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An Analysis for the Whispering Gallery Modes on a Millimeter Wave Dielectric Disk Resonator by a Point Matching Method
Yoshiro TOMABECHI Yoshinori KOGAMI Mari MATSUBARA Kazuhito MATSUMURA
Publication
IEICE TRANSACTIONS on Electronics
Vol.E84C
No.10
pp.15541560 Publication Date: 2001/10/01 Online ISSN:
DOI: Print ISSN: 09168516 Type of Manuscript: Special Section PAPER (Special Issue on MillimeterWave Circuits and Fabrication Technologies Opening up the 21st Century) Category: Keyword: point matching method, whispering gallery mode, location of matching points, millimeter wave band, dielectric disk resonator,
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Summary:
Using a point matching method, we have numerically analyzed resonance frequencies and unloaded Q factor of whispering gallery modes in a millimeter wave region that are well known as an intrinsic mode of a dielectric disk resonator. We express field distributions of the resonance modes by a summation of spherical waves. Tangential electromagnetic fields inside the disk are matched to those outside the disk at appropriate matching points on a boundary. As the result, a 4N 4N (N; number of matching points) determinant is derived as an eigenvalue equation of the disk resonator. Since elements of the determinant are complex numbers, a complex angular frequency is introduced to make a value of the determinant zero. For a location of the matching points, we also introduce a new technique which is derived from a field expression of the whispering gallery modes. Since an azimuthal angle dependence of the field distributions with a resonance mode number m is presented by the associated Legendre function P_{n}^{m}(cos θ), we define abscissas θ_{i} of the matching points as solutions of P_{m+2N1}^{m} (cos θ) = 0. Considering the field symmetry, we also modify the eigenvalue equation to a new eigenvalue equation which is expressed (4N  2) (4N  2) determinant. From the results of our numerical analysis, we can find that the resonance frequencies and unloaded Q factor well converge for number of matching points N. A comparison of numerical results and experimental ones, in a millimeter wave band (50  100 GHz), shows a good agreement with each other. It is found that our analysis is effective for practical use in the same wave band.


