Department of Mathematics and Statistics
Arizona State University
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.