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.
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.
High sensitivity detection of quantum absorption is demonstrated at a sensitivity of
1times1011 integrated absorption, in 1 sec, using 10 mTorr total gas pressure. Achieving highly sensitive detection relies on simple basic principles: 1) The molecule-generated electric field in the forward direction (the "darkness wave") is most precious, and contains the maximum available information. It is the physical manifestation of the -
alpha∗L term appearing when beer#### absorption law is expanded for low opacity, 2) After generating the molecular signal, the detected unabsorbed light sets the "shotnoise" measurement floor. We use an optical transmission cavity for the gas cell, since the high internal "build-up" field will elicit a strong molecular "darkness wave", for a given transmitted de light on the detector, A more conventional explanation of Gavity Enhancement would be the extension of the effective cell length by the factor finesse
∗2/pi.3) To avoid excess low-frequency noise, such small signals should be measured by ac methods, comparing on-resonant and off-resonant cases in quick succession. 4) By SIMULTANEOUSLY obtaining and subtracting these cases, one provides a siginal channel with NO OUTPUT unless there is a resonance. This is conveniently accomplished by using the FM detection method with the optical heterodyne sidebands and carrier being transmitted through the cavity via adjacent axial orders 5). A remarkable property of this configuration, when the modulation frequency= cavity mode spacing, is the suppression of ANY detection of laser frequency noise with the transmitted light. We can refer to this property as (laser FM-) noise-Immune detection. This enables profitable use of cavity finesse in the range above 10,000, without a nois penalty, Altogether, we refer to this new spectroscopy as Noise-Immune, Cavity-Enhanced, Optical Heterodyne Molecular spectroscopy, i.e. "NICE OHMS". We have measured excellent saturated dispersion signals from HCCH in the band near 790 mm (
nu1+3nu3), and recently, using a Nd:YAG source, from the HCCD P(5) line (
nu2+3nu3) at 1064 mm. The saturation peaks broaden from the transit limit of 270 kHz near zero pressure at the rate 34.7 kHz/m Torr. We observe interesting narrow linwidths 8-fold below the transit limit, basically using optical selection of slow molecules by low power and pressure (2 mW and 2 m Torr). The absolute frequency is measurred to be 281, 635,363,960 MHz
pm45 kHz.
We report on the sub-Doppler saturation spectroscopy of the nitrous oxide (N2O) overtone transition at 1.28 μm. This measurement is performed by the noise-immune cavity-enhanced optical heterodyne molecular spectroscopy technique based on the quantum-dot (QD) laser. A high intra-cavity power, up to 10 W, reaches the saturation limit of the overtone line using an optical cavity with a high finesse of 1.14(5)×105. At a pressure of several mTorr, the saturation dip is observed with a full width at half-maximum of about 2 MHz and a signal-to-noise ratio of 71. To the best of our knowledge, this is the first saturation spectroscopy of molecular overtone transitions in the 1.3 μm region. The QD laser is then locked to this dispersion signal with a stability of 15 kHz at 1 s integration time. We demonstrate the potential of the N2O as a marker because of its particularly rich spectrum at the vicinity of 1.28–1.30 μm where there are several important forbidden transitions of atomic parity violation measurements and the 1.3 μm O-band of optical communication.