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Optics Express

Saturation cavity ring-down spectrometry using a dynamical relaxation model

Lei Yang, H. Lin, X. J. Feng, Mark D. Plimmer, J. T. Zhang

Published Jan 22, 2019• 7 citations
Publisher

Abstract

We propose a new simple approximate solution to the two-state rate equation model for analyzing decay signals of saturation cavity ring-down spectrometry in the adiabatic and low-saturation regime. It helps obtain baseline-immune Doppler-free spectra for hyperfine transitions and linear absorption coefficients of a gas in the saturation regime. To demonstrate it, a baseline-immune Lamb dip spectrum of the R1A2 transitions in the 2v2 + v3 band of methane was recorded. The line position was determined to be 6 076.108 457 7(11) cm-1, the relative uncertainty being 1.8 × 10-10.

DOI
10.1364/oe.27.001769

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We propose a new simple approximate solution to the two-state rate equation model for analyzing decay signals of saturation cavity ring-down spectrometry in the adiabatic and low-saturation regime. It helps obtain baseline-immune Doppler-free spectra for hyperfine transitions and linear absorption coefficients of a gas in the saturation regime. To demonstrate it, a baseline-immune Lamb dip spectrum of the R1A2 transitions in the 2v2 + v3 band of methane was recorded. The line position was determined to be 6 076.108 457 7(11) cm-1, the relative uncertainty being 1.8 × 10-10.
The theoretical bases of saturated-absorption cavity ring-down (SCAR) spectroscopy are treated and described in detail in different transition broadening regimes. All the approximations that are introduced to achieve a model as simple and accurate as possible are discussed. In the Voigt broadening regime, a calibration factor that relates the measured spectral areas in the saturated and linear absorption regimes is retrieved. A relevant application of this technique to the measurement of radiocarbon dioxide concentration at both enriched and natural abundance (∼10−12) is presented. The population relaxation rate of one ro-vibrational state of the ν3 band is measured for this highly diluted CO2 isotopologue.
The Noise-Immune Cavity-Enhanced Optical Heterodyne Molecular Spectrometry (NICE-OHMS) is a modern technique renowned for its ultimate sensitivity, because it combines long equivalent absorption length provided by a high finesse cavity, and a detection theoretically limited by the sole photon-shot-noise. One fallout of the high finesse is the possibility to accumulating strong intracavity electromagnetic fields (EMF). Under this condition, molecular transitions can be easy saturated giving rise to the usual Lamb dips (or hole burning). However, the unusual shape of the basically trichromatic EMF (due to the RF lateral sidebands) induces nonlinear couplings, i.e., new crossover transitions. An analytical methodology will be presented to calculate spectra provided by NICE-OHMS experiments. It is based on the solutions of the equations of motion of an open two-blocked-level system performed in the frequency-domain (optically thin medium). Knowing the transition dipole moment, the NICE-OHMS signals (``absorption-like'' and ``dispersion-like'') can be simulated by integration over the Doppler shifts and by paying attention to the molecular Zeeman sublevels and to the EMF polarizationfootnote{J. Opt. Soc. Am. B 32, 838 (2015)}. The approach has been validated by discussion experimental data obtained on two transitions of rmC2H2{rm C_{2}H_{2}}rmC2​H2​ in the near-infrared under moderated saturationfootnote{Optics Express 16, 14689 (2008)}. One of the applications of the saturated absorption is to be able to simultaneously determine the transition intensity and the density number while only one these 2 quantities can only be assessed in nonlinear absorption.
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.
An analytical methodology is presented to calculate spectra provided by NICE-OHMS. It is based on the solutions of the equations of motion of an open two-blocked-level system performed in the frequency domain. The polychromaticity of the impinging electromagnetic field, furthermore, trapped inside a high-finesse cavity, is a potential source of induced resonances when this field interacts with a weakly absorbing nonlinear medium. These are optimal conditions to produce the well-established hole burning. However, the radio-frequency sidebands intrinsically associated with the NICE-OHMS technique require a specific treatment for describing both absorption and optical phase shift contributions. To validate the approach, numerical simulations of two transitions of C2H2 in the near-infrared range are discussed. The Doppler broadening-free cross-sideband resonances have been clearly characterized under the regime of moderate electromagnetically induced saturation. Comparison to experimental data available [Opt. Express16, 14689 (2008)OPEXFF1094-408710.1364/OE.16.014689] allowed us to assess the eligibility of the approach.
The influence of optical saturation on noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS) signals from purely Doppler-broadened transitions is investigated experimentally. It is shown that the shape and the strength of the dispersion signal are virtually unaffected by optical saturation, whereas the strength of the absorption signal decreases as (1+G±1)−1/2, where G±1 is the degree of saturation induced by the sideband of the frequency-modulated triplet, in agreement with theoretical predictions. This implies, first of all, that Doppler-broadened NICE-OHMS is affected less by optical saturation than other cavity-enhanced techniques but also that it exhibits nonlinearities in the power and pressure dependence for all detection phases except pure dispersion. A methodology for assessments of the degree of saturation and the saturation power of a transition from Doppler-broadened NICE-OHMS signals is given. The implications of optical saturation for practical trace species detection by Doppler-broadened NICE-OHMS are discussed.
We report what we believe to be the first systematic study of Doppler-free, nonlinear absorption by use of cavity ringdown spectroscopy. We have developed a variant of cavity ringdown spectroscopy for the mid-infrared region between 9 and 11 microm, exploiting the intracavity power buildup that is possible with continuous-wave lasers. The infrared source consists of a continuous-wave CO2 laser with 1-mW tunable infrared sidebands that couple into a high-finesse stable resonator. We tune the sideband frequencies to observe a saturated, Doppler-free Lamb dip in the nu7, 11(1,10) <-- 11(2,10) rovibrational transition of ethylene (C2H4). Power studies of the Lamb dip are presented to examine the intracavity effects of saturation on the Lamb-dip linewidth, the peak depth, and the broadband absorption.