Reconstruction of coupling profiles for scattering media by the Schur algorithm combined with an extrapolation method

We demonstrate an efficient inverse scattering algorithm for reconstructing the coupling profiles or reflection coefficients of a discrete layered medium. The method, called the Schur algorithm combined with an extrapolation method, is based on solving the coupled-mode differential equation in a layer-peeling procedure with a simple extrapolation scheme. In order to reduce the estimation errors caused by discretization of an inhomogeneous medium, we analyze the error propagation of inverse scattering with the Schur algorithm (layer-peeling method) and propose the extrapolation scheme. Numerical examples are provided that compare the Schur algorithm combined with an extrapolation method to the general Schur algorithm in a coarse discretization environment. The comparison shows that the proposed method produces a more accurate reconstruction with a lower order of complexity.