques Greffet Institut d’Optique, Université Paris Sud Institut Universitaire de France CNRS

2. Outline of the lectures • Heat radiation close to a surface • Heat transfer between two planes • Mesoscopic approach, fundamental limits • and Applications d d

3. Outline 1. Some examples of radiative heat transfer at the nanoscale 2. Radiometric approach 3. Fluctuational electrodynamics point of view 4. Basic concepts in near-field optics 5. Local density of states. Contribution of polaritons to EM LDOS 6. Experimental evidences of enhanced thermal fields

4. Heat radiation at the nanoscale : Introduction 0 d Casimir and heat transfer at the nanoscale: Similarities and differences

5. Heat radiation at the nanoscale : Introduction 0 d Casimir and heat transfer at the nanoscale: Similarities and differences Fluctuational fields are responsible for heat transfer and forces between two parallel plates. Key difference: 1. no heat flux contribution for isothermal systems. 2. Spectral range: Casimir : visible frequencies. Heat transfer : IR frequencies.

6. Heat radiation at the nanoscale : Introduction 1 T+DT d T The flux is several orders of magnitude larger than Stefan-Boltzmann law. Microscale Thermophysical Engineering 6, p 209 (2002)

7. Heat radiation at the nanoscale : Introduction 2 d d=10 nm, T=300K Heat transfer can be quasimonochromatic Microscale Thermophysical Engineering 6, p 209 (2002)

8. Heat radiation at the nanoscale : Introduction 3 Density of energy near a SiC-vacuum interface z T=300 K Energy density close to surfaces is orders of magnitude larger than blackbody energy density and monochromatic. PRL, 85 p 1548 (2000)

9. Heat radiation at the nanoscale : Introduction 4 Thermally excited fields can be spatially coherent in the near field. de Wilde et al. Nature (2006)

10. Proof of spatial coherence of thermal radiation Greffet et al., Nature 416, 61 (2002)

11. Modelling Thermal Radiation T+DT The standard radiometric approach d T

12. The standard radiometric approach q

13. The standard radiometric approach Isotropic black body emitter (e=1) What is missing ? Where is the extra energy coming from ?

14. Material with emissivityein front of a black body Kirchhoff’s law: e=a e=1, T1 e, T2 Energy balance for lower medium:

15. Modelling Thermal Radiation The fluctuational electrodynamics approach Rytov, Kravtsov, Tatarskii, Principles of radiophysics, Springer

16. The fluctuational electrodynamics approach T • The medium is assumed to be at local thermodynamic equilibrium volume element = random electric dipole 2) Radiation of random currents = thermal radiation

17. The fluctuational electrodynamics approach 3) Spatial correlation (cross-spectral density) 4) The current-density correlation function is given by the FD theorem Fluctuation Absorption

18. Casimir and Heat transfer d Maxwell-stres tensor can be computed Poynting vector can be computed

19. Dealing with non-equilibrium situation T2+DT T2 d T2 T1 What about the temperature gradient ? Can we assume the temperature to be uniform ?

20. Physical origin of Kirchhoff’s law Kirchhoff’s law: e=a

21. Physical origin of Kirchhoff’s law Physical meaning of emissivity and absorptivity Kirchhoff’s law: e=a T21=T12 1 2

22. Basic concepts of near field What is so special about near field ?

23. Basic concepts of near field Back to basics : dipole radiation 1/r2 and 1/r3 terms Near field 1/r terms Radiation Near field: k0r<<1, k0=2

24. Evanescent waves filtering

25. Basic concepts of near field: evanescent waves Take home message: large k are confined to distances 1/k.

26. Evanescent waves filtering

27. Energy density: in vacuum, close to nanoparticle, close to a surface

28. Black body radiation in vacuum

29. Black body radiation close to a nanoparticle Questions to be answered : Is the field orders of magnitude larger close to particles ? If yes, why ? Is the thermal field quasi monochromatic ? If yes, why ?

30. Black body radiation close to a nanoparticle

31. Black body radiation close to a nanoparticle • The particle is a random dipole. • The field diverges close to the particle: electrostatic field ! • The field may have a resonance, plasmon resonance. Where are these (virtual) modes coming from ?

32. + - + - + - + - - - + - Polaritons Strong coupling between material modes and photons produces polaritons: Half a photon and half a phonon/exciton/electron. +

33. Where are the modes coming from ? Estimation of the number of electromagnetic modes in vacuum: Estimation of the number of vibrational modes (phonons): The electromagnetic field inherits the DOS of matter degrees of freedom

34. Can we define a (larger and local) density of states close to a particle or a surface ?

35. LDOS in near field above a surface LDOS is also used to deal with spontaneous emission using Fermi golden rule Joulain et al., Surf Sci Rep. 57, 59 (2005), Phys.Rev.B 68, 245405 (2003)

36. Lifetime of Europium 3+ above a silver mirror Drexhage, 1970 Local density of states close to an interface

37. Interference effects (microcavity type) Drexhage, 1970 Electrical Engineering point of view Near-field contribution

38. Interference effects (microcavity type) Drexhage, 1970 Quantum optics point of view: LDOS above a surface Near-field contribution

39. Energy density above a SiC surface Density of energy near a SiC-vacuum interface z T=300 K Energy density close to surfaces is orders of magnitude larger than blackbody energy density and monochromatic. PRL, 85 p 1548 (2000)

40. Density of energy near a Glass-vacuum interface z T=300 K

41. Physical mechanism The density of energy is the product of - the density of states, - the energy hn - the Bose Einstein distribution. The density of states can diverge due to the presence of surface waves : Surface phonon-polaritons.

42. First picture of a surface plasmon Dawson, Phys.Rev.Lett.

43. Surface plasmon excited by an optical fiber D Courtesy, A. Bouhelier

44. Dispersion relation of a surface phonon-polariton w k It is seen that the number of modes diverges for a particular frequency. PRB, 55 p 10105 (1997)

45. LDOS in near field above a surface Joulain et al., Surf Sci Rep. 57, 59 (2005), Phys.Rev.B 68, 245405 (2003)

46. LDOS in near field above a surface Joulain et al., Surf Sci Rep. 57, 59 (2005), Phys.Rev.B 68, 245405 (2003)

47. LDOS in the near field above a surface This can be computed close to an interface ! Joulain et al., Surf Sci Rep. 57, 59 (2005), Phys.Rev.B 68, 245405 (2003)

48. LDOS in the near field above a surface Plasmon resonance Electrostatic enhancement

49. Experimental evidence of thermally excited near fields

50. Direct experimental evidence de Wilde et al. Nature 444, p 740 (2006)