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The purpose of this paper is to present a new and accurate, fully explicit finite-difference time-domain method for modeling nonlinear electromagnetics. The approach relies on a stable algorithm based on a general vector auxiliary differential equation in order to solve the curl Maxwell’s equation in a frequency-dependent and nonlinear medium. The energy conservation and stability of the presented scheme are theoretically proved. The algorithms presented here can accurately describe laser pulse interaction with metals and nonlinear dielectric media interfaces where Kerr and Raman effects, as well as multiphoton ionization and metal dispersion, occur simultaneously. The approach is finally illustrated by simulating the nonlinear propagation of an ultrafast laser pulse through a dielectric medium transiently turning to inhomogeneous metal-like states by local free-electron plasma formation. This free carrier generation can also be localized in the dielectric region surrounding nanovoids and embedded metallic nanoparticles, and may trigger collective effects depending on the distance between them. The proposed numerical approach can also be applied to deal with full-wave electromagnetic simulations of optical guided systems where nonlinear effects play an important role and cannot be neglected.

Full Explicit Numerical Modeling in Time-Domain for Nonlinear Electromagnetics Simulations in Ultrafast Laser Nanostructuring