Karl Joulain

Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field

We review in this article the influence of surface waves on the thermally excited electromagnetic field. We study in particular the field emitted at subwalength distances of material surfaces. After reviewing the main properties of surface waves, we introduce the fluctuation-dissipation theorem that allows to model the fluctuating electromagnetic fields. We then analyse the contribution of these waves in a variety of phenomena. They give a leading contribution to the density of electromagnetic states, they produce both temporal coherence and spatial coherence in the near field of planar thermal sources. They can be used to modify radiative properties of surfaces and to design partially spatially coherent sources. Finally, we discuss the role of surface waves in the radiative heat transfer and the theory of dispersion forces at the subwavelength scale.

Thermal radiation scanning tunnelling microscopy

In standard near-field scanning optical microscopy (NSOM), a subwavelength probe acts as an optical ‘stethoscope’ to map the near field produced at the sample surface by external illumination. This technique has been applied using visible, infrared, terahertz and gigahertz radiation to illuminate the sample, providing a resolution well beyond the diffraction limit. NSOM is well suited to study surface waves such as surface plasmons or surface-phonon polaritons. Using an aperture NSOM with visible laser illumination, a near-field interference pattern around a corral structure has been observed, whose features were similar to the scanning tunnelling microscope image of the electronic waves in a quantum corral. Here we describe an infrared NSOM that operates without any external illumination: it is a near-field analogue of a night-vision camera, making use of the thermal infrared evanescent fields emitted by the surface, and behaves as an optical scanning tunnelling microscope. We therefore term this instrument a ‘thermal radiation scanning tunnelling microscope’ (TRSTM). We show the first TRSTM images of thermally excited surface plasmons, and demonstrate spatial coherence effects in near-field thermal emission.

ENHANCED RADIATIVE HEAT TRANSFER AT NANOMETRIC DISTANCES

We study in this article the radiative heat transfer between two semi-infinite bodies at subwavelength scale. We show that this transfer can be enhanced by several orders of magnitude when the surfaces support resonant surface waves. In these conditions, we show that the transfer is almost monochromatic.

Nanoscale radiative heat transfer between a small particle and a plane surface

We study the radiative heat transfer between a small dielectric particle, considered as a point-like dipole, and a surface. In the framework of electrodynamics and using the fluctuation-dissipation theorem, we can evaluate the energy exchange in the near field, which is dominated by the contribution of tunneling waves. The transfer is enhanced by several orders of magnitude if the surface or the particle can support resonant surface waves. An application to local heating is discussed.

Monte Carlo transient phonon transport in silicon and germanium at nanoscales

Heat transport at nanoscales in semiconductors is investigated with a statistical method. The Boltzmann transport equation (BTE), which characterizes phonon motion and interaction within the crystal lattice, has been simulated with a Monte Carlo technique. Our model takes into account media frequency properties through the dispersion curves for longitudinal and transverse acoustic branches. The BTE collisional term involving phonon scattering processes is simulated with the relaxation times approximation theory. A new distribution function accounting for the collisional processes has been developed in order to respect energy conservation during phonons scattering events. This nondeterministic approach provides satisfactory results in what concerns phonon transport in both ballistic and diffusion regimes. The simulation code has been tested with silicon and germanium thin films; temperature propagation within samples is presented and compared to analytical solutions (in the diffusion regime). The two-material bulk thermal conductivity is retrieved for temperature ranging between 100 K and 500 K. Heat transfer within a plane wall with a large thermal gradient (250 K to 500 K) is proposed in order to expose the model ability to simulate conductivity thermal dependence on heat exchange at nanoscales. Finally, size effects and validity of heat conduction law are investigated for several slab thicknesses.

Definition and measurement of the local density of electromagnetic states close to an interface

We define unambiguously the local density of electromagnetics states (LDOS) close to an interface. We show that we can measure this LDOS by making a thermal emission spectrum with a near-field scanning optical microscope

Effects of spatial dispersion in near-field radiative heat transfer between two parallel metallic surfaces

We study the heat transfer between two parallel metallic semi-infinite media with a gap in the nanometer-scale range. We show that the near-field radiative heat flux saturates at distances smaller than the metal skin depth when using a local dielectric constant and investigate the origin of this effect. The effect of non-local corrections is analysed using the Lindhard-Mermin and BoltzmannMermin models. We find that local and non-local models yield the same heat fluxes for gaps larger than 2nm. Finally, we explain the saturation observed in a recent experiment as a manifestation of the skin depth and show that heat is mainly dissipated by eddy currents in metallic bodies.

Monte Carlo simulation of phonon confinement in silicon nanostructures: Application to the determination of the thermal conductivity of silicon nanowires

The authors study the thermal conductivity of silicon nanowires by simulation of phonon motion and interactions through a dedicated Monte Carlo model. This model solves the Boltzmann transport equation, taking into account silicon acoustic mode dispersion curves and three phonon interactions (the normal and umklapp processes). The confinement, which limits the thermal conductivity in such structures, is described by diffuse reflection at lateral boundaries of the nanowire without any adjustment by a boundary collision time, which depends on a specularity factor. They compare simulation results to experimental measurements on similar nanostructures. A good agreement is achieved for almost all the considered diameters.

Nanoscale heat flux between nanoporous materials.

By combining stochastic electrodynamics and the Maxwell-Garnett description for effective media we study the radiative heat transfer between two nanoporous materials. We show that the heat flux can be significantly enhanced by air inclusions, which we explain by: (a) the presence of additional surface waves that give rise to supplementary channels for heat transfer throughout the gap, (b) an increase in the contribution given by the ordinary surface waves at resonance, (c) and the appearance of frustrated modes over a broad spectral range. We generalize the known expression for the nanoscale heat flux for anisotropic metamaterials.

Spatial coherence of thermal near fields

We analyze the spatial coherence of the electromagnetic field emitted by a half-space at temperature T close to the interface. An asymptotic analysis allows to identify three different contributions to the cross-spectral density tensor in the near-field regime: thermally excited surface waves, skin-layer currents and small-scale polarization fluctuations. It is shown that the coherence length can be either much larger or much shorter than the wavelength depending on the dominant contribution.