Computational and Applied Math Proseminar

Department of Mathematics and Statistics
Arizona State University

Thursday, November 4, 2002, 3:40 p.m. in GWC 604

Jan S. Hesthaven

Division of Applied Mathematics
Brown University

High-Order Accurate Computational Methods for Micro Optics

Abstract The modeling and design of diffraction dominated micro optics continues to challenge existing computational methods. This can be traced to a number of issues, e.g., high phase sensitivity, large electric, yet finite, size and significant geometric complexity. The significant current interest in integrated optics and MOEMS suggests that the development of new computational tools are timely and required.

Motivated by a few examples, we shall discuss some of the difficulties associated with the modeling of micro optics in a bit more detail. This leads to the discussion of two complementary computational techniques which we are currently pursuing.

The first one, a spectral multi-element scheme, solves Maxwell's equations in the time-domain in general heterogeneous geometries. This technique is entirely general, albeit typically too expensive to be used in a design loop. We shall discuss the central elements of the formulation.

The second approach, a boundary variation technique, solves Maxwell's equations in the frequency domain by means of a high-order perturbation technique. This approach is characterized by being extremely efficient, however, more limited in its application.

We shall illustrate the use of the two methods, compare the accuracy and efficiency, and show a few examples of applications.

This work is done in collaboration with Palle Dinesen, Kaleido Technology, Denmark, and Lucas Wilcox, Brown University.

For further information please contact: mittelmann@asu.edu