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Physical Review A

Birefringence-induced frequency beating in high-finesse cavities by continuous-wave cavity ring-down spectroscopy

Patrick Dupré

Published Nov 6, 2015• 23 citations
Publisher

Abstract

By analyzing the decaying intensity, leaking out a high-finesse cavity previously ``filled'' by a cw laser source (using the cavity ring-down spectroscopy technique), we observed frequency beating between what we think are two orthogonal eigenpolarization states of the intracavity electromagnetic field. The time decay (ring down) is analyzed by varying the angle of the polarization analyzer located in front of the detector. A full modeling of the observed signal is proposed. It is based on the Jones matrix formalism required for modeling the cavity behavior following a rotated phase shifter. The full transfer function is first established in the frequency domain, and then Fourier transformed to recover the temporal response. The same optical cavity, i.e., constituted of the same set of mirrors, is used at two different wavelengths ($\ensuremath{\sim}800$ and $\ensuremath{\sim}880$ nm). It demonstrates the differences in behavior between a high-finesse cavity $(\ensuremath{\sim}400\phantom{\rule{0.16em}{0ex}}000)$ and a lower finesse cavity $(\ensuremath{\sim}50\phantom{\rule{0.16em}{0ex}}000)$. Beating frequency, characteristics time, and beat amplitude are mainly discussed versus the analyzer angle. A cavity birefringence of $\ensuremath{\sim}1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ rad, resulting from the mirror birefringence is suggested. If the current analysis is in agreement with pulsed CRDS experiments (polarimetry) obtained in an isotropic moderate-finesse cavity, it differs from a recent work report on a high-finesse cavity associated with a source mode locking [Phys. Rev. A 85, 013837 (2012)].

DOI
10.1103/physreva.92.053817

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Journal of the Optical Society of America A•Sep 22, 2025•1 citation
By analyzing the decaying intensity, leaking out a high-finesse cavity previously ``filled'' by a cw laser source (using the cavity ring-down spectroscopy technique), we observed frequency beating between what we think are two orthogonal eigenpolarization states of the intracavity electromagnetic field. The time decay (ring down) is analyzed by varying the angle of the polarization analyzer located in front of the detector. A full modeling of the observed signal is proposed. It is based on the Jones matrix formalism required for modeling the cavity behavior following a rotated phase shifter. The full transfer function is first established in the frequency domain, and then Fourier transformed to recover the temporal response. The same optical cavity, i.e., constituted of the same set of mirrors, is used at two different wavelengths (\ensuremath∼800\ensuremath{\sim}800\ensuremath∼800 and \ensuremath∼880\ensuremath{\sim}880\ensuremath∼880 nm). It demonstrates the differences in behavior between a high-finesse cavity (\ensuremath∼400000)(\ensuremath{\sim}400\phantom{\rule{0.16em}{0ex}}000)(\ensuremath∼400000) and a lower finesse cavity (\ensuremath∼50000)(\ensuremath{\sim}50\phantom{\rule{0.16em}{0ex}}000)(\ensuremath∼50000). Beating frequency, characteristics time, and beat amplitude are mainly discussed versus the analyzer angle. A cavity birefringence of \ensuremath∼1.6\ifmmode×\else\texttimes\fi10\ensuremath−5\ensuremath{\sim}1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\ensuremath∼1.6\ifmmode×\else\texttimes\fi10\ensuremath−5 rad, resulting from the mirror birefringence is suggested. If the current analysis is in agreement with pulsed CRDS experiments (polarimetry) obtained in an isotropic moderate-finesse cavity, it differs from a recent work report on a high-finesse cavity associated with a source mode locking [Phys. Rev. A 85, 013837 (2012)].
It is experimentally demonstrated that a narrow band continuous wave (cw) light source can be used in combination with a high-finesse optically stable cavity to perform sensitive, high-resolution direct absorption and optical rotation spectroscopy in an amazingly simple experimental setup, using ideas from the field of cavity ring down spectroscopy. Light from a scanning narrow band cw laser is coupled into the cavity via accidental coincidences of the laser frequency with the frequency of one of the multitude of modes of the cavity. The absorption and polarization rotation information is extracted from a measurement of the time-integrated light intensity leaking out of the cavity as a function of laser wavelength.
We study the response of a high-finesse optical cavity to a cw laser during the laser frequency passage through resonance. For a laser that is spectraly larger than the cavity resonance, laser-field phase fluctuations are converted into amplitude fluctuations, and cavity injection is intrinsically noisy. We develop a model based on Schawlow-Townes spontaneous-emission laser broadening and discuss in detail its effects on high-sensitivity spectroscopic techniques such as cavity-enhanced absorption or cavity ring-down spectroscopy. We present realistic simulations of cavity injection during a sweep through resonance and calculation of statistical quantities such as the average injection efficiency. Agreement with experimental observations is established.
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.
Cavity Ring Down Spectroscopy has become an important method in gas phase spectroscopy and its uses promise to expand. While previous investigators have considered the decay of the stored energy in the cavity ring down cell following short pulsed excitation, this paper considers the effects of pulse reshaping during cavity ring down. It is found that in order to properly model these effects, one must consider not only the mode dependent loss of the ring down cavity, but also dispersion that shifts the resonant modes of the cavity. Only by considering the latter effect does one get a "causal" result where the free induction decay signal of the absorber occurs after the excitation pulse. It is demonstrated that in the limit that the cavity round trip time is long compared to both the T 2 time of the intracavity absorber and the temporal width of the excitation pulse, the reshaping of the n'th pulse out of the ring down cavity is the same as the reshaping produced by free space propagation over a distance of (2 n + 1) L where L is the separation of the mirrors in the cell. However, when the absorber T 2 becomes comparable to or longer than the cavity round trip time, then discrete modes of the ring down cavity become important. A general expression for the output is given for the important case of a weak absorber, and changes in the output are computed for a single absorption line as a function of the ratio of T 2 to the cavity round trip time for several values of the optical thickness of the sample. Lastly, it is suggested that monitoring changes in the pulse shape of the cavity ring down signal provides a way to characterize an absorption spectrum on a frequency scale of the laser bandwidth down to the cavity free spectral range.
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.
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.