The electrodynamics of crystals and the theory of excitons

Abstract

General aspects of the electrodynamics of media with spatial dispersion are discussed in relation to crystals. In particular, the character of the approximation corresponding to the introduction of the tensor of the complex dielectric permeability ϵ ij (ω, χ) is elucidated. Some properties of the tensor ϵ ij are considered and also the problem of its evaluation within the limits of the quantum mechanical theory. The use of the tensor ϵ ij (ω, χ) and field equations are basic to crystal optics taking into account spatial dispersion (normal crystal optics is its limiting case at κ → 0). The tensor ϵ ij (ω, χ) defines all the properties of “normal” electromagnetic waves in a crystal (refractive index, absorption coefficient, polarization), providing the ratio ( a λ 0 ) 2 is sufficiently small (here a is the lattice constant and λ 0 = 2 πc/ ω the wavelength in vacua). Such waves, of course, are identical with the long-wave excitations in crystals that are considered in the exciton theory with adequate allowance for the electromagnetic interaction. Hence, crystal optics, which takes account of spatial dispersion, embraces the corresponding section of the general exciton theory.