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Optics Express

Step-modulated decay cavity ring-down detection for double resonance spectroscopy

Juho Karhu, Kevin K. Lehmann, Markku Vainio, Markus Metsälä, Lauri Halonen

Published Oct 24, 2018• 14 citations
Publisher

Abstract

A method of measuring double resonant two-photon signal and background from a single cavity ring-down decay is introduced. This is achieved by modulating the double resonance loss via one of the light sources exciting the transition. The noise performance of the method is characterized theoretically and experimentally. The addition of a new parameter to the fitting function introduces a minor noise increase due to parameter correlation. However, the concurrent recording of the background can extend the stable measurement time. Alternatively, the method allows a faster measurement speed, while still recording the background, which is often advantageous in double resonance measurements. Finally, the method is insensitive to changes in the cavity decay rate at short timescales and can lead to improved performance if they have significant contribution to the final noise level compared to the detector noise.

DOI
10.1364/oe.26.029086

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A method of measuring double resonant two-photon signal and background from a single cavity ring-down decay is introduced. This is achieved by modulating the double resonance loss via one of the light sources exciting the transition. The noise performance of the method is characterized theoretically and experimentally. The addition of a new parameter to the fitting function introduces a minor noise increase due to parameter correlation. However, the concurrent recording of the background can extend the stable measurement time. Alternatively, the method allows a faster measurement speed, while still recording the background, which is often advantageous in double resonance measurements. Finally, the method is insensitive to changes in the cavity decay rate at short timescales and can lead to improved performance if they have significant contribution to the final noise level compared to the detector noise.
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 present an ac heterodyne technique in cavity ringdown spectroscopy that permits $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ absorption sensitivity with microwatt-level light power. Two cavity modes, one probing the empty cavity and the other probing intracavity absorption, are excited simultaneously but with their intensities temporally out of phase, with one mode decaying and the other rising. Heterodyne detection between the two modes reveals the dynamic time constants associated with the empty cavity and the additional intracavity gas absorption. The method offers a quick comparison between the on- and off-resonance information, a prerequisite to reaching the fundamental shot-noise limit. This simple and yet important improvement of cavity ringdown spectroscopy should lead to the enhanced performance of a wide range of applications.
This paper presents a theoretical analysis of the optical properties of an optical cavity with both one- and two-photon intracavity absorption loss, without saturation. The cavity two-photon absorption loss per pass is assumed to be small, but otherwise the analysis is general. Analytical results for the cavity transmission as a function of cavity parameters, linear and two-photon intracavity loss, and detuning from resonance are derived and limiting cases discussed. Extraction of the two-photon loss from both cavity ring-down and cavity-enhanced absorption spectroscopy methods is analyzed and the predicted shot-noise limited sensitivities derived and compared. Numerical results are computed using the parameters of a recent experimental intracavity measurement of two-photon absorption of nitrous oxide. The results will be useful in the design and interpretation of cavity-enhanced, two-photon absorption spectroscopy.
A technique for reducing background and improving the signal-to-noise ratio in optical spectroscopy of weak atomic transitions is described. In this technique an incident laser is square-wave amplitude modulated and the resonance fluorescence from the atom is then detected out of phase with the excitation when the laser is off. Due to the finite lifetime of the atom’s excited state, appreciable signal is observed when the laser is off and instrumental scattering background is virtually eliminated. Applying this technique to an experiment on single laser-cooled In+ ions, we have observed a factor of 500 reduction in background and a factor of 5 increase in the signal-to-noise ratio.
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.
Low signal-to-noise ratios are a common problem in experiments attempting to measure photon-photon scattering. In the optical regime, where petawatt lasers with femtosecond pulse durations are used, the large beam sizes cause the major contribution of the background to be spread over up to 100 ps in arrival time, whereas the signal is confined to the femtosecond scale. We present a balanced homodyne measurement scheme, which exploits this property to suppress the background. By interfering the signal with a short reference pulse, the measurement becomes effectively gated to the pulse duration and is therefore only sensitive to the co-timed part of the light, reducing the effective background by 3-4 orders of magnitude. Additionally, increasing the reference pulse energy increases the amplitude of the measured quantity without changing the intrinsic signal-to-noise ratio. Using this property, other external noise sources can be made negligible by boosting the measured quantity above the noise floor. Using two-dimensional detectors further enhances the scheme by improving sensitivity and enabling self-referenced single-pulse measurements. In addition, an evaluation procedure based on maximum-likelihood estimation is presented and demonstrated. The robustness and performance of this scheme are demonstrated on simulated data, where a more than 100-fold reduction of measurement time compared to conventional photon-counting methods under realistic conditions is found.