Asymptotic methods for thin high-contrast two-dimensional PBG materials
Abstract
This paper surveys recent analytic and numerical results on asymptotic models of spectra of electromagnetic (EM) waves in two-dimensional (2D) thin high-contrast photonic bandgap (PBG) materials. These models lead to discovery of interesting phenomena, including extremely narrow bands that can be used for spontaneous emission enhancement, gaps in the long wave regions, and asymptotic periodicity of the spectrum. The asymptotic results provide unexpectedly good qualitative (and sometimes quantitative) description of spectral behavior for materials of finite 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.
Additional Information
© 1999 IEEE. Reprinted with permission. Manuscript received March 18, 1999; revised August 17, 1999. This work was supported in part by the NSF through Grant DMS 9 610 444 and by the Department of Army, Army Research Office, through a DEPSCoR Grant. The authors express their gratitude to Prof. J. W. Haus and Prof. R. Hempel, Dr. D. Sievenpiper, and graduate students M. Boroditsky, R. Vrijen, and H. Zeng for information about their work and discussion. P. Kuchment is indebted to Prof. A. Figotin for numerous discussions and collaboration. The authors thank the NSF, ARO, and the state of Kansas for their support.Files
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- Eprint ID
- 2892
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- CaltechAUTHORS:AXMjlt99
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2006-05-04Created from EPrint's datestamp field
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2021-11-08Created from EPrint's last_modified field