Nonstandard Finite Difference Time Domain Methodology to Simulate Light Propagation in Nonlinear Materials

We extend the nonstandard (NS) finite difference time domain (FDTD) methodology, originally developed to solve Maxwell’s equations in linear materials, to nonlinear ones. We validate it by computing harmonics generation in a nonlinear dielectric and comparing with theory. The methodology also applies to the quantum electrodynamics that describes the interaction of charged particles with electromagnetic fields, and also to the Ginzburg-Landau model of superconductivity.