Interfaces between materials having opposite dielectric constants support electromagnetic waves confined close to these interfaces called surface waves. For metals and polar crystals, they are respectively called surface plasmon-polaritons and surface phonon-polaritons. The goal of this thesis is to revisit some theoretical aspects associated to these surface waves.Using the Green formalism, we derive an expression of the surface wave field as a sum of modes. With losses, these waves must have a complex wave vector or frequency. Thus we give two expressions of their field, for each of these cases, and discuss when each of these expressions should be used.We then give the basis of a surface wave Fourier optics and geometrical optics. We derive a 2D Helmholtz equation for surface waves, a Huygens-Fresnel principle for surface waves, and an eikonal equation for surface waves. We then take a look at Pendry’s superlens, in which surface waves play a major role. We study the behavior of the superlens in pulsed mode taking losses into account, and show that its resolution can be increased for some pulse shapes compared to the steady state, at the expense of a signal decay.We then develop a quantum treatment of surface waves. We first calculate their energy, and then give an expression of their hamiltonian and field operators. Without losses, we show that the Purcell factor given by our quantum theory is perfectly equal to the Purcell factor given by the classical theory. We then compare this Purcell factor to the lossy case on an example, and show that losses can often be neglected. We then derive the Einstein coefficients associated to surface wave emission and absorption, which allow studying the population inversion dynamics of a gain medium. We then use this quantum formalism to study the interaction between electrons and surface phonon-polaritons in quantum wells, particularly their interaction with a phonon mode which features high confinement thanks to an epsilon near zero (ENZ) effect.
