Abstract

The Born and Rytov methods are applied to a study of the propagation and the scattering of waves in a one-dimensional (1-D) half-space medium with a permittivity either depending on the wave intensity or having a stochastic property. Both Born and Rytov series in the 1-D nonlinear half-space case are compared with their counterparts in a 1-D homogeneous dielectric half-space case. The multiple scattering in a 1-D random half-space, consisting of a host material and randomly distributed scatterers, is treated with a random medium model. We have derived the autocorrelation function for the case in which 1-D scatterers are randomly distributed in a host medium. We show that the autocorrelation function has an exponential-decay shape and depends on the fractional length, the average physical length, and the scattering strength of these scatterers. Under the bilocal approximation the effective permittivity for this 1-D random half-space medium is shown to have an oscillatory dependence on range. When it is applied to estimate the ensemble-averaged scattered fields in the 1-D random half-space case, the Rytov method is not as useful as the Born method because the Rytov method suffers a more serious divergence problem than the Born method.

© 1993 Optical Society of America

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