Quantitative, nonlinear sub-Doppler sensitive spectroscopy requires reliable formalism for optimizing the detection of weak molecular absorption patterns. Phase modulation spectroscopy (FMS) is a common technique used to challenge the ultimate photon-shot-noise limit. In addition, nonlinear spectroscopy can exhibit surprising effects like resonance narrowing, i.e., resonance width below the transit-time rate, like it has been pointed out in the seventies. Here, by extending our previous work, we propose an analytical development associated with numerical integration to simulate the equivalent Lamb-dip under Gaussian beam conditions. Simulations of nonlinear profiles of two transitions belonging to the polyad Delta P11 of acetylene are discussed, and analyzed by fitting with standard functions. The respective roles of the transit-time, of the collision rate, and of the Rabi frequency (including the power broadening) are carefully discussed and reviewed. It shows "super-narrowing" effects under specific low pressure and low power conditions. A reviewing introduction states previous experimental reports as well about previous modeling. (C) 2019 Elsevier Ltd. All rights reserved.

Weak transitions in the (2,0) overtone band of the hydrogen deuteride molecule at λ=1.38  μm were measured in saturated absorption using the technique of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. Narrow Doppler-free lines were interrogated with a spectroscopy laser locked to a frequency comb laser referenced to an atomic clock to yield transition frequencies [R(1)=217105181895(20)  kHz; R(2)=219042856621(28)  kHz; R(3)=220704304951(28)  kHz] at three orders of magnitude improved accuracy. These benchmark values provide a test of QED in the smallest neutral molecule, and they open up an avenue to resolve the proton radius puzzle, as well as constrain putative fifth forces and extra dimensions.

With the advent of new accurate and sensitive spectrometers, cf. combining optical cavities (for absorption enhancement), the requirement for reliable molecular transition modeling is becoming more pressing. Unfortunately, there is no trivial approach which can provide a definitive formalism allowing us to solve the coupled systems of equations associated with nonlinear absorption. Here, we propose a general approach to deal with any spectral shape of the electromagnetic field interacting with a molecular species under saturation conditions. The development is specifically applied to Gaussian-shaped beams. To make the analytical expressions tractable, approximations are proposed. Finally, two or three numerical integrations are required for describing the Lamb-dip profile. The implemented model allows us to describe the saturated absorption under low pressure conditions where the broadening by the transit-time may dominate the collision rates. The model is applied to two specific overtone transitions of the molecular acetylene. The simulated line shapes are discussed versus the collision and the transit-time rates. The specific collisional and collision-free regimes are illustrated, while the Rabi frequency controls the intermediate regime. We illustrate how to recover the input parameters by fitting the simulated profiles. (C) 2017 Elsevier Ltd. All rights reserved.

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 (similar to 800 and similar to 880 nm). It demonstrates the differences in behavior between a high-finesse cavity (similar to 400 000) and a lower finesse cavity (similar to 50 000). Beating frequency, characteristics time, and beat amplitude are mainly discussed versus the analyzer angle. A cavity birefringence of similar to 1.6 x 10(-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)].

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 side-bands 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. Express 16, 14689 (2008)] allowed us to assess the eligibility of the approach. (C) 2015 Optical Society of America

Around 398 nm, the jet-cooled-spectrum of NO2 exhibits a well identified dissociation threshold (D-0). Combining the continuous-wave absorption-based cavity ringdown spectroscopy technique and laser induced fluorescence detection, an energy range of similar to 25 cm(-1) is analyzed at high resolution around D-0. In addition to the usual molecular transitions to long-lived energy levels, similar to 115 wider resonances are observed. The position, amplitude, and width of these resonances are determined. The resonance width spreads from similar to 0.006 cm(-1) (i. e., similar to 450 ps) to similar to 0.7 cm(-1) (similar to 4 ps) with large fluctuations. The identification of at least two ranges of resonance width versus the excess energy can be associated with the opening of the dissociation channels NO2 -> NO(X-2 Pi(1/2), v = 0, J = 1/2) + O(P-3(2)) and NO2 -> NO(X-2 Pi(1/2), v = 0, J = 3/2) + O (P-3(2)). This analysis corroborates the existence of loose transition states close to the dissociation threshold as reported previously and in agreement with the phase space theory predictions as shown by Tsuchiya's group [Miyawaki et al., J. Chem. Phys. 99, 254-264 (1993)]. The data are analyzed in the light of previously reported frequency-and time-resolved data to provide a robust determination of averaged unimolecular dissociation rate coefficients. The density of reactant levels deduced (rho(reac) similar to 11 levels/cm(-1)) is discussed versus the density of transitions, the density of resonances, and the density of vibronic levels. (C) 2015 AIP Publishing LLC.

