Existence of guided modes on periodic slabs

Stephen P. Shipman; Darko Volkov

doi:10.3934/proc.2005.2005.784

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2005, Volume 2005: 784-791. Doi: 10.3934/proc.2005.2005.784 open access

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Existence of guided modes on periodic slabs

Stephen P. Shipman^1, and
Darko Volkov^2,

1.
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803
2.
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609

Received: September 2004

Revised: March 2005

Published: September 2005

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Abstract

We prove the existence of bound guided modes for the Helmholtz equation on lossless penetrable periodic slabs. We handle both robust modes, for which no Bragg harmonics propagate away from slab, as well as nonrobust standing modes, which exist in the presence of propagating Bragg harmonics. The latter are made possible by symmetries of the slab structure, which prevent coupling of energy to the propagating harmonics. These modes are isolated in wavevector-frequency space, as they disappear under a perturbation of the wavevector. The main tool is a volumetric integral equation of Lippmann-Schwinger type that has a self-adjoint kernel.

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Mathematics Subject Classification: 78A25.

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