High-resolution cavity enhanced absorption spectroscopy using phase-sensitive detection

Abstract

High-resolution cavity enhanced absorption spectroscopy (CEAS) using a fast power-modulated laser with a phase-sensitive detection scheme has been adopted. A detailed investigation into the effects of laser chopping frequency and cavity modulation frequency (via a piezoelectric translator) on the sensitivity will be presented. The observed detection sensitivity has been improved by more than an order of magnitude after the implementation of phase sensitive detection. The observed single-scan sensitivity of the present setup is about 4.4 ppm Hz^−1/2 in fractional absorption using cavity mirrors with moderate reflectivity of ∼0.9997 and a ringdown cavity cell of 175 cm in length.

Introduction

The detection of weak spectral absorptions due to molecules either at very low abundance or with very small absorption cross sections has been a main concern in the gas phase spectroscopy. Over the years, a variety of approaches to the issue have been developed [1]. Most of these techniques require complex experimental setup and experienced personnel to obtain satisfactory results. Cavity ring down spectroscopy (CRDS) and related techniques [2] initiated by O’Keefe and Deacon [3] are relatively new and simple approaches in direct absorption spectroscopy that have been widely used recently. Based on the original idea of measuring the reflectivity of laser mirrors by means of a high finesse optical cavity [4], [5], CRDS measures the rate of absorption instead of the amplitude of absorption. In a typical CRD experiment, a fast response detector is used to measure the time variation of the signal leaking from the high finesse optical cavity in which a light pulse is trapped. This signal, which is proportional to the light intensity in the cavity, decays according to a first-order rate law. By comparing the decay rate constants (i.e. the inverse of the so-called ringdown time τ) of a cavity before and after filling with gaseous molecular species, one can obtain the molecular absorption coefficients κ(ν) of the particular species as a function of frequency based on equations

$$\text{τ(ν)=}\text{d}\text{c[1−R]}\text{(}\text{for}\text{empty}\text{cell}\text{)}$$

and

$$\text{τ(ν)=}\text{d}\text{c[1−R+κ(ν)d]}\text{(}\text{for}\text{filled}\text{cell}\text{),}$$

where d is the separation of cavity mirrors, R is the reflectivity of cavity mirrors, and c is the speed of light, respectively.

This approach, as pointed out by O’Keefe and Deacon [3], provides effective optical paths on the order of tens of kilometers. In addition, CRD techniques are insensitive to laser source noise since the determination of κ(ν) from the decay curve is in principle independent of the initial power trapped in the cavity. The ultimate sensitivity of CRDS is limited by the reflectivity of the cavity mirrors, which determines the effective optical path and the ringdown time. Using mirrors with reflectivity better than 0.99, O’Keefe and Deacon [3] obtained a sensitivity in absorbance of $\text{10}{}^{\mathrm{-8}}\text{cm}{}^{\mathrm{-1}}$ with signal averaging. Since this remarkable work, CRDS has been widely recognized as a sensitive direct absorption technique.

In their original CRDS experiments, O’Keefe and Deacon [3] used a pulsed laser to ensure that sufficient power was injected into the cavity and the subsequent decay was completed before the next injection of light pulse. The use of high-resolution cw lasers in CRDS promises better resolution for revealing more detailed spectral features. Nevertheless, the difficulties of their application in CRDS are twofold: (1) the low energy output of cw lasers requires a resonance condition (i.e., the mode-matching condition, in which the frequency of laser is equal to the frequency of one of the cavity modes) for the light injection process and (2) the laser needs to be blocked subsequently for monitoring the power decay. These difficulties have been overcome by a number of approaches [6], [7], [8], [9], [10], [11], [12]. One of these approaches involves a mode-locking scheme in which the cavity frequency was actively locked to the laser frequency to maintain the resonance condition at all time together with an optical switch to interrupt the laser light periodically [6], [7], [8]. While an excellent sensitivity of $\text{10}{}^{\mathrm{-10}}\text{cm}{}^{\mathrm{-1}}$ has been reported using this approach [7], it has only be implemented by a handful of laboratories because of the complexity in the apparatus.

In a different approach, the phase shift form of CRDS was reported by Meijer and coworkers [11], [12] using an unstabilized cavity aligned to have dense multi-fold of high-order transverse modes. The injection of laser power occurs when there is an accidental mode matching between the cavity and laser. This approach was later adopted in the form of cavity enhanced absorption spectroscopy (CEAS) [13] and cw-integrated cavity output spectroscopy (cw-ICOS) [14] in which the time-integrated signal of the power buildup but not the power decay in the cavity is measured. In order to efficiently couple the laser light into the cavity, piezoelectric-controlled mounts may be used for the cavity mirrors. CEAS-type techniques require only simple experimental setup yet achieve comparable sensitivity as CRDS. The fact that CEAS signals are measured from the power buildup in the cavity has introduced new sources of noise due to the power fluctuation of laser and the shot-to-shot fluctuation in power injection during each resonance [15]. These factors, on the other hand, have little effect on the sensitivity of CRDS. Signal averaging has been a common routine to improve the signal-to-noise ratio (S/N) since the reduction of random noise is proportional to the square root of the number of scans used in signal averaging. In the initial CEAS experiments, 500 scans of time-integrated signals of a fast scanning laser were co-added to obtain a sensitivity comparable to CRDS. As pointed out by Maijer et al. [13] in the note of their original report, CEAS can be performed either using a fast scanning laser with unstabilized cavity or equivalently, a slow scanning laser with piezo-modulated cavity. This latter approach has recently been adopted by Cheung et al. [16]. A sensitivity of $\text{4.8×10}{}^{\mathrm{-9}}\text{cm}{}^{\mathrm{-1}}$ has been reported using ultrahigh reflectivity mirrors (R∼0.99999) together with a different data processing scheme in which only the highest buildup signal in each 1-s interval (instead of the time-integrated signal) was taken to obtain the spectrum.

The use of phase-sensitive detection (PSD) in CEAS was first demonstrated by Peeters et al. [17] in the study of ethylene absorption in the $\text{10}\text{μm}$ region using a line-tuned CO₂ laser. In a rather simple setup they have obtained a sensitivity of $\text{1.6×10}{}^{\mathrm{-6}}\text{cm}{}^{\mathrm{-1}}\text{Hz}{}^{\mathrm{-1/2}}$ by modulating the laser beam at a frequency of 30 Hz, which was used as the reference frequency for lock-in detection. PSD greatly improves the detection sensitivity as a result of the reduction of detection bandwidth. It is expected that PSD reduces the 1/f noise in the high reference frequency regime for better detection sensitivity. We report here an extensive investigation of the sensitivity of CEAS using lock-in detection of a fast power-modulated Ti:sapphire laser beam at slow scanning rate. By comparing the observed S/N ratio with and without the use of lock-in technique, an improvement of at least an order of magnitude was found in the former case. This work demonstrates that the use of phase-sensitive detection can compensate for the low reflectivity of cavity mirrors to achieve good sensitivity with simple experimental setup. Our implementation of phase-sensitive detection scheme in CEAS will be discussed below.