1. Introduction

Cavity-ringdown spectroscopy (CRDS) [1] measures the rate of absorption of an analyte and can be implemented with pulsed and continuous-wave light sources. A resonator with a high finesse ensures long photon-lifetimes and thereby permits the detection of small changes in the total loss of the resonator, which typically arises from intracavity absorption of an analyte. Comparison of the photon lifetime between an empty cavity and one that contains an absorber, such as a gas, is a direct measure of the concentration of the absorber. The smaller the loss of the empty resonator, i.e. the higher the reflectivity of the cavity mirrors, the higher the photon-lifetime, and thus the potential for very sensitive measurements [2]. The coupling of light into (and out of) such a high-finesse resonator becomes correspondingly more difficult as the light has to pass cavity mirrors with low transmissivities. Different coherent and incoherent coupling scenarios have been reported for pulsed and continuous light sources [3–8], including nonlaser based sources [9–12], to maximize the signal intensity at the detector. For incoherent (and short pulse) sources the transmission through an empty two-mirror cavity is on the order of the transmissivity of one cavity mirror. Typically, lasers with relatively high (peak) powers are used, to ensure that enough photons reach the photodetector [13]. CRDS also needs photodetectors that are sensitive, yet with enough bandwidth to follow the exponential cavity ringdown with good time resolution [14]. For a single pixel detector and a high-Q cavity this is routinely achieved, but in the low-power broadband case, especially when the analyte concentration rises, the speed of the detector array can be a limiting factor.

Here we demonstrate a new implementation of cavity enhanced absorption spectroscopy which permits ringdown measurements with low power broadband light sources and slow multipixel detectors. The principal advantage of the method is that it works even for relatively high losses. This allows for broadband ringdown measurements in the presence of scattering or if the concentration of the analyte can cause significant absorption, as might be the case in liquids.

We show that a low-loss intracavity acousto-optic modulator (AOM) can directly couple light into (and out-of) the cavity at specified times and thus permits CRDS with high-reflectivity cavity mirrors, low-power incoherent light sources, and slow and thus potentially much more sensitive photodetectors. The AOM by-passes the cavity mirrors and makes it possible to load the cavity efficiently and to actively ‘dump’ the total energy that is present in the cavity at any point of the exponentially decaying lifetime onto a photodector. We term this “cavity dump spectroscopy” (CDS) and demonstrate its versatility with absorption measurements of the forbidden $b^1\hspace{0.17em}{\Sigma }_g^{+}\hspace{0.17em}\leftarrow \hspace{0.17em}{X}^1\hspace{0.17em}{\Sigma }_g^{+}\hspace{0.17em}$ transition in gaseous O₂ at ∼760nm using a cw-superluminescent diode. CDS does not reach the detection thresholds of conventional CRDS, due to the additional loss introduced by the intracavity AOM, but due to its operation principle it can be electronically adapted to a wide range of loss conditions without changing the optics. CDS measurements are presented with intracavity losses of up to 7.5%.

2. Theory

The photon-lifetimes in the actively switched cavity ringdown setup are described by rate equations for the load, decay, and dump phases. For practical reasons, which are described in Section 3.1, we focus on a unidirectional ring cavity, so all formulas deduced here are valid for this type of resonator. Because we are especially interested in light-sources for which standard CRDS is difficult (i.e. low-power and low coherence pulsed and cw broadband light sources in conjunction with an unstabilized cavity) we choose, in contrast to [3], an incoherent ansatz.

Light with intensity I ₀ is coupled into the cavity by the AOM with a coupling efficiency of η, which is assumed to be constant in time. The intensity measured after one round-trip is reduced by the round-trip loss L, given by the losses of the empty cavity L ₀ = 1 − R _eff and losses that are due to an absorber L_A = αd with L = L ₀ + L_A. R _eff is the effective total reflectivity of the cavity, α is the attenuation coefficient, and d the path-length of one cavity round-trip. In addition, a small fraction of the light inside the cavity is diffracted out of the cavity whenever the AOM is switched on. The rate equation is then given by

After switching the input coupler off at t = t ₁, the intensity decays exponentially

The system is described by two time constants, one for the load phase, τ _load = d/[c(η + L)], and one for the ring-down phase, τ _decay = d/(cL). We note, that in general, the parameters in Eqs. (2) and (3), including η, are frequency (wavelength) and time dependent. For each wavelength, this approximation is valid for fast switching times compared with the cavity roundtrip time.

