Inverse medium scattering for a nonlinear Helmholtz equation
In this paper, the authors discussed a direct and inverse scattering problem for a class of nonlinear Helmholtz equations in unbounded free space. Assuming that the intensities of the incident waves are sufficiently small relative to the size of the nonlinearity, they established existence and uniqueness of solutions to the direct and inverse scattering problem, and showed that the nonlinear index of refraction is uniquely determined based on linearization techniques and estimates for the linearization error. The authors also generalized two shape reconstruction methods, a factorization method and a monotonicity method, to recover the support of such nonlinear scattering objects. Numerical results were also provided to illustrate their theoretical findings.
scientific article