Our laboratory seeks to apply novel cavity-enhanced spectroscopic techniques to present problems in atmospheric and physical chemistry. Primarily we use cavity ring-down spectroscopy in which the passive decay of optical power within a Fabry-Pérot resonator is utilized to extract an absorption signal. With this technique we have demonstrated quantum (shot) noise limited sensitivities in both the near-infrared and mid-infrared spectral regions. Both commercial and home-built optical frequency combs are employed either to serve as absolute frequency references for molecular spectra or in a multiheterodyne approach for multiplexed sensing. I will discuss this novel instrumentation as well as measurements we have made of atmospherically relevant species such as CO₂, H₂O, O₂, CH₄, and CO with implications for in situ and remote (i.e. satellite-based) sensing. I will conclude by discussing future directions and plans for challenging measurements in the mid-infrared.

We present the first demonstration of cavity-enhanced direct frequency comb spectroscopyA. Foltynowicz et al. Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide. Applied Physics B, vol. 110, pp. 163–175, 2013.n buffer-gas cooled moleculesD. Patterson and J. M. Doyle. Cooling molecules in a cell for FTMW spectroscopy. Molecular Physics 110, 1757–1766, 2012. By coupling a mid-infrared frequency comb to a high-finesse cavity surrounding a helium buffer-gas chamber, we can gather rotationally resolved absorption spectra with high sensitivity over a broad wavelength region. The measured  ∼ 10 K rotational and translational temperatures of buffer-gas cooled molecules drastically simplify the observed spectra, compared to those of room temperature molecules, and allow for high spectral resolution limited only by Doppler broadening (10-100 MHz). Our system allows for the extension of high-resolution spectroscopy to larger molecules, enabling detailed analysis of molecular structure and dynamics, while taking full advantage of the powerful optical properties of frequency combs.

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A. Foltynowicz et al. Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide. Applied Physics B, vol. 110, pp. 163–175, 2013.o D. Patterson and J. M. Doyle. Cooling molecules in a cell for FTMW spectroscopy. Molecular Physics 110, 1757–1766, 2012..

The ultimate precision of highly sensitive cavity-enhanced spectroscopic measurements is often limited by interferences (etalons) caused by weak coupled-cavity effects. Differential measurements of ring-down decay constants have previously been demonstrated to largely cancel these effects, but the measurement acquisition rates were relatively low [1,2]. We have previously demonstrated the use of frequency agile rapid scanning cavity ring-down spectroscopy (FARS-CRDS) for acquisition of absorption spectra [3]. Here, the method of rapidly scanned, frequency-agile differential cavity ring-down spectroscopy (FADS-CRDS) is presented for reducing the effect of these interferences and other shot-to-shot statistical variations in measured decay times. To this end, an electro-optic phase modulator (EOM) with a bandwidth of 20 GHz is driven by a microwave source, generating pairs of sidebands on the probe laser. The optical resonator acts as a highly selective optical filter to all laser frequencies except for one tunable sideband. This sideband may be stepped arbitrarily from mode-to-mode of the ring-down cavity, at a rate limited only by the cavity buildup/decay time. The ability to probe any cavity mode across the EOM bandwidth enables a variety of methods for generating differential spectra. The differential mode spacing may be changed, and the effect of this method on suppressing the various coupled-cavity interactions present in the system is discussed. Alternatively, each mode may also be differentially referenced to a single point, providing immunity to temporal variations in the base losses of the cavity while allowing for conventional spectral fitting approaches. Differential measurements of absorption are acquired at 3.3 kHz and a minimum detectable absorption coefficient of 5 x10⁻¹² cm⁻¹ in 1 s averaging time is achieved.


1. J. Courtois, K. Bielska, and J.T Hodges J. Opt. Soc. Am. B, 30, 1486-1495, 2013
2. H.F. Huang and K.K. Lehmann App. Optics 49, 1378-1387, 2010
3. G.-W. Truong, K.O. Douglass, S.E. Maxwell, R.D. van Zee, D.F. Plusquellic, J.T. Hodges, and D.A. Long Nature Photonics, 7, 532-534, 2013

We report a highly sensitive mid-infrared spectrometer capable of recording cavity ring-down events in the quantum (shot) noise limit. A linear optical cavity of finesse 31,000 was pumped by a distributed feedback quantum cascade laser (DFB-QCL) operating at 4.5 μm until a cavity transmission threshold was reached. A fast optical switch then extinguished optical pumping and initiated a cavity decay which exhibited root-mean-square noise proportional to the square root of optical power (quantum noise) for several cavity time constants until a detector noise floor was reached. This spectrometer has achieved a noise-equivalent absorption of NEA = 2.6×10⁻¹¹ cm⁻¹Hz^−1/2 and a minimum absorption coefficient of α = 2.3×10⁻¹¹ cm⁻¹in 3 seconds. Applications for such a highly sensitive spectrometer operating in the mid-infrared region, including ultra-trace molecular spectroscopy of CO₂ isotopologues and the direct interrogation of weak mirror birefringence and polarization-dependent losses, will be discussed.

