A theoretical description of Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) under optically saturated conditions is presented. Expressions for the strength and shape of the Doppler-broadened NICE-OHMS signals are given for both the absorption and the dispersion phase, in the Voigt regime as well as in the Doppler limit. It is shown that Doppler-broadened NICE-OHMS is affected less by optical saturation than other cavity-enhanced techniques; in the Doppler limit the absorption signal decreases by a factor of (1+G±1)−1/2, where G±1 is the degree of saturation for one of the frequency modulation sidebands, whereas the dispersion signal is virtually unaffected by optical saturation. In the Voigt regime both signals show additional dependence on optical saturation. The concept of saturation-insensitive detection is introduced and its conditions are identified.
A theoretical description of Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) under optically saturated conditions is presented. Expressions for the strength and shape of the Doppler-broadened NICE-OHMS signals are given for both the absorption and the dispersion phase, in the Voigt regime as well as in the Doppler limit. It is shown that Doppler-broadened NICE-OHMS is affected less by optical saturation than other cavity-enhanced techniques; in the Doppler limit the absorption signal decreases by a factor of (1+G±1)−1/2, where G±1 is the degree of saturation for one of the frequency modulation sidebands, whereas the dispersion signal is virtually unaffected by optical saturation. In the Voigt regime both signals show additional dependence on optical saturation. The concept of saturation-insensitive detection is introduced and its conditions are identified.
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.
An expression for the peak-to-peak sub-Doppler optical phase shift of two counterpropagating modes of light, to which the noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) dispersion signal is proportional, valid for arbitrary degree of saturation, is derived. For low degrees of saturation it agrees with the expression for weakly saturating (ws) conditions, [(1+S)−1/2−(1+2S)−1/2]α0/2, where S is the degree of saturation and α0 is the unsaturated peak absorption. However, the new expression, which can be written as 0.45S(1+S)−1α0/2, does not predict a distinct maximum as the ws expression does; instead it predicts an optical phase shift that increases monotonically with S and levels off to 0.45α0/2 for large S. This alters the optimum conditions for the sub-Doppler NICE-OHMS technique and improves its shot-noise-limited detectability. The new expression is based upon the same explicit assumptions as the ws expression but not the Kramers-Kronig relations, which are not valid for nonlinear responses, and is supported by experimental results up to S=100. The new expression is expected to be valid for all techniques measuring sub-Doppler dispersion signals.
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 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.
Noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) based on a fiber-coupled electro-optic modulator (EOM) provides a compact and versatile experimental setup. It has, however, been limited by background signals originating from an imbalance of the phase modulated triplet created by a cross-coupling between the principal axes of the polarization maintaining fibers and the extraordinary axis of the EOM. Two strategies for reducing these background signals are investigated: (i) using an EOM with a titanium diffused waveguide, in which the balance of the triplet is controlled by active feedback, and (ii) using an EOM with a proton exchanged waveguide that does not support light propagation along the ordinary axis. It is shown that both approaches significantly reduce drifts and noise in the system. Using a cavity with a finesse of 5700, an absorption sensitivity of 3.2×10−12 cm−1 in 1 min of integration time (i.e., 1.8×10−11 cm−1 Hz−1/2) is demonstrated for Doppler-broadened detection, the lowest reported so far for Doppler-broadened NICE-OHMS. For sub-Doppler detection, a minimum detectable optical phase shift of 1.3×10−12 cm−1 in 400 s of integration time is obtained.
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.
We present a theoretical analysis of high-frequency optical heterodyne saturation spectroscopy in Doppler-broadened coupled three-level systems. The saturating beam, which is assumed to be amplitude modulated at frequency δ (double-sideband suppressed carrier amplitude modulation) is resonant for one of the transitions. Through non-degenerate four-wave mixing processes, this modulation is transferred to a probe beam, resonant for the coupled transition. Saturating and probe fields may be either co-propagating or counter-propagating. The lineshape of the probe modulation is analysed via a third-order perturbation expansion of the atomic density matrix with respect to the incident field amplitudes. The resulting signal is integrated over velocities, in the Doppler limit approximation. Both population saturation effects and coherent (Raman-type, or two-photon) processes contribute to the signal. The various contributions appear as Lorentzian-type resonance doublets. We show that, in the absence of relaxation processes (collisional dephasing, or radiative cascades), destructive interferences between population saturation and coherent two-photon processes are responsible for the disappearance of one resonance doublet. Phase-interrupting collisions are thus predicted to lead to the existence of a « pressure-induced extra-resonance » (PIER) doublet, which could yield information on collisional processes in the impact regime. The properties of the predicted PIER doublets are analysed in relation with other types of PIER signals studied in four-wave mixing, and in time-resolved saturation spectroscopy.