FIT-formulation for non-linear dispersive media

Abstract

A new approach using FIT‐formulation (Finite Integration Technique) (T. Weiland, Electron. Commun., 31, 116–120 (1977); Int. J. Numer. Model., 9, 295–319 (1996)) for simulating waveguide propagation of optical pulses is presented. FIT‐methods are widespread in use for broadband linear simulations. In recent years, several attempts have been made to describe different dispersive material‐characteristics such as Drude, Debye or Lorentz dispersion. Today advanced FDTD‐formulations (Finite Difference Time Domain) also consider non‐linear effects (P. M. Goorjian and A. Taflove, IEEE Opt. Lett., 17(3), 180–182 (1992); D. M. Sullivan, IEEE Trans. Microwave Theory Techniques, 43(3), 676–682 (1995)). In the following presented method third‐order non‐linear effects were described, which can be observed in isotropic media in frequency ranges of optical pulses, by updating material polarization terms using classical descriptions of Lorentz dispersion, Raman scattering and the Kerr effect. The basic idea is transforming these description formulas into sets of linear differential equations and solving them with the help of the general exponential solution. Copyright © 1999 John Wiley & Sons, Ltd.

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