Time-domain modeling of finite coherence in resonance-based spectroscopic sensing

Optical cavities serve as powerful tools for sensing experiments, often relying on narrow-linewidth laser sources to minimize the impact of optical coherence on measurements. However, demands for affordable integrated and miniaturized sensing platforms in point-of-care diagnostics, environmental monitoring, and similar applications motivate switching to sources with broader linewidths suitable for both monolithic and heterogeneous integrations. Time-domain measurement techniques such as cavity ring-down spectroscopy (CRDS) are widely used in conjunction with optical cavities, but to date there has been no universal model that quantifies the impact of partial coherence on the cavity temporal transfer function. We apply a linear systems theory approach to develop a closed-form analytic model for cavity-based sensing that quantifies the influence of source bandwidth (i.e., temporal coherence) on spectroscopic measurements in the time domain. This approach can be applied to a variety of cavity-based spectroscopies. In this study, cavity-enhanced absorption spectroscopy (CEAS) and CRDS paradigms have been examined using standing- and traveling-wave resonator examples. Results show that although increased cavity loss is the primary factor reducing output power and photon lifetime in both CEAS and CRDS, broader source linewidths can also influence cavity buildup and transmission and must be accounted for when modeling the system response. The model is consistent with known results in the literature and provides a framework for evaluating source detuning and coherence effects on cavity dynamics.