Rapidly swept continuous-wave cavity-ringdown spectroscopy

Abstract

Continuous-wave (cw) cavity-ringdown (CRD) spectroscopy provides a highly sensitive way to measure optical absorption by observing the decay rate of light from a high-finesse optical cavity containing the sample of interest (usually gas-phase molecules). In rapidly swept cw-CRD spectroscopy, optical build-up and subsequent ringdown decay are initiated by rapidly sweeping the cavity length or the wavelength of the monochromatic tunable cw laser radiation, thereby establishing and interrupting optical resonance between the laser light and the longitudinal-mode frequencies of the cavity. We review the experimental methodology and applications of this technique, indicating its advantages and prospects for spectroscopic sensing.

Introduction

The cavity-ringdown (CRD) technique was first used for spectroscopy in 1988 [1] with pulsed lasers, which led to many significant early applications [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], (e.g., to laser-ablated molecules cooled in supersonic beams [2], [5], [6], [8], [9]). Continuous-wave (cw) lasers, on which this article focuses, were not employed for CRD spectroscopy [12], [13], [14], [15], [16], [17] until almost 10 years after O’Keefe’s pioneering work [1]. Reviews [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44] show that CRD spectroscopy is now well established and widely used. The sample of interest (which usually comprises gas-phase molecules) is contained in a high-finesse optical cavity into which coherent (e.g., laser) light is introduced. This light is allowed to build up in intensity and then to decay away (or ‘ring down’) with a characteristic exponential time constant τ once the build-up process is interrupted, by one means or another.

The ringdown time τ depends on the reflectivity of the cavity mirrors and additional intra-cavity optical losses (due to processes such as absorption and scattering). At particular wavelengths λ, optical absorption causes the ringdown rate constant τ⁻¹ to increase relative to that for an absorber-free cavity or for that at non-absorbing wavelengths. This enables optical absorption by constituents of the sample medium inside the cavity to be observed with high sensitivity and photometric accuracy.

The CRD approach is a form of cavity-enhanced laser spectroscopy, stemming from the realization (by Jackson [45] and Kastler [46], soon after the discovery of lasers 50 years ago) that particularly high laser-spectroscopic sensitivity could be achieved by placing an absorbing medium of interest inside a Fabry–Perot optical cavity which was external to the cavity of the laser itself. Assorted forms of cavity-enhanced laser spectroscopy have subsequently evolved, yielding remarkably low noise-equivalent detection sensitivity limits (for example, ∼10⁻¹⁴ cm⁻¹ Hz^−1/2 from the NICE-OHMS technique [47], [48]).

Such cavity-enhanced techniques benefit from the fact that, for light resonating in an optical cavity with high finesse $\mathcal{F}$, the equivalent effective absorption pathlength is enhanced (and like wise the detection sensitivity or contrast) by a factor G = 2$\mathcal{F}$/π [47], [48]. Optical interaction over extremely long effective pathlengths x (up to tens of kilometers) can be attained by using highly reflective, low-loss cavity reflectors. For a linear cavity with mean reflectivity R = (R₁R₂)^1/2, in terms of the reflectivities R₁ and R₂ of its two mirrors, the finesse $\mathcal{F}$ is given by πR^1/2/(1 − R), which reduces to π(1 − R)⁻¹ for the very highly reflective mirrors that are used in cavity-enhanced spectroscopy. Optical cavities with mean reflectivities R = 0.9990, 0.99990, and 0.999990 therefore yield pathlength enhancement factors G of 2 × 10³, 2 × 10⁴, and 2 × 10⁵, respectively.

An additional advantage of CRD spectroscopy is that it measures temporal decay of radiation inside the cavity, rather than transmitted optical power or energy as in conventional absorption spectroscopy. This allows the CRD approach to be insensitive to amplitude fluctuations of the tunable coherent light. Generally, the CRD decay of the intensity of monochromatic radiation inside the cavity is of a simple exponential form:

$$I(t\text{,}\lambda )=I(0\text{,}\lambda )\exp [-t/\tau (\lambda )]\text{,}$$

where intensities observed when the optical build-up process is interrupted and at a later time t are denoted by I(0,λ) and I(t,λ), respectively.

