99-153 Wally Axmann, Peter Kuchment, Math.Dept, Wichita State University; Leonid Kunyansky, Applied Math. Caltech

Asymptotic methods for thin high contrast 2D PBG materials (5386K, huge PS file) May 8, 99

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Abstract. The paper surveys recent analytic and numerical results on asymptotic models of spectra of EM waves in 2D thin high contrast PBG materials. These models lead to discovery of interesting phenomena, including flat bands that can be used for spontaneous emission enhancement, gaps in the long wave regions, asymptotic periodicity of the spectrum, and others. The asymptotic results provide unexpectedly good qualitative (and sometimes quantitative) description of spectral behavior for materials of finite width and contrast. In some cases simple ordinary differential models can be derived that yield a good approximation of the spectra. In such situations one can obtain approximate analytic formulas for the dispersion relations.

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