General aspects of Hertzian potentials modeling in integrated optics

This work introduces a novel time-domain numerical simulator of integrated optical waveguides. Only solutions of two scalar Helmholtz-equations are used in the evaluation of electric and magnetic Hertzian-potentials that yields the electromagnetic field in the time domain, and the frequency response by the discrete Fourier transform. All the field components are obtained directly from the scalar potentials, and are not interrelated as in finite-difference time domain method. The Hertzian potential method (HPM) considers the field-perturbation effect in proximity of the dielectric discontinuities by generators modeling and takes into account the numerical error of a wave that travels in a dielectric multilayered optical guide. We present in this work the general finite difference discretization and the numerical setting of the HPM related to optical waveguide full-wave modeling. Copyright (C) 2011 John Wiley & Sons, Ltd.