Fast and Accurate Extraction of Ultra-High Quality Factor from Cavity Ring-Down Measurement

In this letter, we clarify the basic property of cavity ring-down and present a specified algorithm that enables extraction of the overall quality factor, as well as the intrinsic loss and coupling state of UHQ cavities with superior fidelity and simplicity than prior schemes. First, we conduct detailed analysis on how to correctly extract the photon lifetime $\tau_{\mathrm{P}}$ from the cavity ring-down. Then we revisit the ring down measurement and demonstrate a step-by-step recipe to derive the quality factor and actual coupling state of a fiber cavity. Finally, we set up an experiment to verify the validity and feasibility of the method. Our study provides useful technological tools to facilitate the design and implementation of UHQ fiber cavities for ultra-stable lasers, reference cavities, and ultranarrow optical filters.