Abstract
The coupling coefficients of the disk microresonators consisting of different dielectrics are presented. The analytical expressions for the coupling coefficients are obtained. The basic regularities of the coupling coefficient changing on the structure parameter variations are considered. The coupling coefficients as functions of main structure parameters are studied. The calculation results of the transmission coefficients as well as the reflection coefficients of the bandpass filters building up on different disk microresonators with different modes are presented. The S-matrix frequency dependences of the bandpass filters on different disk microresonators in the infrared wavelength range are calculated. The necessary for acceptable measure of the scattering dielectric Q-factor values are determined. The amplitude-frequency characteristics of the bandpass filters on the vertically coupled as well as laterally coupled disc microresonators are investigated. Most optimal configurations of coupled microresonators allowing to achieve the best scattering characteristics are determined. It's shown that using of microresonators with whispering gallery modes relatively easy allows to obtain frequency-symmetrical characteristics of the filters.
Highlights
Disk dielectric microresonators with whispering gallery (WG) modes inscribes in the planar integral circuits quite naturally
The goal of the present work is the analytical calculation of the coupling coefficients of different disk microresonators with WG modes in the open space
Coupling coefficients as functions of the coordinates for different disk microresonators in the position showed in fig. 2a (a, b) k0∆x = 0; k0∆z = 1, 05(q1⊥ + q2⊥) (a); k0∆x = k0∆y = 0 (b); in the position showed in fig. 3a (c, d); k0∆y = 0; k0∆z = q1⊥ + q2⊥ (c); k0∆x = 0; k0∆z = 3.7 (d); ε1r = 16; ε2r = 9, 6;
Summary
Disk dielectric microresonators with whispering gallery (WG) modes inscribes in the planar integral circuits quite naturally. Eigenoscillations of two disk dielectric microresonators were considered in [4,5,6,7], but its coupling coefficients were not calculated and not studied in full measure. For calculation and optimization of the device parameters, it’s convenient to carry out on basis of electrodynamic modeling with using coupling coefficients [8]. The goal of the present work is the analytical calculation of the coupling coefficients of different disk microresonators with WG modes in the open space. We use the scattering theory for S-matrix coefficients calculation of different microresonator bandpass filters
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