Beam propagation in two-dimensional media with spatial dispersion

Abstract

We theoretically investigate the propagation of a paraxial beam in two-dimensional media with spatial dispersion. Based on the spatial dispersion theory and the (1 + 1)-dimensional paraxial wave equation, we get an expression which determines the diffraction of the beam. By fitting the dispersion surface of a typical spatial dispersion medium (a photonic crystal) calculated by the plane-wave-expansion method, the value of the diffraction term is determined, with which one can predict the diffraction of the paraxial beam that propagates in such media. Numerical simulations based on the finite-difference time-domain method confirm the theoretical results.