A cavity ring-down spectrometer calibrated with a set of precise atomic lines was built to retrieve precise line parameters in the near infrared. [1,2] The spectrometer allows us to detect absorptions with a sensitivity of 10⁻¹¹ cm⁻¹ and a spectral precision up to 10⁻⁶ cm⁻¹. Ro-vibrational lines in the second overtone of H₂ have been observed, including the extremely weak S₃(5) line with a line intensity less than 1×10⁻³⁰cm/molecule, which is among the weakest molecular lines detected by absorption in the gas phase. The absolute line positions of H₂ agree well with the high-level quantum chemical calculations including relativistic and QED corrections, with the deviation being less than 5×10⁻⁴ cm⁻¹. [3,4] A quantitative study has also been carried out on the ν₁+5ν₃ band of CO₂. [5] It was the first CO₂ band observed 80 years ago in the spectrum of Venus. We determined the line positions with an accuracy of 3×10⁻⁵ cm⁻¹, two orders of magnitude better than previous studies. Similar studies have been carried out to determine the line parameters of H₂O [6] and CO [7] in the spectral regions near 0.8 μm. The spectroscopic parameters can be used in varies studies, from the atmospheres of the earth-like planets to the test of fundamental physics. References [1] H. Pan, et al. Rev. Sci. Instrum. 82, 103110 (2011). [2] C.-F. Cheng, Opt. Expr. 20, 9956 (2012). [3] C.-F. Cheng, et al. Phys. Rev. A 85, 024501 (2012). [4] y. Tan, et al. J. Mol. Spectrosc. 300, 60 (2014). [5] Y. Lu, et al. Astrophys. J. 775, 71 (2013). [6] Y. Lu, et al. JQSRT 118, 96 (2013). [7] Y. Tan, et al. "Ro-vibrational analysis of the fifth overtone of CO at 802 nm", under preparation.

Optical cavities enhance sensitivity in absorption spectroscopy. While this is commonly done with single wavelengths, broad bandwidths can be coupled into the cavity using frequency combs. The combination of cavity enhancement and broad bandwidth allows simultaneous measurement of tens of transitions with high signal-to-noise for even weak near-infrared transitions. This removes the need for time-consuming sequencing acquisition or long-term averaging, so any systematic errors from long-term drifts of the experimental setup or slow changes of sample composition are minimized. Resolving comb lines provides a high accuracy, absolute frequency axis. This is of great importance for gas metrology and data acquisition for future molecular lines databases, and can be applied to simultaneous trace-gas detection of gas mixtures. Coupling of a frequency comb into a cavity can be complex, so we introduce and demonstrate a simplification. The Pound-Drever-Hall method for locking a cavity and a frequency comb together requires a phase modulation of the laser output. We use the graphene modulator that is already in the Tm fiber laser cavity for controlling the carrier envelope offset of the frequency comb, rather than adding a lossy external modulator. The graphene modulator can operate at frequencies of over 1  MHz, which is sufficient for controlling the laser cavity length actuator which operates below 100 kHz. We match the laser cavity length to fast variations of the enhancement cavity length. Slow variations are stabilized by comparison of the pulse repetition rate to a GPS reference. The carrier envelope offset is locked to a constant value chosen to optimize the transmitted spectrum. The transmitted pulse train is a stable frequency comb suitable for long measurements, including the acquisition of comb-resolved Fourier transform spectra with a minimum absorption coefficient of about 2×10⁻⁷ cm⁻¹. For our 38 cm long enhancement cavity, the comb spacing is 394 MHz. With our 300 cm⁻¹ bandwidth at 2 μm, we simultaneously measure the full comb line resolved CO₂ vibrational manifold at 4850 cm⁻¹. Other spectral ranges can be accessed by using graphene with different gain fibers or nonlinear frequency conversion.

Dual-comb spectroscopy is arguably the natural successor to FTIR. Based on the interference between two frequency combs, this technique can record broadband spectra with a resolution better than 0.0003 cm⁻¹. Like FTIR, dual-comb spectroscopy measures an entire spectrum simultaneously, allowing for suppression of systematic errors related to temporal dynamics of the sample. Unlike FTIR it records the entire spectrum with virtually no instrument lineshape or error in the frequency axis. The lack of moving parts in dual-comb spectroscopy means that spectra can be recorded in milliseconds to microseconds with the desired signal-to-noise being the only real constrain on the minimum recording time. Finally the high spacial beam quality of the frequency combs allows for increased sensitivity through long interaction paths either in free-space, multi-pass cells or enhancement cavities. This talk will explore the recent use of dual-comb spectroscopy in the near-infrared to measure atmospheric carbon dioxide, methane and water concentrations over a 2-km outdoor open-air path. Due to many of the strengths just mentioned, precisions of < 1 ppm for CO₂ and < 3 ppb for CH₄ in 5 min are achieved making this system very attractive for carbon monitoring at length scales relevant to carbon transport models. Additionally this presentation will address recent work on robust, compact, and portable dual-comb spectrometers as well as dual-comb spectroscopy further into the IR.

