Inverse scattering method for one-dimensional inhomogeneous layered media

Abstract

An inverse scattering method to reconstruct simultaneously the permittivity profile and the conductivity profile of one-dimensional inhomogeneons medium which makes use of the transverse electric (TE) wave and/or transverse magnetic (TM) wave, is proposed. The medium is illuminated by the TE and/or TM plane wave at oblique incidence, and the data are taken as the reflection coefficients for a set of discrete frequencies and/or a finite number of incident angles. Furthermore, the reflection coefficient data contain the Gaussian noise. The nonlinear integral equation relating the unknown constitutive parameter of the medium to the reflection coefficient for TE wave and/or TM wave is solved by the Newton iteration method. The inverse operator in the Newton method is determined by the regularization method. It is demonstrated in terms of the numerical examples that this method utilizing both polarizations and the incident angle of the incident plane wave is very effective even if the reflection coefficient contains the practical measurement error, or the phase of the reflection coefficient is unknown. Moreover, the relationships between the errors of reconstructed profile and the measured reflection coefficient are also discussed.