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Martínez et al. Vol. 23, No. 4 /April 2006 /J. Opt. Soc. Am. B 727

Laser-locked, high-repetition-rate cavity ringdownspectrometer

R. Z. Martínez,* Markus Metsälä, Olavi Vaittinen, Tommi Lantta, and Lauri Halonen

Laboratory of Physical Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FIN-00014 University of Helsinki, Finland

Received September 1, 2005; accepted October 17, 2005; posted November 7, 2005 (Doc. ID 64498)

We describe the design, construction, and initial performance evaluation of a high-repetition-rate cavity ring-down spectrometer. The spectrometer is based on the use of the Pound–Drever–Hall technique to lock the laserfrequency to the maximum of a transmission fringe of the interferometer used as a sample cell. This results incontinuous injection of light into the interferometer. The injection is repetitively interrupted with an acousto-optical modulator to generate ringdowns (exponential decays) at a typical rate of 10 kHz. Averaging of theselarge numbers of fitted ringdown times allows us to attain a minimum detectable absorption of 1.43�10−11 cm−1 Hz−1/2 short term and 9.0�10−11 cm−1 Hz−1/2 long term. In addition, the spectrometer has a con-tinuous tuning capability of �1 cm−1, which allows the use of standard linearization and frequency calibrationtechniques for the spectrum. To illustrate the operation and sensitivity of the spectrometer, part of theQ-branch of a weak acetylene overtone has been recorded. © 2006 Optical Society of America

OCIS codes: 120.6200, 300.6390, 300.6340.

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. INTRODUCTIONince its introduction in 1988,1 cavity ringdown spectros-opy (CRDS) has been acknowledged as a powerful toolor gas-phase applications requiring high-sensitivity de-ection, such as the recording of very weak bands, the de-ection of trace concentrations of an absorber,2 or experi-ents in molecular beams.3 The fundamentals of the

echnique as well as its different experimental implemen-ations have been thoroughly described in a number ofublications and will not be covered here. Suffice it to sayhat the technique owes its outstanding sensitivity, whichan match and even exceed that of the most sensitive pho-oacoustic and intracavity spectroscopic setups, to a com-ination of factors. The most important of these factorsre the long effective path length of the light inside thenterferometer that doubles as sample cell and the insen-itivity of the technique to laser amplitude noise. An ad-itional advantage is the capability of providing absolutebsorption intensities, something that is considerablyore difficult with other high-sensitivity schemes. Fi-

ally, CRDS experiments are technically simple to imple-ent, which no doubt helps to explain their growing

opularity. Detailed descriptions of the technique and itsany incarnations and applications can be found, for ex-

mple, in the reviews by Wheeler et al.4 and Berden et al.5

Initial implementations of CRDS used pulsed lasers tonject light into the cavity. As early as 1993, Romaninind Lehmann6,7 demonstrated a minimum detectable ab-orption (noise equivalent absorption) of 7�10−10 cm−1

sing a pulsed dye laser. It was soon acknowledged, how-ver, that the broad linewidths associated with pulsed la-ers resulted in the excitation of multiple longitudinalodes of the cavity, which in turn superimposed a pattern

f frequency beats to the exponential decay, limiting theverall accuracy of the measurement. Also, as a rule, thebsorption coefficient of the sample will have a slightly

0740-3224/06/040727-14/$15.00 © 2

ifferent value at the frequency of each one of the excitedavity modes, thus giving rise to exponential decays withifferent decay times (multiexponential decays) that can-ot be fitted by a single exponential curve. These band-idth effects were analyzed by a number of authors8–13

nd it became clear that in order to reach the maximumossible sensitivity in a CRDS experiment, the excitationf a single cavity mode was desirable, thus avoiding allhese effects. This single-mode excitation could be doneith Fourier-transform-limited pulsed lasers or with cw

asers, and a patent application on cw-CRDS was filedand later awarded) in 1994.14

