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

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.