A new FDTD scheme for Maxwell's equations in Kerr-type nonlinear media

In this paper, we develop a totally new direct finite difference solver for solving the Maxwell's equations in Kerr-type nonlinear media. The direct method is free of iteration error and more efficient than the classic iteration method. We also prove the continuous stability for the Kerr model and the discrete stability for the proposed scheme. Extensive numerical results are presented to validate our analysis.