The first demonstration of the use of cw lasers in aRDS setup was performed by Romanini, Gambogi, andehmann using a diode laser,15 and their use was furtherxplored by Romanini et al. in a series of experiments16–18

n which commercial single-mode dye and diode lasersere used to study samples in both a static cell and a mo-

ecular beam. Ringdowns were generated by a methodhich in later years became common in cw-CRDS experi-ents: The cavity length was periodically modulated withpiezoceramic transducer (PZT) to sweep the cavity

ringe over the laser line and initiate the injection of light;hen the laser beam was “switched off” with an acousto-ptical modulator (AOM) after a brief interval of light in-ection. The interruption of the laser beam was necessaryn order to avoid Doppler beats in the exponential decayurves.19–22 A noise equivalent absorption of 210−10 cm−1 was reached through the use of these cw la-

ers and mirrors of exceptional reflectivity �R99.999% �. While these experiments constituted an im-

ressive demonstration of the capabilities of CRDS, theylso made clear that the sensitivity of the technique couldot be pushed much further without resorting to exten-ive modifications.

The normal means of increasing the sensitivity of a

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728 J. Opt. Soc. Am. B/Vol. 23, No. 4 /April 2006 Martínez et al.

RDS experiment are—as can be easily deduced from theasic equations that govern the free decayrocess5—increasing the physical length of the cavity orhe reflectivity of the mirrors. Additionally, and since inost CRDS experiments several exponential decays are

veraged in order to obtain a more precise value of the de-ay time, increasing the rate of generation of exponentialecays will also translate into increased sensitivity asong as the value of the decay time being measured doesot change during the measurement. The length of theavity is limited by stability considerations and ulti-ately by the space available in a laboratory, and, while

avities several meters long have been used, most CRDSxperiments utilize cavities with lengths that range be-ween a few centimeters and little more than a meter. Theest mirrors available nowadays have reflectivities simi-ar to those used by Romanini et al.,16–18 and while fur-her improvements are possible as coating technologiesre improved, it is doubtful whether in the near future re-ectivities can be pushed much beyond the values alreadychieved in some regions of the spectrum, or whether these of such mirrors would even be practical. For example,he mirrors used by Romanini et al. had a transmittivityf only 10 ppm and surface losses estimated at 1 ppm.ven if these figures can be improved, other drawbacksecome very apparent, the main one being the reducedmount of light that can be injected into the cavity as mir-or reflectivity increases. This can be problematic as oneets close to the noise level of the detectors. Finally, theate of generation of decays for a typical cw-CRDS experi-ent ranges between a few hertz and 1 kHz, with theain limiting factor again being the small amount of light

hat can be injected into the cavity as the modulation fre-uency is increased.Besides those already mentioned, other avenues have

een explored in order to increase the sensitivity of CRDSnd approach the shot noise limit. A number of experi-ents have been carried out using optical heterodyning,

nd the most recent developments in this direction showromising results.23 In this work, however, we will con-entrate on the high-repetition-rate approach.

In order to push even further the sensitivity of CRDS,aldus et al. implemented successfully for the first time aavity-locked ringdown scheme,24 a possibility alreadyentioned in some of the previous work of Romanini.his scheme used the Pound–Drever–Hall (PDH)echnique,25 which we describe briefly in the experimen-al section, to achieve a tight frequency lock of the lasernd the cavity. The underlying idea is that by locking theaser frequency to the center of a transmission fringe ofhe interferometer through a feedback system, the laserermanently injects light into the cavity. A ringdown canhen be initiated by “switching off” the beam with anOM, and once the decay has been recorded the beam iswitched on and light injected again into the cavity to ini-iate a new cycle. The repetition of these ringup/ringdownycles allows the acquisition of exponential decays atates of tens of kilohertz, since dead times between theingdown and ringup parts of the cycle are eliminated.ith this setup, Paldus et al., using an external cavity di-

de laser (ECDL) as source, demonstrated an initial sen-itivity (expressed as baseline noise) of 5�10−9 cm−1 at a

epetition rate of 50 kHz. Two years later, in an improvedxperiment in which an analog detection scheme wassed to record exponential decays generated at 80 kHz, a

