Scientific Computing Group Seminars - Detail View

Speaker: H. Zhou

Affiliation: Georgia Institute of Technology

Talk Title: Fast Numerical Methods for Stochastic Maxwell Equations and Applications in Photonic Crystal Spectrometer Design

Notes: Note -- special time for semiar

Time: May 02 2007 3 p.m.

Location: 182 George Street, Room 110

Abstract:

The simplest form of the photonic crystal is a one-dimensional periodic structure, such as a multilayer film (a Bragg mirror). A prominent example of the photonic crystal phenomenon is the naturally occurring gemstone opal. Its play of colors is essentially a photonic crystal phenomenon based on Bragg diffraction of light on the crystal's lattice planes. In this presentation, we propose a new stochastic model for general spatially incoherent sources with applications to photonic crystal spectrometer design .The model naturally incorporates the incoherent property and leads to stochastic Maxwell equations. We propose fast numerical methods based on Wiener Chaos Expansions (WCE), which converts the random equations into system of deterministic equations, so that they can be solved using efficient deterministic methods. Comparing to the Monte Carlo methods for stochastic PDE's, the WCE methods are more efficient and have better error control. In addition, they do not require random number generation. In applications to the photonic crystal, the new method provides up to two orders of magnitude improvement in the speed of computations as compared to the standard methods. This is a joint work with S.N. Chow, Ali Adibi and M. Badiei.