Doppler-free transition frequencies for ν₄ and ν₅ hot bands in the band of C₂H₂ have been measured using saturation dip spectroscopy with an extended cavity diode laser referenced to a frequency comb. The frequency accuracy of the measured transitions, as judged from line shape model fits and the spectrometer stability, is better than 30 kHz. This is some 2-3 orders of magnitude improvement on the accuracy and precision of previous measurements of the line positions derived from the analysis of high-resolution Fourier transform infrared absorption spectra. The data were analyzed by determining the upper state energies, using known lower state level positions, and fitting them to a J(J+1) polynomial expansion to identify perturbations. The results reveal that the upper rotational energy level structure is mostly regular but suffers J−localized perturbations causing level shifts between one and several hundred MHz. These perturbations are due to accidental near degeneracies with energy levels of the same J and larger bending vibrational excitation. Acknowledgements: We are most grateful to Prof. D.S Perry (U. of Akron) and Prof. M. Herman (U. Libre de Bruxelles) for providing us with detailed results from their work and helpful discussions. Work at Brookhaven National Laboratory is funded by the Division of Chemical Sciences, Geosciences and Biosciences within the Offices of Basic Energy Sciences, Office of Sciences, U.S. Department of Energy under Contract Nos. DE-AC02-98CH10886 and DE-SC0012704.

In work reported by Twagirayezu et al. at this meeting, the rest frequencies of more than 100 lines in the ν₄ and ν₅ hot bands in the ν₁ + ν₃ combination band of acetylene have been measured by saturation dip spectroscopy using an extended cavity diode laser locked to a frequency comb. This work was orginally directed towards providing a set of accurate frequencies for the hot band line positions to aid in modeling the lineshapes of the main lines in the band. In analyzing the results, we find that many of the upper levels in the hot band transitions suffer small, and in some cases not so small, local perturbations. These arise because of J-dependent near degeneracies between the title levels and background levels of the same symmetry, mostly derived from zero order states involving multiple quanta of bending excitation. The vibration-rotation levels at the energies in question have previously been modeled using a polyad-based HamiltonianM. Herman and D. S. Perry, Phys. Chem. Chem. Phys., 15, 9970-9993 (2013)nd the present data can be interpreted on the basis of this model, but they also provide information which can be used to refine the model, and point to terms that may have previously been neglected. The most important result is that the high precision of the measurements gives the opportunity to calibrate the effects of background levels associated with high bending quantum numbers and angular momentun states that are otherwise very difficult to access. Acknowledgments: We are most grateful to D. S Perry (U. Akron) and M. Herman (U. Libre de Bruxelles) for helpful discussions. Work at Brookhaven National Laboratory is funded by the Division of Chemical Sciences, Geosciences and Biosciences within the Offices of Basic Energy Sciences, Office of Sciences, U.S. Department of Energy under Contract Nos. DE-AC02-98CH10886 and DE-SC0012704.

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M. Herman and D. S. Perry, Phys. Chem. Chem. Phys., 15, 9970-9993 (2013)a

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 polarizationJ. Opt. Soc. Am. B 32, 838 (2015) The approach has been validated by discussion experimental data obtained on two transitions of C₂H₂ in the near-infrared under moderated saturationOptics 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.

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J. Opt. Soc. Am. B 32, 838 (2015). Optics Express 16, 14689 (2008).

