Inverse Scattering Problem for the Wave Equation in a One-Dimensional Inhomogeneous Medium

A one-dimensional inverse scattering problem for the Helmholtz wave equation is considered. The problem consists in reconstruction of the refractive index of transparent inhomogeneous media from a specified complex reflection spectrum. A method previously proposed by the authors for reconstruction of the Bragg gratings in the coupled mode approximation is used. Numerical simulations of the inverse scattering problem for the classical Rayleigh layer and for an exponentially smooth transitional layer are performed. The solutions obtained demonstrate the high efficiency of the proposed approach. The accuracy of refractive index reconstruction turns out to be essentially dependent on the degree of layer smoothness. The proposed approach can be applied in problems of the development of coated and interference optics, in synthesis of the Bragg gratings and multilayer optical mirrors, and in radiophysics and acoustics.