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