Resonant phenomena accompanying the scattering of a plane wave on an inhomogeneous layer and on a pack of inhomogeneous layers

Abstract

The problem of scattering of a plane monochromatic wave impinging obliquely on an inhomogeneous plane parallel layer or on a pack of identical inhomogeneous layers, is considered. The inhomogeneity of the medium is described by the dependence of its refractive index n on the coordinate x orthogonal to the layer boundaries. The angle of incidence of the wave is such, that total internal reflection occurs. The case in which the corresponding differential equation has two inflection points, is studied. The coefficients of transmission and reflection are computed for the high frequency region, and it is shown that resonant transmissions are possible when the function n ( x ) exhibits certain symmetry properties, i. e the whole layer is “transparent” for certain angles of incidence even though these angles exceed the critical angle.