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

Martin Norgren

Mathematics and Computers in Simulation (MATCOM), 1999, vol. 50, issue 5, 553-575

Abstract: Two different kinds of frequency-domain inverse problems for nonlinear media are considered. In the first problem, the linear permittivity and the nonlinear parameter for a stratified slab of a Kerr-like medium are reconstructed as functions of the position from reflection and transmission data by using a conjugate gradient method. In the second problem, the nonlinear permittivity of a medium with arbitrary nonlinear behavior is reconstructed as a function of the electric field. The nonlinearity is approximated as a rational 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 clean and noisy data. A formalism based on dual fields is utilized for a fast and explicit calculation of gradients and Jacobian matrices.

Keywords: Nonlinear media; Inverse problem; Kerr media; Optimization; Gradient; Dual fields (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:50:y:1999:i:5:p:553-575

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