Reflection of electromagnetic waves from nonstationary media (exactly solvable models)

An analysis is made of propagation of electromagnetic waves in media which are nonstationary because of relaxation of the refractive index. A series of models of oscillatory and transient regimes of such relaxation is developed. Several characteristic times are used in these models and exact analytic solutions of the Maxwell equations can be obtained for these regimes. In contrast to the traditional approaches, the exact solutions are obtained without assuming smallness or slowness of temporal variations of the parameters of the medium and these solutions are valid even when the characteristic relaxation time is comparable with the period of oscillations of the wave field. A nonstationary generalisation of the Fresnel formulae is derived. It is shown that waves reflected from a nonstationary surface experience amplitude and frequency modulation, and the modulation effect is localised in an interval of the order of one relaxation time. It is shown that a short broadband perturbation pulse forms in the reflected wave and that this pulse contains one or several oscillations of the field. It should be possible to use nonstationary broadening of the spectrum of a probe wave reflected from a surface perturbed by a powerful laser pulse in estimating the relaxation times of fast optical processes.