# American Institute of Mathematical Sciences

2005, 2005(Special): 784-791. doi: 10.3934/proc.2005.2005.784

## Existence of guided modes on periodic slabs

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

Received  September 2004 Revised  March 2005 Published  September 2005

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.
Citation: Stephen P. Shipman, Darko Volkov. Existence of guided modes on periodic slabs. Conference Publications, 2005, 2005 (Special) : 784-791. doi: 10.3934/proc.2005.2005.784
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