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Integrated optical biosensors based on high-Q microcavities can achieve exceptionally low detection limits; however, their operation typically requires tracking narrow resonance features using highly stable, tunable, narrow-linewidth lasers. These coherence and wavelength-control requirements impose constraints on system cost, footprint, and power consumption, and remain a primary barrier to full on-chip integration. A more scalable approach would enable accurate extraction of cavity loss without reliance on high-coherence sources or active wavelength tuning. Partially coherent phase-shift cavity ring-down spectroscopy (PS-CRDS), a time-domain cavity interrogation technique, addresses this need by determining photon lifetime from the phase response of an intensity-modulated optical carrier. This approach enables the use of broadband, partially coherent sources while still resolving cavity loss, thereby supporting compact, low-cost, and fully integrated microresonator-based biosensors suitable for portable and point-of-care applications.

This thesis advances the theoretical foundations required to realize such systems by developing two analytical frameworks that quantify coherence effects in cavity-based sensing. The first contribution is a closed-form model describing how finite optical coherence influences the temporal transfer function of optical cavities. Using a linear-systems formulation, the model captures the impact of source bandwidth on cavity buildup, decay dynamics, and transmitted intensity for both cavity-enhanced absorption spectroscopy (CEAS) and traditional cavity ring-down spectroscopy (CRDS) in standing- and traveling-wave resonators. The results show that, while intrinsic cavity loss remains the dominant factor governing photon lifetime, partial coherence introduces measurable modifications to the cavity response that must be considered in accurate time-domain analysis.

The second contribution is a closed-form analytical model for partially coherent PS-CRDS, which characterizes the dependence of phase shift, sensitivity, and signal-to-noise ratio (SNR) on source linewidth and modulation frequency. This framework clarifies the trade-offs associated with replacing narrow-linewidth lasers with broader-bandwidth sources such as laser diodes or LEDs. The analysis shows that absorption-induced loss changes can be reliably detected using both coherent and partially coherent sources, with only moderate sensitivity reduction when the source bandwidth remains within the cavity free spectral range (FSR). Beyond this regime, performance saturates, indicating that broadband sources can still be effectively used in integrated implementations. Experimental measurements using silicon-on-insulator (SOI) microring resonators are presented to validate these concepts under both narrow linewidth (tunable laser source, TLS) and effectively broader-bandwidth (swept VCSEL) excitation. The measured phase response and analytical fitting show good agreement with theoretical predictions, confirming the feasibility of photon-lifetime extraction under partially coherent operation. While the TLS configuration achieves higher sensitivity and lower detection limits, the VCSEL-based implementation demonstrates competitive performance while reducing the need for active resonance tracking.

Overall, this work establishes a comprehensive theoretical and experimental framework for partially coherent PS-CRDS, providing a practical pathway toward integrated, low-cost, and scalable microresonator biosensors. These results support the development of robust photonic sensing platforms capable of operating without highly stable narrow-linewidth lasers, enabling compact lab-on-chip and point-of-care diagnostic systems.

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