Analytical time-domain model of partially coherent phase-shift cavity ringdown spectroscopy for sensor design and...

High-quality optical cavities are widely used in sensing due to their exceptional sensitivity. However, most commercial systems rely on narrow-linewidth tunable lasers and active frequency tracking, increasing the system cost and complexity, making them bulky, and adding integration challenges. Partially coherent phase-shift cavity ringdown spectroscopy (PS-CRDS) offers a time-domain alternative by extracting cavity loss information from the phase shift of an intensity-modulated signal, eliminating the need for wavelength tracking. This study introduces a closed-form analytical time-domain model for PS-CRDS that explicitly accounts for partial source coherence, enabling the use of partially coherent sources such as laser diodes and LEDs, which support integrated, low-cost system design. The model quantifies the impact of the source linewidth, modulation frequency, and cavity parameters on phase sensitivity, signal strength, and signal-to-noise ratio (SNR). We show that absorption-induced loss can be robustly detected with partially coherent sources, with only a modest reduction in sensitivity compared to fully coherent excitation. Importantly, the performance metrics saturate once the source linewidth exceeds the cavity free spectral range, revealing a wide design tolerance to coherence and detuning. These results provide practical design guidelines for PS-CRDS-based sensors and support the development of compact, low-cost, and fully integrated silicon photonic microring biosensors.