Around 398 nm, the jet-cooled NO2 spectrum exhibits a well identified dissociation threshold (D0). Combining LIF detection and continuous-wave absorption-based CRDS technique a frequency range of ∼ 25 cm−1 is analyzed at high resolution around D0. In addition to the usual rovibronic transitions towards long-lived energy levels, ∼ 115 wider resonances are observed. Over this energy range, the resonance widths spread from ∼ 0.006 cm−1 (∼ 450ps) to ∼ 0.7 cm−1 (∼ 4 ps) with large fluctuations. At least two ranges of resonance width can be identified when increasing the excess energy. They are associated with the opening of the dissociation channels NO2 → NO ( X Π1/2, v = 0, J = 1/2 ) + O ( P2 ) and NO2 → NO ( X Π1/2, v = 0, J = 3/2 ) + O ( P2 ) . Weighted mean unimolecular dissociation rate coefficients kuni are calculated. The density of reactants (following the RRKM predictions) is deduced, and it will be discussed versus the density of transitions, the density of resonances and the density of vibronic levels. The data are analyzed in the light of time-resolved data previously reported. This analysis corroborates the existence of loose transition states along the reaction path close to the dissociation energy in agreement with the phase space theory predictionsa.

The R-q(0)(0) rotational transition in the (A) over tilde B-2(2) <- (X) over tilde (2)A(1) system of jet-cooled NO2 located around 12 536 cm(-1) is analyzed using a nonlinear-susceptibility formalism designed to describe the saturated absorption due to two identical counter-propagating radiations in an n-level system. An analytical solution of the equations of motion is obtained in the frequency space by considering the pertinent experimental conditions, mainly a high-finesse cavity and a slit-shaped supersonic expansion. Calculation of the nonlinear absorption coefficient requires the summing of all Zeeman-component contributions and a final numerical integration over the frequency detuning assuming a Maxwell-Boltzmann speed distribution. Determination of the experimental absorption coefficients is obtained by converting the shape of the temporal decay of the electromagnetic field amplitude initially captured inside the cavity. The molecular Hamiltonian includes both spin-rotation and hyperfine interactions. Molecular constants relative to the upper level are derived by exploiting Doppler-broadening-free so-called saturated-absorption cavity-ring-down spectroscopy. The dipole moment of the partially assigned hot band is obtained [mu(band) = 0.0047(12) D] together with the number density and the effective population relaxation rates. The model is validated by varying the intracavity power from 0 to 230W(i. e., up to a maximum peak irradiance of 240 x 10(3) W/cm(2)), representing saturation coefficients up to 120. The experimental position, shape, and width of the Lamb and crossover dips are well reproduced. The spatial shape and modulation of the electromagnetic field are discussed.

A new approach avoiding double (two-step) diagonalization is proposed to deal with internal rotation. The development of this method was stimulated by the jet-cooled high resolution spectrum of the vibrationless (A) over tilde <- (X) over tilde transition of the deuterated species of the methyl peroxy radical. This spectrum, originally analyzed with a rigid rotor Hamiltonian including spin-rotation but neglecting internal rotation, has been revisited in the previous paper (P. Dupre, J. Chem. Phys. 134, 244308 (2011)) and a determinable yaw of the molecular principal axes of inertia about the c-axis (axis-switching) during the electronic transition was established. The spectral resolution of the jet-cooled data of the vibrationless transition (similar to 7355 - 7390 cm(-1)) does not allow the observation of splitting due to internal rotation of the methyl top, but when these data are combined with the low resolution room temperature data (similar to 7200 - 8000 cm(-1)) accurate fits or simulations of the two sets of data are possible. A recent study of the room temperature data has been reported in this journal (G. M. P. Just et al., J. Chem. Phys. 127, 044310 (2007)) showing evidence of the internal rotation coupling by analyzing the intensity of the torsional mode energy progression. That investigation combined ab initio quantum chemistry calculations and the rho-axis-method (RAM) to model the internal rotation. Here, a comparison of full spectral intensity analyses based on both the usual RAM and on the new approach requiring a single-diagonalization principal-axis-method is presented. The comparison favors the single-diagonalization approach. Axis-switching and spin-rotation coupling are incorporated in the analysis, in which the use of the principal axes of inertia is maintained. Symmetries, energy levels, and advantages are carefully discussed for all methods. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3599954]