Comparison of the decay time constant τ ₀ for the empty cavity with the decay constant τ for the cavity in the presence of an absorber yields the absorption coefficient of the analyte:

It is possible to directly monitor the ringdown of the intracavity intensity, if one places a detector behind one of the cavity mirrors or if one monitors the residual surface reflection of the AOM. This corresponds to a traditional CRDS measurement, but with increased power levels.

To perform a CDS measurement, the intracavity AOM is switched on once more after the load-phase to dump the entire energy stored inside the resonator at t = t ₂ onto a detector. Since all the photons remaining in the cavity are ‘dumped’ onto the detector, the photodetector does not have to be fast. All timing information is provided by the switching electronics, which defines the duration of the decay phase between t ₁ and t ₂.

The measured signal at the detector at a specific decay time dt = t ₂ − t ₁ is given by

The functional form of the decay of intracavity power can be measured by varying t ₂. Due to the properties of the exponential in Eq. (5), the decay-time is the same as in classical CRDS. As the decay curve is reconstructed from subsequent load and dump cycles, the noise immunity (e.g. pulse-pulse fluctuations) of CRDS is no longer given in CDS. The main advantage of the present method, however, is the power level at the detector. It follows from Eq. (5) that for realistic coupling efficiencies (η >> L) this power level is on the order of I ₀, as discussed in section 3.3.

3. CDS setup

Several features of our setup are crucial for a successful implementation of CDS. One is the low loss of the Brewster-cut cavity-dumper itself, as the loss of the empty cavity limits the detection threshold. In one roundtrip the total loss due to the AOM is less than 0.002 and therefore permits decay times on the order of a few microseconds. Furthermore, fast electronics is needed so that the acousto-optical cavity-dumper can be switched within a few nanoseconds, on the order of the roundtrip time and small compared to a typical decay time.

3.1. Optical setup

The experimental setup for actively switched cavity ringdown spectroscopy is shown in Fig. 1. A unidirectional bow-tie resonator contains a Brewster-cut acousto-optic TeO₂ cavity dumper, specified for operation between 700nm and 1200nm (Brimrose TECD-380-92-BR-800), originally designed to dump Ti:Sapphire oscillators [15]. The use of a bow-tie geometry is advantageous as it keeps insertion losses to a minimum whilst allowing for a focus in the acousto-optic modulator (AOM), which is necessary for fast switching. The light source is directed via one of the curved cavity mirrors, so that its focus overlaps with the cavity mode inside the cavity dumper. The resonator is designed to have a focus diameter of 45.2μm, which is smaller than the acoustic aperture of the cavity dumper (≈ 100μm), and a roundtrip time on the order of the acoustic switching time (≈ 10ns).

 

Fig. 1 (Color online) The CDS setup: light source, collimation lens (CL), polarizer (P), routing mirrors (M), cavity mirrors (CM1-CM4), acousto-optic modulator (AOM) with driver (AOM driver), beam stop (BS), spectrometer and computer. The beam from the light source (dotted, red) is directed to the cavity dumper and coupled into the cavity mode (solid, blue), the undiffracted part hits the beam stop. After coupling out of the cavity, the light follows a different path (dashed, green) to the spectrometer.

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The focussing cavity mirrors (CM1, CM4) are specified with R ≥ 0.9998% at 740nm ≤ λ ≤ 870nm, have a radius of curvature of 150mm, and are placed at a distance of 156mm – about 2mm beyond the confocal point. The non-focusing cavity mirrors (CM2, CM3) have reflectivities R ≥ 0.9998 at 740nm ≤ λ ≤ 870nm. One cavity roundtrip has a length of 3.14m, which gives a roundtrip time of about 10ns and a free spectral range of 95MHz.

