Resonance Analysis of Multilayered Filters with Triadic Cantor-Type One-Dimensional Quasi-Fractal Structures

Ushio SANGAWA

Publication
IEICE TRANSACTIONS on Electronics   Vol.E88-C    No.10    pp.1981-1991
Publication Date: 2005/10/01
Online ISSN: 
DOI: 10.1093/ietele/e88-c.10.1981
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Electromagnetic Theory
Keyword: 
multilayered filter,  fractal,  Cantor set,  Clifford algebra,  γ matrices,  localization,  self-similarity,  stage number,  

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Summary: 
Multilayered filters with a dielectric distribution along their thickness forming a one-dimensional quasi-fractal structure are theoretically analyzed, focusing on exposing their resonant properties in order to understand a dielectric Menger's sponge resonator [4],[5]. "Quasi-fractal" refers to the triadic Cantor set with finite generation. First, a novel calculation method that has the ability to deal with filters with fine fractal structures is derived. This method takes advantage of Clifford algebra based on the theory of thin-film optics. The method is then applied to classify resonant modes and, especially, to investigate quality factors for them in terms of the following design parameters: a dielectric constant, a loss tangent, and a stage number. The latter determines fractal structure. Finally, behavior of the filters with perfect fractal structure is considered. A crucial finding is that the high quality factor of the modes is not due to the complete self-similarity, but rather to the breaking of such a fractal symmetry.