Dispersion of electromagnetic waves in stratified and nonstationary media (exactly solvable models)

The propagation and reflection of electromagnetic waves in stratified and nonstationary media are considered on the basis of a unified approach, using exact analytical solutions of Maxwell's equations. In this approach, the spatial structure of a wave field in an inhomogeneous medium is presented as a function of the optical path length of the wave (a one-dimensional problem). These solutions predict strong dispersion of both normal and abnormal types to occur in a given medium, the magnitude of dispersion depending on the gradient and curvature of the continuous smooth profile of the material's inhomogeneous dielectric susceptibility e(z). The effect of such a nonlocal dispersion on the reflection of waves is described by generalized Fresnel formulas. Exactly solvable models are introduced to describe the effects of both monotonic and oscillatory e(t) dependences on the wave dispersion due to the finite relaxation time of the dielectric constant.