Session S02 - Diverse Aspects of Elliptic PDEs and Related Problems

Thursday, July 15, 18:00 ~ 18:30 UTC-3

Bloch waves in 3-dimensional high-contrast photonic crystals

Robert Viator

Swarthmore College, United States of America   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We investigate the Bloch eigenvalues of a 3-dimensional high-contrast photonic crystal. The Bloch eigenvalues (for a fixed quasi-momentum) can be expanded in a power series in the material contrast parameter $k$ about $k=\infty$. We achieve this power series, together with a radius of convergence, by decomposing an appropriate vector-valued Sobolev space into three mutually orthogonal subspaces which are curl-free in certain subdomains of the period cell. We will also identify the limit spectral problem as contrast becomes large, and (time permitting) we will describe a class of crystal geometries which permit the power series structure of Bloch eigenvalues described above.

Joint work with Silvia Jimenez (Colgate University) and Robert Lipton (Louisiana State University).

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