Towards Spectroscopy of Partially Coherent Sources

Avshalom Gamliel

Wolfgang Demtröder

Mohammad Hossein Motavas, Mohamed Najih, Andrew G. Kirk

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.

Wolfgang Demtröder

Kwan K. Lee, Amit Ashok

Tsang et al. have shown that the Fisher information of the two incoherent point source separation, below the Rayleigh limit, is finite and achievable using optical modes measurements.1 However, recent claims regarding partial coherence of sources, no matter how small, leads to necessarily zero Fisher information as the source separation decreases below the Rayleigh limit approaching zero have proved to be controversial.2, 3 Thus, the impact of partial coherence on the photon counting optical modal measurements merits further exploration. In this work, we derive the mutual coherence function (image plane) of two partially coherent point sources and find the classical Fisher information of the source separation using both direct image plane and photon counting modal measurements. A classical Fisher information analysis of partially coherent source(s) leads to some rather surprising results for two-point source resolution as the source separation approaches zero. We find that the magnitude of the Fisher information strongly depends on the degree of (positive/negative) partial coherence, which can be understood using an intuitive semi-classical analysis of direct image plane and photon counting modal measurements. We also provide an error analysis of the maximum likelihood estimators for both measurements.

S. A. Wadood, Yiyu Zhou, Jing Yang +7 more

Partial coherence between two photon sources sets a bound on their spatial resolution. We demonstrate that partial anticorrelation between the sources increases the resolution sensitivity. We also show decreased sensitivity for complete coherence.