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Graphical Representation and Evaluation of Attenuation and Coupling Parameters of Whispering-Gallery-Mode Resonators

A new graphical approach for extracting the attenuation and coupling coefficients of traveling-wave whispering-gallery-mode (WGM) resonators is proposed. This approach starts by representing the transmission coefficient circle on the complex plane at the resonance frequency. From the metrics of this circle (center position and radius), both the attenuation and coupling coefficients can be extracted. This technique simplifies the evaluation of the loaded and unloaded Q factors of WGM resonators directly from the extracted coefficients. It is applied to a K-band planar WGM resonator coupled to a dielectric image guide in a reaction-mode configuration. The extracted values from both simulations and measurements show a close agreement with the mathematical model of traveling-wave WGM resonators.