Spectroscopic information at a particular wavelength λ is derived from the total round-trip intra-cavity optical loss L_total, which comprises the sum of a wavelength-dependent optical-absorption contribution L_absorption(λ) for the sample gas in the cavity and additional cavity losses L_cavity (from scattering, mirror reflectivity, etc.). The first-order rate constant τ(λ)⁻¹ in Eq. (1) equals L_total divided by the round-trip time, which is (2d/c) for a linear two-mirror cavity with inter-mirror distance d and intra-cavity speed of light c:

$$\tau (\lambda {)}^{-1}=L_{\text{total}}/(2d/c)=L_{\text{tota}l}\times \mathit{FSR}=[L_{\text{absorption}}(\lambda )+L_{\text{cavity}}](c/2d)\text{,}$$

where FSR is the free spectral range, which equals the interval between the cavity’s longitudinal-mode resonance frequencies and is expressed as (c/2d) (i.e., the inverse of the round-trip time). Intra-cavity optical absorption contributes linearly to τ(λ)⁻¹ and a CRD spectrum is typically derived by measuring τ(λ)⁻¹ as a function of laser wavelength or frequency.

In conventional absorption spectroscopy, losses over an optical pathlength x can be expressed in terms of the absorption coefficient σ(λ) and the molar absorption (or extinction) coefficient ϵ(λ), so that the round-trip optical-absorption loss contribution L_absorption(λ) is then given by:

$$L_{\text{absorption}}(\lambda )=2d\sigma (\lambda )=2\mathit{dC}ϵ(\lambda )\text{,}$$

and Eq. (2) becomes:

$$\tau (\lambda {)}^{-1}=L_{\text{cavity}}(c/2d)+c\sigma (\lambda )=L_{\text{cavity}}(c/2d)+\mathit{cC}ϵ(\lambda )={\tau }_0(\lambda {)}^{-1}+\mathit{cC}ϵ(\lambda )\text{,}$$

where C is the molar sample concentration (mol L⁻¹). The ‘absorber-free’ ringdown rate constant τ₀(λ)⁻¹, equal to L_cavity (c/2d), can be determined by making measurements either of an absorber-free cavity (i.e., with C = 0) or (if scattering and other cavity losses are effectively wavelength-independent) at adjacent wavelengths at which there is zero absorption. It follows that σ(λ) is simply proportional to [τ(λ)⁻¹–τ₀(λ)⁻¹], the difference between the two ringdown rate constants (apart from small refractivity-based corrections for the dependence of the speed of light c on gas composition or wavelength). It is not necessary to know the cavity length d explicitly.

Accurate absolute concentrations can then be determined if ϵ(λ) is known for a spectroscopic feature at a particular wavelength λ, as follows:

$$C=\left[\tau (\lambda {)}^{-1}-{\tau }_0(\lambda {)}^{-1}\right]c^{-1}ϵ(\lambda {)}^{-1}$$

Such measurements are ‘absolute’ only in the sense that the spectroscopic database (e.g., HITRAN [49]) is sufficiently reliable and that adequate correction can be made for the effects (on c, (λ) and spectroscopic lineshape) of temperature, pressure, wavelength and gas composition.

Incidentally, as a precursor to CRD spectroscopy, measurements of τ₀(λ) for an absorber-free ringdown cavity were recognized [50] and realized experimentally [51], [52], [53], [54], [55] as a way to determine mirror reflectivity R, for which the single-mirror contribution to L_cavity is (1 − R); this early work on CRD reflectometry has been surveyed more comprehensively in Ref. [31].

A recently published book on CRD spectroscopy [42] demonstrates the technique’s scope and relevance, including its basic principles [56] and its operation with cw lasers [57], with broad-band light sources [58] and in optical waveguides [59]; it also reviews key CRD-spectroscopic applications to analytical chemistry [60], astrophysical molecules [61], atmospheric chemistry [62], medicine and the life sciences [63] and surface science [64].

In view of the extensive pre-existing and rapidly growing literature on CRD spectroscopy, we limit the scope of this Frontier Article by concentrating on a variant of cw-CRD spectroscopy, first developed in 1998, in which ringdown decay is measured by rapidly sweeping either the cavity length or the monochromatic tunable laser wavelength λ. Optical resonance between the laser and cavity frequencies during such sweeps enables automatic build-up and subsequent decay of the intensity of radiation in the cavity. We review progress in experimental methodology and in applications for this rapidly swept cw-CRD technique, indicating and examining its advantages and prospects as a convenient spectroscopic sensing method.