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

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.

Effects of exciton-plasmon strong coupling on third harmonic generation by two-dimensional WS2 at periodic plasmonic interfaces

“…[14], further developed and validated in Ref. [15]. We found that this algorithm leads to the same results as obtained by the commonly used GVADE method by Greene and Taflove [16].…”

“…the numerical approach used in this manuscript can be found in Ref. [15]. The numerical convergence in both linear and nonlinear regimes is achieved for the spatial resolution of 3.0 nm and the time step of 0.005 fs.…”

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“…Note that this widely used superposition of uncoupled oscillators provides a valid description of the time-domain polarization only in the limit of linear response. For a generalization to a non-linear Lorentz model see references [24,25].…”

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