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

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  • Norgren, Martin

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.

Suggested Citation

  • Norgren, Martin, 1999. "Optimization approaches to frequency-domain inverse problems for Kerr-like and non-Kerr-like nonlinear media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 50(5), pages 553-575.
    • Handle: RePEc:eee:matcom:v:50:y:1999:i:5:p:553-575
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