Document Type

Article

Publication Date

3-1-2007

Publication Title

SIAM Journal on Applied Mathematics

Abstract

For homogeneous lossless three-dimensional periodic slabs of fixed arbitrary geometry, we characterize guided modes by means of the eigenvalues associated with a variational formulation. We treat robust modes, which exist for frequencies and wavevectors that admit no propagating Bragg harmonics and therefore persist under perturbations, as well as nonrobust modes, which can disappear under perturbations due to radiation loss. We prove the nonexistence of guided modes, both robust and nonrobust, in "inverse" structures, for which the celerity inside the slab is less than the celerity of the surrounding medium. The result is contingent upon a restriction on the width of the slab but is otherwise independent of its geometry.

Volume

67

Issue

3

First Page Number

687

Last Page Number

713

DOI

10.1137/050647189

Publisher Statement

© 2007, SIAM Publications.

Included in

Mathematics Commons

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