The calculated beam diameter at the face of the AOM is 47.8μm, and the Rayleigh range is 4.8mm, such that Brewster losses due to beam divergence are negligible (<< 10⁻⁴). Considering only the specified optical loss of the cavity mirrors and the transmission of the AOM (specified as T ≥ 0.998), the roundtrip loss of the resonator is 0.28%, which gives a maximum decay constant of 3.7μs. As the measured cavity loss without an absorber amounts to ≈ 0.3%, other loss sources like surface scattering, bulk absorption, Brewster mismatch due to beam fluctuations, or polarization effects at the Brewster interfaces are not limiting the performance of the described setup.

3.2. Electronics

The AOM driver was constructed using standard components from the wireless telecom market. The electronics permits full control over the timing, duration, and efficiency of the load- and dump-phases. The logic elements in the setup offer a transmission bandwidth of more than 2GHz and switching times of ≈ 2ns, fast enough so that the HF signal has steep edges which ensures a defined time delay between the end of the load- and the start of the dump-phase. The electronics setup is schematically depicted in Fig. 2.

 

Fig. 2 Schematic of the electronics: Frequency generators (FG1, FG2), voltage controlled oscillators (VCO1, VCO2), pulse generators (PG1, PG2), HF switches (S1-3), HF combiner (C), power amplifier (PA) and acousto-optical device (AOM). The straight lines mark the route of the HF signal, the dashed lines are the control connections for the pulse sequence.

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The diffraction angle of the AOM is a function of the drive frequency. We choose two discrete HF carrier frequencies (HF1 and HF2, 328MHz and 266MHz) which result in two diffraction angles: at one frequency (angle 1) the light is deflected into the cavity during the load-phase and at another frequency (angle 2) the photons in the cavity are dumped out of the cavity and onto a photodetector. Due to the different diffraction angles the undiffracted pump light does not reach the detector.

The two HF carrier frequencies (HF1 and HF2) are provided by voltage controlled oscillators (VCOs), switched by fast HF switches (Minicircuits ZFSW-2-46). To generate the pulse pattern shown in Fig. 3, the switches are controlled by pulse generators (PG1, PG2), which are triggered by frequency generators (FG1, FG2). After the two HF signals are combined (C) and power amplified (PA), the pulse sequence is applied to the AOM with a repetition frequency f_{r 1}, so that for constant dt there is a constant intensity at the detector. By varying dt, with the help of a delay generator, or by slightly detuning f_{r 1} from f_{r 2} to scan the delay at the rate of the beat frequency, the entire decay curve can be sampled.

 

Fig. 3 Graph (a) and (c), respectively, show the HF1 and HF2 signal intensity over time, (b) and (d) show the optical intracavity power, respectively, without and with HF2 applied. The time interval between the end of the load phase (t ₁, see Eq. (5)) and the start of the dump phase (t ₂) defines the duration of the ring-down phase. Measuring the dumped power for different delay times dt gives the decay curve of the resonator for one wavelength.

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Fitting of the experimental datasets at each wavelength to Eq. (5) gives the decay time constant, and therefore the cavity loss. Depending on the bandwidth of the detector, the signal intensity may be sampled either at its peak or at its mean value. For the measurements presented in this paper, a slow CCD spectrometer was used to measure the integrated intensity averaged over many cycles.

3.3. Comparison of CDS with CEAS and CRDS

Actively coupling light into the resonator in CDS means that the method is not immune to intensity fluctuations as traditional CRDS is, but CDS has the advantage that it works even when the losses are high. In Fig. 4 we compare the expected power levels at the detector at the start of a ring-down event for coherent and incoherent coupling in standard cavity enhanced absorption and ringdown spectroscopy (CEAS, CRDS), with those of actively coupled CDS. All calculations assume a four-mirror cavity as used in the present experiments. For both, coherent and incoherent coupling in traditional CRDS, the power level at the detector drops significantly when the losses of the sample exceed those of the empty cavity. In contrast, in actively coupled CDS the power level hardly drops, even when the total loss approaches 10s of %. This is due to the high coupling efficiency of the AOM and allows CDS to cover a wide range of analyte absorptivities and sample losses. Unlike traditional ringdown measurements, CDS can therefore operate even under conditions of high loss, as may be the case in solutions where the analyte concentration can vary over several orders of magnitude, or when measurements have to be performed in lossy environments, such as in the presence of scattering or turbulence.

