A study on resonance characteristics of whispering gallery modes on a dielectric disk resonator; Whispering gallery mode; Location of matching points

摘要

Using a point matching method, we have analyzed the resonance frequencies and unloaded Q factor of the whispering gallery modes on a dielectric disk resonator. We express field distributions of the resonance modes by a summation of spherical waves. Introducing a novel manner, we locate matching points on a boundary of the disk. Namely, abscissas θ{sub}i of the matching points are given by solutions of P{sup}m{sub}(m+2N)(cos θ) = 0. Considering the field Symmetry, we obtain an eigenvalue equation which is presented by (4N - 2)×(4N - 2) determinant expression. We can obtain numerical results of the resonance frequencies and unloaded Q factor in a good convergence. A comparison of numerical results and experimental ones shows a good agreement with each other.