Introducing a general method for solving electromagnetic radiation problem in an arbitrary linear medium

Abstract

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.

26 pages, 2 figures, accepted for publication in Phys. Rev. A

References in corpus (4)

• Fundamental transfer matrix and dynamical formulation of stationary scattering in two and three dimensions
• One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
• A Class of Exactly Solvable Scattering Potentials in Two Dimensions, Entangled State Pair Generation, and a Grazing Angle Resonance Effect
• Spectral singularities and tunable slab lasers with 2D material coating