Guided Modes in Periodic Slabs: Existence and Nonexistence

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...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 2007-01, Vol.67 (3), p.687-713
Main Authors: Shipman, Stephen, Volkov, Darko
Format: Article
Language:English
Subjects:
Coefficients
Dielectric materials
Eigenfunctions
Eigenvalues
Fourier coefficients
Geometry
Harmonics
Helmholtz equations
Integers
Nonexistence
Radiation
Symmetry
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Summary: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.
ISSN:0036-1399
1095-712X
DOI:10.1137/050647189