ong-term sensitivity of 8.8�10−12 cm−1 Hz−1/2 (with ahort-term sensitivity of 1�10−12 cm−1 Hz−1/2) waseached by Spence et al.26 To our knowledge, this is theighest sensitivity demonstrated by a standard CRDS ex-eriment to this day. It must be noted, however, that thisarticular setup cannot be considered a usable spectro-copic tool: The source used for the experiment was ad:YAG laser; thus the frequency could be scanned onlyithin the width of the laser line, less than 1 cm−1.One feature makes the experimental implementation of

aldus et al. particularly attractive: The two laser polar-zations are initially separated and given different uses.he p polarization is used to lock the laser and cavity,hile the s polarization is sent through an AOM prior toeing injected. This AOM is then used to generate the ex-onential decays by interrupting the s-polarized beam. Inhis way, it is possible to generate and register decays atigh repetition rates, thus detecting only one polarizationhile the other is used to keep the laser and cavity tightly

ocked at all times.A detailed account of all the technical requirements in-

olved in the construction of a PDH-locked system isiven by Fox et al.27 This is probably the most exhaustiveescription of such a setup available in the literature.mong a wealth of other information, the authors alsoropose a simpler alternative for repetitive ringdown gen-ration, namely, shifting the laser frequency off resonanceo start the decay and letting the system reacquire theock afterward.

To our knowledge, the most recent demonstration of aDH-locked CRDS setup is due to van Leeuwen et al.28

he novelty in this setup is that the authors generate ex-onential decays by repetitively switching the laser beamff and on with an AOM, as is typically done in nonlockedetups. The system is thus effectively unlocked during theime the decay is being monitored, but is able to recoverock quickly when the beam is switched on again. This in-eresting experiment falls again into the proof-of-conceptategory: Although the laser used was an ECDL, the lackf a long-range cavity PZT limited the continuous fre-uency scan to a maximum of 4 GHz, which created prob-ems for frequency calibration and made its use as a spec-roscopic tool impractical. Moreover, and although theaximum theoretical sensitivity of the setup is of 5.910−10 cm−1 Hz−1/2, the lack of an acquisition system able

o keep up with the rate of decay generation �16 kHz� re-uced this sensitivity to a more modest 4.7�10−9 cm−1.In the following sections, we present what we believe to

e the first implementation of a PDH-locked CRDS appa-atus that combines the very high sensitivity achievableith these techniques—up to 1.43�10−11 cm−1 Hz−1/2

hort term and 9.0�10−11 cm−1 Hz−1/2 long term in ourase—with the broad tunability and all the associatedharacteristics (simple and accurate frequency calibra-ion, stability, ease of use) that are required in order topply it routinely to high-resolution, gas-phase spectros-opy experiments. Thus, the setup presented here is a us-ble high-sensitivity spectroscopic tool and not a proof-of-oncept experiment. The system is described and its

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erformance evaluated. To demonstrate its usability andensitivity, a very weak Q-branch corresponding to anvertone of acetylene has been recorded and is presentedere.

. EXPERIMENTAL SETUP. Pound–Drever–Hall Locking Systemhe PDH locking scheme was devised in 1983, and hasince become the standard setup when stabilization of therequency of a laser to a high-finesse external cavity—ypically a Fabry–Perot interferometer (FPI) is required.ore traditional stabilization schemes rely on monitoring

he transmission of the interferometer when the laser fre-uency is within one of its fringes. Laser frequency varia-ions are in this way converted to intensity variations,nd these are used to generate an error signal that is fedo an electronic system. The system then amplifies andonditions the signal and uses it to apply the appropriaterequency corrections to the laser, usually through a PZTr a similar element. Typical examples of these setups areringe-side locking, which requires only the interferom-ter transmission signal, and fringe-top locking, which re-uires frequency modulation of the laser and phase-ensitive detection of the transmission signal.nfortunately, these schemes are difficult to apply toigh-finesse interferometers29 of lengths of the order ofens of centimeters like the ones used for CRDS. The rea-on is that the mean path of a photon inside such a cavityan be of several kilometers, and thus the arrival of thenformation regarding any frequency fluctuation of the la-er light will be affected by a large propagation delay.his delay will cause a certain lag in the frequency cor-ections applied to the laser, and thus a less tight and ro-ust locking with higher residual jitter. This can be espe-ially problematic if the laser source has important noiseomponents at high frequencies. Still, these classical lock-ng techniques can be used in some cases. A good examplef the fringe-side locking technique applied to a high-nesse interferometer (mirrors of 99.95% reflectivity) was