 

Fig. 4 (Color online) Calculation of the power level at the detector for standard coherent (red, dashed) and incoherent (black, dotted) mirror coupling as well as active (blue) AOM coupling (CDS). The curve for the actively AOM-coupled CDS corresponds to the present four-mirror cavity with mirror reflectivities R = 0.9998 and a coupling efficiency of the AOM η = 0.3 (transmission of the AOM of 0.998). The curves for passive mirror coupling are calculated for a four-mirror cavity of the same finesse as in the CDS setup.

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4. CDS experiments

We performed CDS measurements with a super-luminescent diode (SLED, EXALOS), operated in cw mode. The SLED delivers 3mW of unpolarized light out of a single mode fiber. The emission is spectrally broad and has a FWHM of ∼ 30nm. Ring-down measurements recorded with a 25nm broad part of the SLED spectrum centered around the oxygen absorption line are shown in Fig. 5. The repetition frequency of the load and dump cycle was set to f_r = 31kHz, which gives, for load- and dump pulses of 200ns duration, a measurement window of more than 29μs for a ringdown event (about 10 times the decay constant). The light was analyzed by a grating spectrograph (Avantes Avaspec 3648) with 0.27nm nominal resolution. For each delay step dt = 50ns, 4 spectra were averaged on the spectrograph and the delay has been scanned between 100ns and 29μs. The integration time of the CCD was set to 10μs per spectrum, which is the lower limit of this spectrograph. The standard deviation of the calculated absorption coefficient in a 10nm window around the emission peak of the SLED is 1.8 × 10⁻⁸cm⁻¹ per spectral channel in a measurement time of 25s.

 

Fig. 5 (a) (Color online) Absorption coefficient resulting from the analysis of the decay of each wavelength channel on a spectrometer (nominal resolution 0.27nm). The solid (blue) line shows the simulation results for 21% O₂ in pure nitrogen under standard temperature and pressure. The dashed line and circles (black) mark the experimental data of the corresponding measurement performed in ambient air. The baseline was measured by purging the resonator with pure nitrogen and has been substracted from the data. (b) The simulated power level inside the resonator after the load phase. The O₂ absorption is already visible, as it influences the intra cavity power level during the load phase.

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A quantitative interpretation of the measured spectra requires that the cavity dynamics in CDS is considered: different frequency components ν of the incident spectrum experience different losses during the load phase, and the intensity inside the resonator after the load phase I _load(t = t ₁) is therefore a function of ν (see Eq. 2). It follows that at the start of the ringdown phase, the spectrum of the light inside the resonator already contains absorption features of the analyte. In order to predict the outcome of a CRDS measurement starting from HITRAN data, one has to convolute the HITRAN absorption data with the lineshape of the light after the load phase [16]. The lineshape depends on the coupling efficiency and the absorption characteristics of the analyte, since the spectrum is broader than the individual absorption lines. Thus, the intensity build-up and ring-down for each frequency component has to be calculated for the load-and ring-down phases, respectively. The spectrum is then convoluted for each time-step with the detection bandwidth, i.e. here the spectral resolution of the spectrometer.

Due to the cavity load effect, the actual absorption coefficient has to be reconstructed simulating both the load and decay dynamics. The absorption coefficient resulting only from the ringdown signal of a broadband CDS measurement will be smaller than that of a single pass (or high resolution) measurement. Fig. 5 shows the absorption coefficient, deduced from the time constants of the measured ring-down curves, as well as the results of a full cavity dynamics simulation for 21% O₂ in N₂ at standard temperature and pressure.

