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Existence of guided modes on periodic slabs

Pages: 784 - 791, Issue Special, August 2005

 Abstract        Full Text (189.4K)              

Stephen P. Shipman - Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, United States (email)
Darko Volkov - Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, United States (email)

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.

Keywords:  acoustics, electromagnetics, bound state, guided mode, volumetric integral, Lippmann-Schwinger equation, Helmholtz equation, Bloch wave, dielectric, periodic.
Mathematics Subject Classification:  78A25.

Received: September 2004;      Revised: March 2005;      Published: September 2005.