Interaction of Light with Arbitrarily Shaped Dielectric Media: Compactness and Robustness in Electromagnetic Scattering

Monday, April 12, 2010 -
4:00pm to 6:00pm
The scattering of electromagnetic waves by homogeneous dielectric media is characterized by a strongly singular integral equation, corresponding to the identity operator perturbed by a non-compact Green operator. Using the Kondrachov-Rellich compact imbedding and the Calderon-Zygmund theory, we prove that the Green operator is polynomially compact if the dielectric boundary is a compact smooth manifold. We then show that the electromagnetic scattering problem admits a robust solution for all non-accretive media ($\mathrm{Im}\chi\leq0$) satisfying certain geometric and topological constraints, except for the critical point $\chi=-2$, where unbounded electromagnetic enhancement may occur. Combining the polynomial compactness of the Green operator with the Arendt-Batty-Lyubich-Vu theorem in semigroup theory, we devise a non-perturbative approach to the solution of electromagnetic scattering problem, as an improvement of the Born approximation.This work was part of the speaker's PhD thesis project completed at Harvard University.
Yajun Zhou
Princeton University
Event Location: 
Fine Hall 110