Transmission of Electromagnetic Waves Through Plane-Parallel Layers Under Total Reflection Conditions

Introduction. The boundary value problem for the re? ectance (transmittance) of transparent plane-parallel layers in the plane wave approximation has already been discussed in the scientio c literature [1–3]. Thus, analytic expressions have been obtained [1] for the amplitude (and energy) re? ectances and transmittances of layers in the special cases of linearly polarized incident waves for which the azimuth of the wave oscillations (the angle between the electric o eld vector of the wave and the plane of incidence) is equal to zero or to Σ/2, i.e., with s- and p-polarization. In an examination [3] of the same problem of the transmission of linearly polarized radiation through a plane-parallel layer, primary attention was paid to a detailed analysis of the phase shifts between the s- and p-polarizations in the re? ected and transmitted radiation. (A solution to a similar boundary problem for an amplifying layer is given in [4], but also only for the special cases of s- and p-polarization.) In this paper we consider the more general case of polarization where the azimuth of the oscillations of an incident linearly polarized wave can take arbitrary values ranging from zero to �a /2. This represents a generalization of the earlier results for the special cases of s- and p-polarization. Calculations. Let a layer of thickness h and refractive index n2 = H2 be in contact with surrounding transparent