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| Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |
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THE ORIGIN OF ELECTROMAGNETIC RESONANCES IN THREE-DIMENSIONAL PHOTONIC FRACTALSBy U. SangawaAbstract: After a report on strange electromagnetic resonances emerging in an isotropic paraelectric Menger sponge (MS) now known as a photonic fractal, vigorous studies began to reveal their properties. However, the mechanics of how the resonances occur is still unknown. This report focuses on the findings that the resonances can be perturbation-theoretically identified as those originally occurring in an isolated dielectric cube, and that they arise within band gaps and uncouple with Bloch modes for a certain multiperiodic lattice. This interpretation is justified by the fact that the MS can be considered as a cube embedded in the lattice rather than the outcome of conventional recursive fractal structuring operations. An experimental formula for resonance conditions already reported can be derived from this interpretation.
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2. Takeda, M. W., S. Kirihara, Y. Miyamoto, K. Sakoda, and K. Honda, "Localization of electromagnetic waves in three-dimensional fractal cavities," Phys. Rev. Lett., Vol. 92, No. 093902, 2004.
3. Kirihara, S., Y. Miyamoto, M. W. Takeda, K. Honda, and K. Sakoda, "Strong localization of electromagnetic wave in ceramic/epoxy photonic fractals with Menger-sponge structure," Proc. on Ceramic Engineering and Science, Vol. 26, No. 3, 367-372, 2005. 4. Semouchkina, E., Y. Miyamoto, S. Kirihara, G. Semouchkin, and M. Lanagan, "Analysis of electromagnetic response of 3-D dielectric fractals of Menger sponge type," IEEE Trans. Microw. Theory Tech., Vol. 55, No. 6, 1305-1313, 2007. 5. Miyamoto, Y., H. Kanaoka, and S. Kirihara, "Terahertz wave localization at a three-dimensional ceramic fractal cavity in photonic crystals," J. Appl. Phys., Vol. 103, No. 10, 103106.1-103106.5, 2008. 6. Mori, A., S. Kirihara, Y. Miyamoto, M. W. Takeda, K. Honda, and K. Sakoda, "Integration of ceramic/epoxy photonic fractals with localization of electromagnetic waves," Proc. on Ceramic Engineering and Science, Vol. 26, No. 3, 361-366, 2005. 7. Sakoda, K., "Scaling property and symmetry-dependent escape time of the localized electromagnetic modes in the metallic Menger sponge fractal," Laser Physics, Vol. 18, No. 12, 1378-1385, 2008. 8. Sakoda, K., "Electromagnetic eigenmodes of a three-dimensional photonic fractal," Phys. Rev. B, Vol. 72, No. 18, 184201, 2005. 9. Sangawa, U., "Non-resonant electromagnetic scattering properties of Menger's sponge composed of isotropic paraelectric material," IEICE Trans. Electron., Vol. E90-C, No. 2, 484-491, 2007. 10. Sangawa, U., "Resonance analysis of multilayered filters with triadic Cantor-type one-dimensional quasi-fractal structures," IEICE Trans. Electron., Vol. E88-C, No. 10, 1981-1991, 2005. 11. Itoh, T. and C. Chang, "Resonant characteristics of dielectric resonators for millimeter-wave integrated circuits," Proc. IEEE Microw. Theory Tech. Soc. Int. Symp., Vol. 78, No. 1, 121-123, 1978.
12. Marcatili, E. A. J., "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J., Vol. 48, 2071-2102, 1969.
13. Zhang, K. and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics, 2nd editon, 348-352, Springer, New York, 2007.
14. Noda, S., A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature, Vol. 407, 608-610, 2000. 15. Itoh, T., "Spectral domain immitance approach for dispersion characteristics of generalized printed transmission lines," IEEE Trans. Microw. Theory Tech., Vol. 28, No. 7, 733-736, 1980. 16. Arrighetti, W. and G. Gerosa, "Spectral analysis of Serpinskij carpet-like prefractal waveguides and resonators," IEEE Microw. Wireless Compon. Lett., Vol. 15, No. 1, 30-32, 2005. |