General method for solving electromagnetic radiation problems in an arbitrary linear medium

Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as discretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms of the evolution operator for an effective nonunitary quantum system. We use the fundamental transfer matrix to develop a general method for the solution of the problem of radiation of an oscillating source in an arbitrary, possibly nonhomogeneous, anisotropic, and active or lossy linear medium. This allows us to obtain an analytic solution to this problem for an oscillating source located in the vicinity of a planar collection of possibly anisotropic and active or lossy point scatterers such as those modeling a two-dimensional photonic crystal.