Our recent progress in mathematical analysis and computation of time
harmonic Maxwell's equations in complicated media will be discussed.
For the direct problems, recent regularity results will be introduced.
Various types of boundary conditions will be discussed to reduce
the scattering problem into a bounded domain. The first convergence
analysis of the recent Perfect Matched Layer (PML) approach for Maxwell's
equations will be presented. For the inverse medium scattering,
a continuation approach based on uncertainty principle will be
presented for both multiple and fixed frequency boundary data.
Issues on convergence will be addressed. Our on-going research on
related topics and multiscale modeling of nano optics will be