Quantization of electromagnetic field in an inhomogeneous medium based on scattering matrix formalism (S-quantization)

Abstract

We have developed a procedure for quantization of the electromagnetic field in a layered inhomogeneous media based on analysis of the eigenvalues of the scattering matrix (S-matrix). In contrast to the method involving quantization of the electromagnetic field, involving the use of periodic boundary conditions (Born–von Karman conditions), the proposed procedure (S-quantization) is based on equality of the amplitudes of waves incident on a quantization box and waves outgoing from the quantization box, which is equivalent to equating unity eigenvalues of the scattering matrix. We perform a comparison of the density of states and spatial structure of the field calculated with periodic boundary conditions and using the procedure of S-quantization.