The jet-cooled high resolution spectrum of the vibrationless Ã←X̃ transition of the deuterated species of the methyl peroxy radical has been recently published in this journal (S. Wu, P. Dupré, P. Rupper, and T. A. Miller, J. Chem. Phys. 127, 224305 (2007)). The spectrum was analyzed using a rigid-rotor model with quadratic spin-rotation coupling. The analysis was based on the fit of ∼350 partially resolved line positions and was quite satisfactory. However, the full simulation of the spectral intensity clearly identifies a lack of ability to reproduce relatively small line clumps ("extra" lines) located between the two main central Q branches. This is indicating of an incomplete initial analysis. In the present paper we reanalyze this electronic transition by considering a reference-frame axis-switching resulting from the nuclear rearrangement associated to the electronic transition (spectra obtained at two different temperatures are considered). The potential energy hypersurfaces of the two electronic states are sufficiently dissimilar to induce changes in the molecule geometry, particularly, the angle COÔ, which induces a rotation (∼1.7°) of the principal axes of inertia located in the molecule symmetry plane. The present analysis is supported by a global fitting of the spectrum intensity and gives rise to a slightly different set of molecular constants. Attention is paid to the wavefunction symmetry assignment of a non-orthorhombic molecule. Couplings due to the torsion of the methyl group are discussed in the following paper (P. Dupre, J. Chem. Phys. 134, 244309 (2011)).

This paper supplements two papers by the same author [J. Chem. Phys. 134, 244308 and 224309, (2011)] devoted to the analysis of the experimental spectra of methyl radicals CH3O2 and CD3O2. It is devoted to the analysis of the lowest order terms of the rotational and of the centrifugal distortion Hamiltonian of molecules exhibiting an internal rotation (three-fold potential) or requiring a rotation of the reference frame with the perspective of determining the line intensity. It deals with different Hamiltonian expansions by keeping the uniqueness of the molecular parameters referenced in the principal-inertia-axis system (PAS) reference frame. The reduction of the effective second-order internal rotation Hamiltonian is discussed in the PAS and rho-axis-system (RAS) frames for application to standard (double-diagonalization) and new ‘non-approximate’ (single-diagonalization) approaches, i.e. PAM, RAM, SDPAM or SDRAM, which have been implemented to analyse the methyl peroxy radical spectra.

Author Institution: Department of Chemistry, The Ohio State University, 120 W $18^{\rm th}$ Ave, Columbus OH, 43210

A tunable injection seeded Ti:sapphire laser source has been developed and tested. Slave-master tandem cavity and ramp-lock-and-fire concepts have been implemented and fully controlled by a digital signal processor. A Fourier-transform-based analysis, as well as direct measurements, have demonstrated spectral linewidths in the range of 3.5-15 MHz (HWHM), with potential tunability over the entire Ti:sapphire lasing range. A quasi-Fourier-transform limited spectral linewidth is demonstrated assuming a secant hyperbolic shape of the electromagnetic field. Output energies >100 mJ have been reached with approximately 300 mJ of pump energy. The highest spectral purity is obtained using the quadruple pumping scheme.

Author Institution: Laser Spectroscopy Facility, Department of Chemistry, The Ohio; State University, 120 W. 18th Avenue, Columbus OH 43210

The nearly rotationally resolved spectrum of the A (2)A(')<--X (2)A(") 0(0)(0) transition of perdeutero methyl peroxy near 1.35 microm has been studied via pulsed cavity ringdown spectroscopy. Albeit, this is a weak transition, it is possible to observe the spectrum under jet-cooled conditions (approximately 15 K) by combining a source of narrow-bandwidth radiation (approximately 250 MHz) with a supersonic slit-jet expansion incorporating an electric discharge. The near infrared radiation was obtained by using stimulated Raman scattering and a pulsed, nearly Fourier-transform-limited Ti:sapphire amplifier seeded by a scanable cw Ti:sapphire ring laser. The experimental spectrum has been fitted using a model Hamiltonian that includes the rigid body rotation of an asymmetric top and the spin-rotation interaction. An excellent quality fit was obtained resulting in the determination of 15 molecular parameters characterizing the A and X states. Other results reported for CD(3)O(2) include an estimate of the radical concentration and the vibronic transition dipole from the observed absorption intensities. Details about the spectral linewidths are also discussed.