Resonance Analysis of Multilayered Filters with Triadic Cantor-Type One-Dimensional Quasi-Fractal Structures(Electromagnetic Theory)

概要

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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.
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2005-10-01