Abstract :

The field scattered by a plane composed of several homogenous layers on a perfectly reflecting plane [1]-[6] is generally given by its plane wave expansion (Fourier representation). We here develop another approach to express the field, more suitable for point source illumination. For this, we sum the contributions of modes corresponding to zeros 14 (or poles 14 ) of the reflection coefficient of the imperfectly reflecting surface, developing original expressions valid for arbitrary mode, which can be passive or active. Particular attention has been paid to active modes with Reg_j < 0, and to the vicinity of the mode with g_j = -1. We then obtain novel exact expressions for the field in acoustics and for potentials in electromagnetism where singular parts are explicitely extracted.