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.
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.
Cavity ring-down is becoming a widely used technique in gas phase spectroscopy. It holds promise for further important extensions, which will lead to even more frequent use. However, we have found widespread confusion in the literature about the nature of coherence effects, especially when the optical cavity constituting the ring-down cell is excited with a short coherence length laser source. In this paper we use the superposition principle of optics to present a general and natural framework for describing the excitation of a ring-down cavity regardless of the relative values of the cavity ring-down time, the input pulse coherence time, or the dephasing time of absorption species inside the cavity. This analysis demonstrates that even in the impulsive limit the radiation inside a high finesse cavity can have frequency components only at the natural resonance frequencies of the cavity modes. As an immediate consequence, a sample absorption line can be detected only if it overlaps at least one of the cavity resonances. Since this point is of particular importance for high resolution applications of the technique, we have derived the same conclusion also in the time domain representation. Finally, we have predicted that it is possible to use this effect to do spectroscopy with a resolution much higher than that of the bandwidth of the excitation laser. In order to aid in the design of such experiments, expressions are derived for the temporal and spatial overlap of a Fourier transform limited input Gaussian beam with the TEMmn modes of the cavity. The expressions we derive for the spatial mode overlap coefficients are of general interest in applications where accurate mode matching to an optical cavity is required.
The dynamic response of optical resonant cavity has been theoretically studied,by taking resonant cavity as a linear and time invariant system and through the approach of Signal Processing.The mathematical description obtained could fit any form of light waves.From the perspective of Signal Processing,the traditional pulse and continues wave cavity ring-down spectroscopy could be considered as observation of impulse response and step response respectively.Furthermore,the cavity response to the light-wave linearly frequency chirped has been studied,in the condition of slow chirp.The Fourier analysis of light power passed through cavity has been made and an analytic description has been given,which reveals the fact that the signal spectrum of light power is related to the absorption spectrum of material inside cavity.Based on this theoretic analysis,a new approach of cavity enhanced absorption spectroscopy has been put forward,called Frequency Domain Cavity Ring-Down Spectroscopy.The result would facilitates the research of cavity enhanced spectroscopy techniques,as well others using resonant cavity,such as P-D-H laser frequency stabilization.
Abstract Measurements of ultrahigh-fidelity absorption spectra can help validate quantum theory, engineer ultracold chemistry, and remotely sense atmospheres. Recent achievements in cavity-enhanced spectroscopy using either frequency-based dispersion or time-based absorption approaches have set new records for accuracy with uncertainties at the sub-per-mil level. However, laser scanning or susceptibility to nonlinearities limits their ultimate performance. Here we present cavity buildup dispersion spectroscopy (CBDS), probing the CO molecule as an example, in which the dispersive frequency shift of a cavity resonance is encoded in the cavity’s transient response to a phase-locked non-resonant laser excitation. Beating between optical frequencies during buildup exactly localizes detuning from mode center, and thus enables single-shot dispersion measurements. CBDS can yield an accuracy limited by the chosen frequency standard and measurement duration and is currently 50 times less susceptible to detection nonlinearity compared to intensity-based methods. Moreover, CBDS is significantly faster than previous frequency-based cavity-enhanced methods. The generality of CBDS shows promise for improving fundamental research into a variety of light–matter interactions.
Cavity-enhanced absorption spectroscopy is now widely used as an ultrasensitive technique in observing weak spectroscopic absorptions. Photons inside the cavity are reflected back and forth between the mirrors with reflectivities R close to one and thus (on average) exploit an absorption pathlength L that is 1/(1 − R ) longer than a single pass measurement. As suggested by the Beer-Lambert law, this increase in L results in enhanced absorbance A (given by αL with α being the absorption coefficient) which in turn favours the detection of weak absorptions. At the same time, however, only (1 − R ) of the incident light can enter the cavity [assuming that mirror transmission T is equal to (1 − R )], so that the reduction in transmitted light intensity Δ I caused by molecular absorption equates to that would be obtained if in fact no cavity were present . The enhancement in A = Δ I / I , where I is the total transmitted light intensity, achievable from CEAS therefore comes not from an increase in Δ I , but a sharp decrease in I. In this paper, we calculate the magnitudes of these two terms before and after a cavity is introduced, and aim at interpreting the sensitivity improvement offered by cavity-enhanced absorption spectroscopy from this observable-oriented (i.e. Δ I and I ) perspective. It is first shown that photon energy stored in the cavity is at best as intense as the input light source, implying that any absorbing sample within the cavity is exposed to the same or even lower light intensity after the cavity is formed. As a consequence, the intensity of the light absorbed or scattered by the sample, which corresponds to the Δ I term aforementioned, is never greater than would be the case in a single pass measurement. It is then shown that while this “numerator” term is not improved, the “denominator” term, I , is reduced considerably; therefore, the increase in contrast ratio Δ I / I is solely contributed by the attenuation of transmitted background light I and is ultimately down to the suppression of any measurement noise that is associated with it. The noise component that is most effectively suppressed is the type whose magnitude scales linearly with light intensity I , as is typical of noise caused by environmental instabilities, followed by the shot noise which scales as square root of I . No suppression is achievable for noise sources that are independent of I , a notable example being the thermal noise of a detector or of detection electronics. The usefulness of this “noise suppression” argument is that it links the sensitivity gain offered by a cavity with the property of measurement noise present in the system, and clearly suggests that the achievable sensitivity is dependent on how efficient the various noise components are “suppressed” by the cavity.
We introduce optical feedback frequency stabilized cavity ring-down spectroscopy (OFFS-CRDS), a near-shot-noise-limited technique that combines kilohertz resolution with an absorption detection sensitivity of 5×10(-13) cm(-1) Hz(-1/2). Its distributed feedback laser source is stabilized to a highly stable V-shaped reference cavity by optical feedback and fine-tuned by means of single-sideband modulation. The stability of this narrow laser is transferred to a ring-down (RD) cavity using a new fibered Pound-Drever-Hall (PDH) locking scheme without a dedicated electro-optic phase modulator, yielding several hundred RD events per second. We demonstrate continuous coverage of more than 7 nm with a baseline noise of 5×10(-12) cm(-1) and a dynamic range spanning six decades. With its resonant intracavity light intensity on the order of 1 kW/cm2, the spectrometer was used for observing a Lamb dip in a transition of carbon dioxide involving four vibrational quanta. Saturating such a weak transition at 160 μW input power, OFFS-CRDS paves the way to Doppler-free molecular overtone spectroscopy for precision measurements of hyperfine structures and pressure shifts.