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

Abstract

The dependence of Doppler broadened noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS) on the modulation index, β, has been investigated experimentally on C 2 H 2 and CO 2 , both in the absence and the presence of optical saturation. It is shown that the maximum signals are obtained for β that produce more than one pair of sidebands: in the Doppler limit and for the prevailing conditions (unsaturated transition and the pertinent modulation frequency and Doppler widths) around 1 and 1.4 for the dispersion and absorption detection phases, respectively. The results verify predictions given in an accompanying work. It is also shown that there is no substantial broadening of the NICE-OHMS signal for β < 1. The use of β of unity has yielded a Db-NICE-OHMS detection sensitivity of 4.9 × 10 −12 cm −1 Hz −1∕2 , which is the lowest (best) value so far achieved for NICE-OHMS based on a tunable laser. The number of sidebands that needs to be included in fits of the line-shape function to obtain good accuracy has been assessed. It is concluded that it is enough to consider three pairs of sidebands whenever the systematic errors in a concentration assessment should be below 1% when β < 2 are used and <1‰ for β < 1.5.

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

“…This also enabled locking of the FMS modulation frequency to the FSR of the cavity by the DeVoe-Brewer (DVB) technique. To maximize the signal, the modulation index for the FMS, β, was set to unity [11]. The PDH and FSR error signals were created by demodulating the backreflected light at 20 and 361 MHz, respectively.…”

“…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] …”

“…The optimum situation occurs when the mean square of the model line shape function over the scanning range, hχ 2 m i Δv , and thereby also the mean square of the NICE-OHMS signal, are maximal. It can be noticed that this represents a significantly shorter scan than what normally has been used, which is a number of Γ D , which often has been taken as 1500 MHz [9][10][11]16], indicated by the solid vertical lines in the plots in Figs. 2 and 3.…”

“…NICE-OHMS is a laser-based spectroscopic technique that was originally developed for frequency standard applications using its sub-Doppler (sD) mode of operation [3][4][5], demonstrating an excellent detection sensitivity, with a NEAL of 10 −14 cm −1 measured over 1 s [5][6][7] and recently a frequency stability of 5 × 10 −13 over 1 s [8]. In its Doppler-broadened (Db) mode of operation it has repeatedly demonstrated a spectral NEAL in the 10 −12 -10 −13 cm −1 Hz −1∕2 range [9][10][11]. This mode of operation has mostly been used for trace gas applications, e.g., for detection of species such as O 2 [12], N 2 O [13], NO [14,15], C 2 H 2 [10,16], and CH 4 [17,18].…”

“…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.…”