The standard deviation of the difference between the simulated spectrum and the fit to the O₂ absorption data is 1.1 × 10⁻⁷cm⁻¹, which is six times higher than the standard deviation of the absorption coefficient mentioned above. This is expected, as any spectral fluctuation in the setup or source, as well as any uncertainty in the transfer function, will limit the minimum detectable absorption coefficient in a broadband low resolution scheme. Nevertheless, the agreement between the measurement and the simulated HITRAN data demonstrates that CDS is potentially quantitative and can be used to determine absolute absorption coefficients.

To demonstrate the ability of CDS to permit measurements even in the presence of very high losses, an uncoated pellicle beam splitter (Newport PBS-2) was inserted in the cavity. With CDS we measured losses up to 7.5% using the same detector and without the need to change the cavity optics (see Fig. 6). The expected transmission profile of the pellicle beam splitter and the O₂ absorption is reproduced nicely and demonstrates the good dynamic range of the CDS method.

 

Fig. 6 (a)(Color online) Measurement of the cavity rountrip loss after inserting an uncoated pellicle beam splitter (Newport PBS-2). (b) The simulated power level inside the resonator after the load phase. The O₂ absorption is visible in both graphs, although the roundtrip loss exceeds 4% at the O₂ absorption.

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The detection limit in the presence of high loss is given by how well the fast decay can be sampled. A conservative estimate is to consider the transient time for switching, which is on the order of 10ns, as the shortest resolvable time interval. Assuming, that at least 100 data points are required for an exponential fit, and that the measurement lasts 10 time constants, one obtains a loss per roundtrip of 10%. It is interesting to note, that for very high loss, CDS may also be operated with a fixed (shortest possible) time interval between the coupling times, i.e. without sampling the full ringdown.

5. Conclusions

We report a new implementation of cavity ring-down spectroscopy which we term cavity dump spectroscopy (CDS), where light is actively coupled into (and out of) a resonator using an acousto-optical modulator. CDS allows cavity ringdown measurements to be realized with potentially any spatially coherent light source, and is especially suited for spectroscopy in lossy environments.

Proof-of-concept measurements are presented for the forbidden transition of gaseous oxygen in air at ∼760nm. We have shown that the combination of an unstabilized high-Q cavity with a fast acousto optical switch enables one to perform cavity ring-down measurements with μW of power, using a cw-SLED light source and a standard commercial CCD spectrometer. A single wavelength standard deviation of the absorption coefficient of 1.8 × 10⁻⁸cm⁻¹ per spectral channel has been demonstrated, which corresponds to a change of loss per roundtrip of 5.7 × 10⁻⁶. In the same setup, it was also possible to accurately measure round trip losses of 7.5 × 10⁻² without having to change or modify the optical setup.

The minimum detectable absorption in CRDS is proportional to the inverse roundtrip loss of the empty cavity. In the case of the actively-switched cavity-dump spectroscopy (CDS), demonstrated here, the roundtrip loss is dominated by the finite mirror reflectivities and the finite loss at the cavity-dumper, which amounted to ∼ 0.3%. However, perfect mirrors with 100% reflectivity can in principle be used with CDS. Furthermore, Brewster-surface losses can be on the order of a few ppm using highly polished substrates for collimated beams [17]. All the standard noise reduction and signal processing techniques employed in sensitive CRDS measurements can also be used in actively-switched CDS. Additionally, the detection limit can profit from the broadband approach by fitting the simulated spectrum of the analyte to the measured data, as described in [18].

Whilst CDS does not reach the detection limits of sensitive CRDS-setups and whilst CDS does not provide noise-immunity with pulsed laser sources, the higher signals in CDS permit absorption measurements to be performed over many decades of absorptivity including under conditions of very high-loss. We demonstrate measurements that differ by 4 orders of magnitude in the loss due to the sample, including losses of up to 7.5%. This could be of interest in process analytical measurements, or in fluid CRDS.