Abstract

The Finite-Difference-Time-Domain (FDTD) treatment of electromagnetic pulse propagation holds much promise for the complete numerical description of integrated optical device behavior where reflections and/or coherent effects are important. The recent application of FDTD to problems in integrated optics³ has indicated that electronic dispersion must be included to treat realistically the broadband behavior of integrated optical devices. The inclusion of material dispersion (electronic or magnetic) in FDTD calculations has historically been quite limited. The first formulation of broadband dispersion in FDTD was presented in a pioneering paper by Luebbers et. al.⁴ who demonstrated that if the electronic susceptibility was expanded as a series of exponentials that the treatment of dispersion could be reduced to a recursive update. The incorporation of this update, however, requires a substantial rewriting of the standard electric field update equations. More recently, Lee et. al.⁵ and Joseph et. al.⁶ demonstrated a different formulation to the linear problem in which they solve explicitly the equation of motion for the polarizability using finite- differencing. Goorjian and Taflove⁷ have extended this alternative formulation to nonlinear optical propagation. In this paper we follow the general approach of Luebbers et. al. but exploit a simple causality argument that enables us to write dispersion as a simple recursive additive term in the common electric field update equations. This is of particular interest since it will enable the treatment of dispersion in a large number of existing FDTD design codes with minimal computational modification. We then demonstrate the accuracy of our formulation by simulating the reflection of a broadband pulse from an air-water interface.

© 1993 Optical Society of America