Explicit formulation of second and third order optical nonlinearity in the FDTD framework

TL;DR

This paper introduces an explicit, computationally efficient method to incorporate second and third order optical nonlinearities into the FDTD framework, simplifying simulations of complex nonlinear optical phenomena.

Contribution

The authors develop a fully explicit nonlinear Lorentz dispersion model for FDTD, eliminating the need for iterative solutions and enabling easier simulation of extreme nonlinear optics.

Findings

Provides a formal derivation from quantum mechanics

Enables transparent and intuitive nonlinear FDTD simulations

Facilitates modeling of laser filamentation and femtosecond micromachining

Abstract

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.