Résumé
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].