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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
IEICE TRANSACTIONS on Electronics
Publication Date: 2001/10/01
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Issue on Millimeter-Wave Circuits and Fabrication Technologies Opening up the 21st Century)
point matching method, whispering gallery mode, location of matching points, millimeter wave band, dielectric disk resonator,
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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 Pnm(cos θ), we define abscissas θi of the matching points as solutions of Pm+2N-1m (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.