Direct readout of mirror reflectivity for cavity-enhanced gas sensing using Pound-Drever-Hall signals

The operation of cavity-enhanced techniques usually requires independent pre-calibration of the mirror reflectivity to precisely quantify the absorption. Here we show how to directly calibrate the effective mirror reflectivity without using any gas samples of known concentration or high-speed optical/electrical devices. Leveraging a phase modulator to generate sidebands, we are able to record Pound-Drever-Hall error signals shaped by cavity modes that can reveal the effective reflectivity after waveform analysis. As an example, we demonstrated the reflectivity calibration of a pair of near-infrared mirrors over 80 nm with a free spectral range-limited resolution, illustrating a reflectivity uncertainty of 2 × 10^-5 in the center part of the refection wavelength range of the mirrors and larger at the edges. With an effective reflectivity of 0.9982 (finesse ∼1746) inferred at 1531.6 nm, a short ∼ 8-cm Fabry-Pérot cavity achieved a minimum detectable absorption coefficient of 9.1 × 10^-9cm^-1 for trace C₂H₂ detection. This method, by providing convenient calibration in an almost real-time manner, would enable more practical cavity-enhanced gas measurement even with potential mirror reflectivity degradation.