Our recent progress in mathematical analysis and computation of time
harmonic Maxwell's equations in complicated media will be discussed.
For the direct problems, a recent regularity result will be introduced.
Various types of boundary conditions will be reviewed to reduce
the scattering problem into a bounded domain. In particular, 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 the uncertainty principle
will be presented for multiple frequency boundary data. Issues on
convergence will be addressed. Our on-going research on related topics
and multiscale modeling of nano optics will be highlighted.
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