mplemented by Barnes et al.30 The length of the interfer-meter used in this experiment was under 2 cm, which re-

Fig. 1. Ex

uced the propagation delay and gave rise to transmis-ion fringes of more than 1 MHz FWHM.

The PDH scheme overcomes the limitations describedbove through the use of a reflection–interference ratherhan a transmission setup. Briefly, an electro-opticalodulator (EOM) is used before the interferometer to

enerate, through frequency or phase modulation of theaser beam, two sidebands at frequencies ±�m with re-pect to the carrier. The frequency �m is large comparedith the width of the interferometer transmission fringes,

o that the frequency of the carrier can be injected intohe interferometer through one transmission fringe whilehe two sidebands are totally reflected at the front mirror.he reflected radiation (the two sidebands plus a small

raction of the carrier that does not enter the interfero-etric cavity) is separated from the main beam through a

olarization setup and passed to a detector. The detectorill report an AC component due to the beat notes gener-ted by the interference of the three different frequencyomponents. Light leaking from the cavity will also reachhe detector and interfere with the other frequency com-onents, causing variations in the amplitude of the beatotes. These variations carry the information about therequency and phase difference of the reflected (instanta-eous) and leaked (averaged) components of the laser

ight, and can thus be used to extract an error signal afteruitable demodulation. A much more detailed descriptionf the technique can be found in the original article.25

Figure 1 shows a simplified layout of our experimentaletup, which is installed on an optical bench with pneu-atic legs in order to minimize the effect of vibrations.he main light source of the experiment is a cw, single-ode, Ti:sapphire ring laser (Coherent 899-21) tunable

etween 700 and 900 nm. This laser is optically pumpedy a single-mode, solid-state, cw laser that operates at32 nm (Coherent Verdi). For the experiments describedn this paper, pump powers between 5 and 5.5 W weresed to generate an output power between 100 and00 mW from the Ti:sapphire laser. The frequency jitterf the laser when it is in “free running” mode has beeneasured and determined to be �20 MHz.The output of the ring laser, vertically polarized, is sent

hrough a Faraday isolator (FI, isolation�37 dB) that

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revents any reflections coming back from optical ele-ents downstream from being fed back into the laser cav-

ty. After passing through the FI, the beam is focused byn f=15 cm lens into the crystal of an acousto-opticalodulator (Isomet 1205C-2) oriented to maximize the

eneration of first-order radiation. The remaining zeroth-rder radiation emerging from the AOM is blocked by anris, while the first-order radiation, shifted by �80 MHz, goes through the iris after being recollimatedy a second lens. The AOM serves a double purpose inhis setup. First, it is used as a frequency-correction ele-ent in the locking scheme. The AOM driver includes a

oltage-controlled oscillator that determines the fre-uency of the sound wave generated in the crystal, allow-ng the introduction of fast, small-amplitude frequencyhifts in the first-order beam. The speed with which theseorrections can be introduced depends on the speed ofound in the crystal (�3600 m/s in our case) and theeam position and diameter in the crystal. A spectralnalysis of the response of the system shows that, withight focusing and positioning of the beam in the region ofhe crystal closest to the transducer, laser frequency fluc-uations as fast as 200 kHz can be corrected by the AOM.

