Planar structures cannot emit more heat by radiation than predicted by Stefan- Boltzmann’s law. However, when two reservoirs are connected by an intermediate slab which is placed in their near-field one can in principle observe a super-Planckian heat flux at separation distances larger than the thermal wavelength, if the evanescent contributions can be perfectly guided through the intermediate slab. In this case study we discuss in particular how the thermal near-field of the surface modes of two SiC reservoirs can be guided through an ideal dielectric, a perfect lens and a hyperbolic waveguide. A detailed study of the parameters needed in order to have a long-range guiding of thermal radiation shows which properties are ideally needed in order to observe a super-Planckian heat flux. In particular hyperbolic materials which are known for their large penetration depth of radiative heat fluxes are promising materials. This result opens the way to long distance transport of near-field thermal energy.

We show that the electromagnetic forces generated by the excitations of a mode in graphene-based optomechanical systems are highly tunable by varying the graphene chemical potential, and orders of magnitude stronger than usual non-graphene-based devices, in both attractive and repulsive regimes. We analyze coupled waveguides made of two parallel graphene sheets, either suspended or supported by dielectric slabs, and study the interplay between the light-induced force and the Casimir-Lifshitz interaction. These findings pave the way to advanced possibilities of control and fast modulation for optomechanical devices and sensors at the nano- and microscales.

The purpose of this chapter is to present a unified theory for the numerical implementation of modal methods for the analysis of electromagnetic phenomena with specific boundary conditions. All the fundamental concepts that form the basis of our study will be detailed. In plasmonics and photonics in general, solving Maxwell equations involving irregular functions is common. For example, when the relative permittivity is a piecewise constant function describing a dielectric–metal interface, the eigenmodes of the propagation equation are solutions of Maxwell's equations subject to specific boundary conditions at the interfaces between homogenous media. Prior knowledge about the eigenmodes allows one to define more appropriate expansion functions, and the rate of convergence of the numerical scheme will depend on the choice of these functions. In this chapter, we present and explain, a unified numerical formalism that allows one to build, from a set of subsectional functions defined on a set of subintervals, expansion functions defined on a global domain by enforcing certain stresses deduced from electromagnetic field properties. Then numerical modal analysis of a plasmonic device, such as a ring resonator, is presented as an example of an application.

We present a numerical approach for the solution of the dissipative Gross-Pitaevskii equation coupled to the reservoir equation governing the exciton-polaritons Bose-Einstein condensation. It is based on the finite difference method applied to space variables and on the fourth order Range-Kutta algorithm applied to the time variable. Nu- merical tests illustrate the stability and accuracy of the proposed scheme. Then results on the behavior of the con- densate under large Gaussian pumping and around the threshold are presented. We determine the threshold through the particular behavior of the self-energy and characterize it by tracking the establishment time of the steady state.

Heat flux exchanged between two hot bodies at subwavelength separation distances can exceed the limit predicted by the blackbody theory. However, this super-Planckian transfer is restricted to these separation distances. Here we demonstrate the possible existence of a super-Planckian transfer at arbitrary large separation distances if the interacting bodies are connected in the near field with weakly dissipating hyperbolic waveguides. This result opens the way to long-distance transport of near-field thermal energy.

I will present our studies of the Casimir-Lifshitz interaction in a system consisting of two different one-dimensional dielectric lamellar gratings at two different temperatures, immersed in an environment having a third temperature [1]. The calculations are based on the knowledge of the scattering operators, obtained through the Fourier modal method. It will be shown that the interplay between non-equilibrium effects and geometrical periodicity offers a rich scenario for the manipulation of the force. Finally I will present our latest results on a sphere-grating system at equilibrium [2]. 

Heat transfer or between bodies and Casimir-Lifshitz (CL) interactions between them share in common the fact that they can be characterized by the electromagnetic response of these bodies. It has been shown, in the framework of a general theory [1], that the knowledge of the so-called scattering matrix of an object is sufficient to perform its thermal of Casimir interaction with another body. Among the different configurations studied experimentally, those involving gratings and spheres are of special interest. From the theoretical point of view, when one is equipped with the scattering matrix based theory [1], it is “in principle” straightforward to compute the heat transfer or the CL force. In reality, it turns out that computing the S-matrices is not that easy, especially when it has to be determined for a huge number of modes. It is thus of fundamental importance to use extremely efficient methods. We will discuss the different families of existing approaches for diffraction gratings and examine in more details one of the most efficient ones: the Fourier Modal Method that we used recently to compute CL interactions between gratings out of thermal equilibrium [2] and between a sphere and a grating [3].