Abstract

We propose a new algorithm, data-compatible T-matrix completion (DCTMC), for numerically solving nonlinear inverse scattering problems (ISPs). Instead of directly searching for the unknown interaction matrix V, we treat the corresponding T-matrix as the fundamental unknown. While this creates a very underdetermined problem, it is simple to find solutions that are compatible with the data. Moreover, we know any reasonable choice of T must correspond to a diagonally dominated solution V. This allows us to iteratively update T to search for a corresponding diagonal V, while keeping data compatibility intact. Numerical simulations for scalar wave diffraction have demonstrated promising results for DCTMC as a nonlinear solver. Moreover, computational improvements as well as variants of DCTMC have outperformed several Newton-type solvers in large-scale simulations.

© 2016 Optical Society of America