Optimization approaches to frequency-domain inverse problems for Kerr-likeand non-Kerr-like nonlinear media

Two different kinds of frequency-domain inverse problems for nonlinear medi a are considered. In the first problem, the linear permittivity and the non linear parameter for a stratified slab of a Kerr-like medium are reconstruc ted as functions of the position from reflection and transmission data by u sing a conjugate gradient method. In the second problem, the nonlinear perm ittivity of a medium with arbitrary nonlinear behavior is reconstructed as a function of the electric field. The nonlinearity is approximated as a rat ional expression in the electric field and a Levenberg-Marquardt method is applied to reconstruct the coefficients in the approximant from reflection and transmission data. The reconstruction algorithms are tested with both c lean and noisy data. A formalism based on dual fields is utilized for a fas t and explicit calculation of gradients and Jacobian matrices. (C) 1999 IMA CS/Elsevier Science B.V. All rights reserved.