High-frequency asymptotics for Maxwell’s equations in anisotropic media Part I: Linear geometric and diffractive optics

Abstract

This paper is devoted to the derivation of the equations that govern the propagation of pulses in noncentrosymmetric crystals. The method is based upon high-frequency expansions techniques for Maxwell’s equations. By suitable choices of the scalings we are able to derive two classical models: Geometric optics and diffractive optics (Schrödinger-type equations). In the so-called geometric regime we recover the standard results on the propagation of pulses in crystals (dispersion equation, polarization states, group velocity). In the diffractive regime we exhibit original results and give a closed-form expression for the diffraction operator which reads as an anisotropic operator. Given this expression we identify a critical configuration where the diffraction reduces to a one-dimensional second-order operator instead of the standard transverse Laplacian.