Doppler broadened noise-immune cavity-enhanced optical heterodyne molecular spectrometry: optimum modulation and demodulation conditions, cavity length, and modulation order

Abstract

Doppler broadened noise-immune cavity-enhanced optical heterodyne molecular spectrometry (Db-NICE-OHMS) has been scrutinized with respect to modulation and demodulation conditions (encompassing the modulation frequency, ν m , the modulation index, β, and the detection phase, θ), the cavity length, L, and the modulation order, k (defined as ν m ∕ν FSR , where ν FSR is the free-spectral range of the cavity), primarily in the Doppler limit but also for two specific situations in the Voigt regime (for equal Doppler and homogeneous width and for purely Lorentzian broadened transitions), both in the absence and presence of optical saturation (the latter for the case in which the homogeneous broadening is smaller than the modulation frequency). It is found that, for a system with a given cavity length, the optimum conditions (i.e., those that produce the largest NICE-OHMS signal) for an unsaturated transition in the Doppler limit comprise ν m ∕Γ D 1.6 (where Γ D is the half-width at half-maximum of the Doppler width of the transition), β 1.3, and θ 0.78π. It is also found that the maximum is rather broad; the signal takes 95% of its maximum value for modulation frequencies in the entire 0.4 ≲ ν m ∕Γ D ≲ 2.4 range. When optical saturation sets in, θ shifts toward the dispersion phase. The optimum conditions encompass k > 1 whenever L > 0.35L D and 2.6L D for the dispersion and absorption modes of detection, respectively [where L D is a characteristic length given by c∕2Γ D ]. Similar conditions are found under pressure broadened conditions.

Model for in-coupling of etalons into signal strengths extracted from spectral line shape fitting and methodology for predicting the optimum scanning range—demonstration of Doppler-broadened, noise-immune, cavity-enhanced optical heterodyne molecular spectroscopy down to 9 × 10^−14 cm^−1

“…where χ NO G ν c is the NICE-OHMS dispersion line shape function that is given by a combination of individual line shape functions that can be written as [11,19] …”

“…However, although Db NICE-OHMS already has been realized with previously found optimum conditions regarding signal strength [11,19] and reduction of etalons by the use of etalon immune distances (EIDs) [20], resulting in the system used in [16], Allan-Werle plots are in this work used to analyze the limiting factors of this NICE-OHMS setup [16]. By the knowledge gained from this analysis, as well as the noise incoupling model developed, two remaining causes of noise and background signals were identified.…”

Doppler broadened NICE-OHMS beyond the triplet formalism: assessment of optimum modulation index

“…As recently discussed in an accompanying work [4], the technique relies on a fairly large number of entities [5,6], which makes it nontrivial to assess these conditions. However, since it utilizes frequency modulation (FM) for reduction of technical noise, some of its properties are given by those of that technique.…”

“…To remedy this, Ehlers et al [4] recently derived a coherent description of Db-NICE-OHMS that encompasses the most relevant parameters-ν m , β, θ, the cavity length (L), and k-and can serve as a basis for assessment of the optimum design or detection conditions of the technique. Their analysis covered the cases when an existing NICE-OHMS system, based on an existing cavity, is to be optimized and when a NICE-OHMS system is to be designed from scratch for transitions in the Doppler limit and for the specific case with equal amounts of collision and Doppler broadening.…”

Shot-noise-limited Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectrometry

“…Low-frequency feedback (up to 1 kHz) is fed directly to the piezo in the EDFL. The f -EOM, which is equipped with a proton-exchanged waveguide to minimize the generation of RAM, is modulated by two radio frequency signals-one at 20 MHz and another at 380 MHz-to generate the sidebands for the PDH locking and the FMS with modulation indices of 0.1 and 1, respectively, the latter chosen to maximize the NICE-OHMS signal [29]. Before impinging onto the cavity, the laser propagates through an isolator (ISO), a half-wave plate (λ∕2), a modematching lens, a PBS, and a quarter-wave plate (λ∕4).…”