The 2-D Inverse Scattering of Second-Order Nonlinear Media Based on Contrast Source Inversion Method

Optical nonlinear media are the building blocks of nonlinear optics, which are commonly characterized by nonlinear polarizability. The inversion of polarizability for nonlinear media is an important problem in nonlinear optics. However, the maturity and accuracy of nonlinear media inversion methods lag behind those of ordinary linear media inversion methods because analytically and rigorously solving the Maxwell equations with nonlinear media is quite complicated. In order to derive inversion formulas, traditional nonlinear media inversion methods have to make various physical or mathematical approximations to the Maxwell equations. Essentially, the inversion of polarizability in nonlinear media belongs to the inverse scattering problem. Inspired by the advantages of numerical algorithms for solving the inverse scattering problem in linear media, we generalize the contrast source inversion method, which is one of the most popular methods for linear media, to second-order nonlinear media. The two-dimensional media distribution and undepleted-pump approximation are considered. Numerical tests conducted on either transverse magnetic or transverse electric data or joint data show that the generalized method can successfully reconstruct the nonlinear media distributions, and the joint inversion gives the best reconstruction quality in all test cases.