Radiative Heat Transfer at the Nanoscale. Jean-Jacques Greffet. Institut d’Optique, Université Paris Sud Institut Universitaire de France CNRS. Outline of the lectures. Heat radiation close to a surface Heat transfer between two planes Mesoscopic approach, fundamental limits

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Radiative Heat Transfer at the Nanoscale

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

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

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.

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)

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

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

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

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 ?

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 ?

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

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

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)

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

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

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)

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.

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)