Factorization of integro-differential equations of optics of dispersive anisotropic media and tensor integral operators of wave packet velocities

Abstract

The integro-differential one-dimensional tensor wave equations of the electrodynamics of dispersive anisotropic media are factorized. The resulting first-order partial differential equations contain tensor integral functionals that describe light velocities of polarized plane-wave pulses. The velocity operators are written in a compact coordinate-free form. They are defined by kernels of integral representations and provide a general description of the kinematics and dynamics of groups of electromagnetic waves for arbitrary propagation directions and arbitrary initial polarization states in tensor media exhibiting frequency and rotatory dispersion. Some branches of the solutions of wave equations and their spectral representations are analyzed and the relations of these equations to the general systems of Whitham’s wave equations are found.