Saturable Lorentz model for fully explicit three-dimensional modeling of nonlinear optics

TL;DR

This paper introduces a fully explicit, stable Lorentz model for nonlinear optics that accurately reproduces quantum mechanical polarization effects, enabling efficient simulation of intense laser phenomena like filamentation.

Contribution

A novel saturable harmonic oscillator model that provides an explicit, stable, and accurate method for simulating nonlinear optical effects in three dimensions.

Findings

Reproduces quantum harmonic generation up to the 9th harmonic

Enables stable explicit leapfrog integration for intense fields

Accurately models nonlinear polarization in laser filamentation

Abstract

Inclusion of the instantaneous Kerr nonlinearity in the FDTD framework leads to implicit equations that have to be solved iteratively. In principle, explicit integration can be achieved with the use of anharmonic oscillator equations, but it tends to be unstable and inappropriate for studying strong-field phenomena like laser filamentation. In this paper, we show that nonlinear susceptibility can be provided instead by a harmonic oscillator driven by a nonlinear force, chosen in a way to reproduce the polarization obtained from the solution of the quantum mechanical two level equations. The resulting saturable, nonlinearly-driven, harmonic oscillator model reproduces quantitatively the quantum mechanical solutions of harmonic generation in the under-resonant limit, up to the 9th harmonic. Finally, we demonstrate that fully explicit leapfrog integration of the saturable harmonic oscillator is stable, even for the intense laser fields that characterize laser filamentation and high harmonic generation.