Document Type

Article

Publication Date

4-1-2008

Abstract

For the scalar wave equation in periodic structures, we establish rigorously the manifestation of a spectral bandgap as a frequency interval of exponentially small transmission of energy through a slab of the crystal when the thickness of the slab tends to infinity. We extend the result to slabs that contain a planar defect for frequencies that do not coincide with guided mode frequencies for the defect. For one-dimensional crystals, we prove that the transmission approaches a nonzero value at guided mode frequencies and give an explicit formula for the transmission. The main analytical tool in the multidimensional case is the Calderón boundary integral projectors for the Helmholtz equation. © 2008 World Scientific Publishing Company.

Publication Source (Journal or Book title)

Mathematical Models and Methods in Applied Sciences

First Page

543

Last Page

572

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