2016/03/31 by Charles Varin, Rhys Emms, Graeme Bart +2
Engineering · Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Applied mathematics #Computer science #Electromagnetic field #Electromagnetic field solver #Finite-difference time-domain method #Inhomogeneous electromagnetic wave equation #Laser-Matter Interactions and Applications #Mathematical analysis #Mathematics #Maxwell's equations #Nonlinear system #Optical field #Optics #Photonic and Optical Devices #Physics #Quantum mechanics #physics.comp-ph #physics.optics
paper · pdf · doi:10.1016/j.cpc.2017.09.018
published as Computer Physics Communications, 222, 70-83 (2018) · Final version published in Computer Physics Communications
openalex created_date 2016/06/24 · openalex publication_date 2017/10/10 · arxiv created 2017/12/23 · arxiv updated 2017/12/27 · openalex updated_date 2026/08/05
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.