The hyperfine structure of non-rigid molecules in which hyperfine coupling arises from equivalent nuclei that can be exchanged by large amplitude motions is of great interest and lead to unexpected results. In the non-rigid (C₂D₂)₂ and (D₂O)₂ dimers, the hyperfine structure arising for nondegenerate tunneling sublevels can be accounted for using an effective quadrupole coupling Hamiltonian with the same coupling constant for all four deuterium atoms.Bhattacharjee, Muenter, and Coudert, J. Chem. Phys. 97 (1992) 8850; and Stahl and Coudert, J. Mol. Spectrosc. 157 (1993) 161.n the non-rigid species CD₃COH and HCOOCH₃, the large amplitude torsional motion leads to hyperfine patterns which are qualitatively dependent on the torsional symmetry of the levels.Coudert and Lopez, J.\ Mol. Spectrosc. 239 (2006) 135; and Tudorie, Coudert, Huet, Jegouso, and Sedes, J. Chem. Phys. 134 (2011) 074314.he interaction between a large amplitude torsional motion and the hyperfine coupling may also lead to a less known hyperfine effect, the so-called magnetic spin-torsion coupling, which was first studied by Heuvel and DymanusHeuvel and Dymanus, J. Mol. Spectrosc. 45 (1973) 282 and ibid 47 (1973) 363.nd which has not yet been conclusively evidenced. In this talk, the magnetic hyperfine structure of the non-rigid methanol molecule will be investigated experimentally and theoretically. 13 hyperfine patterns were recorded using two molecular beam microwave spectrometers. These patterns, along with previously recorded ones,^c were analyzed in an attempt to evidence the effects of the magnetic spin-torsion coupling. The theoretical approach setup to analyze the observed data accounts for the spin-torsion coupling, in addition to the familiar magnetic spin-rotation and spin-spin couplings, and relies on symmetry considerations to build a hyperfine coupling Hamiltonian and a spin-rotation-torsion wavefunction compatible with the Pauli exclusion principle. In the talk, the results of the analysis will be presented. The hyperfine coupling parameters retrieved will be discussed and we hope to be able to conclusively evidence the effects of the magnetic spin-torsion.

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Bhattacharjee, Muenter, and Coudert, J. Chem. Phys. 97 (1992) 8850; and Stahl and Coudert, J. Mol. Spectrosc. 157 (1993) 161.I Coudert and Lopez, J.\ Mol. Spectrosc. 239 (2006) 135; and Tudorie, Coudert, Huet, Jegouso, and Sedes, J. Chem. Phys. 134 (2011) 074314.T Heuvel and Dymanus, J. Mol. Spectrosc. 45 (1973) 282 and ibid 47 (1973) 363.a

In this talk we present a possible explanation, based on torsionally mediated proton-spin-overall-rotation interaction operators, for the surprising observation in Nizhny Novgorod several years agoG. Yu. Golubiatnikov, S. P. Belov, A. V. Lapinov, "CH₃OH Sub-Doppler Spectroscopy," (Paper MF04) and S.P. Belov, A.V. Burenin, G.Yu. Golubiatnikov, A.V. Lapinov, "What is the Nature of the Doublets in the E-Methanol Lamb-dip Spectra?" (Paper FB07), 68^th International Symposium on Molecular Spectroscopy, Columbus, Ohio, June 2013.f doublets in some Lamb-dip sub-millimeter-wave transitions between torsion-rotation states of E symmetry in methanol. These observed doublet splittings, some as large as 70 kHz, were later confirmed by independent Lamb-dip measurements in Kharkov. In this talk we first show the observed J-dependence of the doublet splittings for two b-type Q branches (one from each laboratory), and then focus on our theoretical explanation. The latter involves three topics: (i) group theoretically allowed terms in the spin-rotation Hamiltonian, (ii) matrix elements of these terms between the degenerate components of torsion-rotation E states, calculated using wavefunctions from an earlier global fit of torsion-rotation transitions of methanol in the v_t = 0, 1, and 2 statesLi-Hong Xu, J. Fisher, R.M. Lees, H.Y. Shi, J.T. Hougen, J.C. Pearson, B.J. Drouin, G.A. Blake, R. Braakman, "Torsion-Rotation Global Analysis of the First Three Torsional States (v_t = 0, 1, 2) and Terahertz Database for Methanol," J. Mol. Spectrosc., 251, 305-313, (2008). and (iii) least-squares fits of coefficients of these terms to about 35 experimentally resolved doublet splittings in the quantum number ranges of K = -2 to +2, J = 13 to 34, and v_t = 0. Rather pleasing residuals are obtained for these doublet splittings, and a number of narrow transitions, in which no doublet splitting could be detected, are also in agreement with predictions from the theory. Some remaining disagreements between experiment and the present theoretical explanation will be mentioned.

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Footnotes:

G. Yu. Golubiatnikov, S. P. Belov, A. V. Lapinov, "CH₃OH Sub-Doppler Spectroscopy," (Paper MF04) and S.P. Belov, A.V. Burenin, G.Yu. Golubiatnikov, A.V. Lapinov, "What is the Nature of the Doublets in the E-Methanol Lamb-dip Spectra?" (Paper FB07), 68^th International Symposium on Molecular Spectroscopy, Columbus, Ohio, June 2013.o Li-Hong Xu, J. Fisher, R.M. Lees, H.Y. Shi, J.T. Hougen, J.C. Pearson, B.J. Drouin, G.A. Blake, R. Braakman, "Torsion-Rotation Global Analysis of the First Three Torsional States (v_t = 0, 1, 2) and Terahertz Database for Methanol," J. Mol. Spectrosc., 251, 305-313, (2008).,