Time domain optical wave propagation method.

摘要

Computer-aided design of optical integrated circuits relies on fast and accurate implementation of Maxwell's equations. However, in the optical domain, this simulation can often take hundreds of megabytes of memory. Therefore, a re-investigation into the wave equation was in order. Much reduction can be made if one were to extract dominant physical behavior. By extracting the center frequency from the optical field, a slowly-varying temporal field is left. The same can be done for forward-propagating waves in space. The final equation is called the Wave Propagation Method (WPM) equation. This equation is solved with the union of both the Method of Characteristics and also the exponential operator expansion. Each of these solution techniques are studied fully. The WPM approach is then applied to longitudinally invariant waveguides as well as adiabatic longitudinally variant waveguides. The propagation constant is found for an analytically solvable diffused waveguide profile. The numerical result is shown to match this propagation constant quite accurately, thus validating the WPM approach. Therefore, the overall numerical efficiency is much better than the current finite-difference time-domain method and should prove to be a useful technique for time-domain optical wave propagation.