Second, the AOM is also used as an “optical switch” totop the injection of light into the cavity, starting a ring-own cycle, and restart the injection once the decay haseen monitored for a certain period of time. A computer-enerated trigger signal, which acts as master clock inhis experiment, is applied to the gate of the AOM driveror this purpose. The ON/OFF intensity ratio (contrast ra-io) for the AOM is typically 2000:1.

After passing through the iris, the first-order beameaches a beam splitter BS that reflects between 5 and0% of the incident light. The transmitted beam is sent tohe optical elements used for scan control and frequencyalibration; these have not been included in Fig. 1 for theake of simplicity. The reflected beam is sent without anyocusing through the EOM configured as frequency modu-ator and operating at 10 MHz with a sine-wave inputoltage provided by a waveform generator (WG). The fre-uency modulation generates two main sidebands of op-osite phase shifted ±10 MHz with respect to the fre-uency of the carrier. The modulation index is adjustedmpirically so that the intensity of each of these side-ands is approximately 10% of the intensity of the carrier.nder these conditions, the contribution of higher-order

idebands is negligible.After the EOM, the beam is sent through a mode-atching telescope with two lenses (f=15 cm and f20 cm) and a 150 �m pinhole to insure proper TEM00ode matching to the interferometer and removal of re-

idual higher-order modes in the beam. Fine tuning of theositions of the lenses and the alignment of the beam al-ows less than 1% of the total injected power to be inransverse cavity modes other than TEM00.

After the telescope, a Glan polarizing cube and a � /4late are used so that the light reflected back from theront mirror of the interferometer, horizontally polarizedfter two passes through the plate, is extracted by theube and sent to a low-noise, silicon, PIN photodiode PD1Hamamatsu S1223, battery biased). A variable filter issed to adjust the level of light reaching the photodiode.

he signal detected by the photodiode is demodulated in aouble balanced mixer (MiniCircuits ADE-6) using as aocal oscillator (LO) the 10 MHz sine wave generated byhe WG. The resulting error signal is sent to the feedbacklectronics where it is amplified and processed to gener-te the final correction signals that will be applied to theaser. Given the complex mechanical design of the lasernd the small width of the transmission fringes of the in-erferometer, a total of three transducers is required toover the entire frequency range in which correctionsave to be applied to the laser to maintain a tight lock.ow-frequency corrections are taken care of by the laseralvo plate, which is also used to scan the laser wave-ength. Medium-frequency corrections are appliedhrough a PZT on which one of the laser mirrors isounted. Both of these transducers are standard ele-ents of the commercial laser design. High-frequency cor-

ections are applied by the external AOM already de-cribed above.

In order to achieve the best possible stability, the inter-erometer, which also serves as a sample cell, is of mono-ithic design with its main body being a solid cylinder oferodur in which a central conduit has been drilled. Theirrors are attached to the cylinder through adjustableetallic mirror mounts, which are in turn glued to the

entral body of the cell, thus allowing fine adjustments ofhe cavity alignment while retaining the monolithic phi-osophy. One of the mounts is glued to the cell through anntermediate cylindrical PZT (PZT2). The mirrors (New-ort Ultra-Low Loss Supermirrors “F” series) have a di-meter of 2.54 cm and a radius of curvature of 1 m. Theiruaranteed reflectivity exceeds 99.97% in the range of61 and 867 nm, and our measurements yield a figure be-ween 99.980% and 99.984% through most of this range.he distance between mirrors is 37.5 cm. With these fig-res, a finesse in excess of 15 000, a FWHM of 25 kHz,nd a free spectral range (FSR) of 400 MHz are calculatedor the interferometer. The decay time of the empty cavityaries between 8 �s at the wavelength where mirror re-ectivity peaks and 6.5 �s near the wings.A more detailed scheme of the electronic system de-

igned for this experiment is presented in Fig. 2(a) includ-ng some elements that for the sake of simplicity had beenmitted in Fig. 1. The sine wave provided by the WG isandpass filtered to eliminate higher-order harmonics,hen amplified to compensate for insertion losses due tohe filter. The resulting signal is applied to the LO port ofhe mixer. The signal coming from the PD1 photodiode isigh-pass filtered to remove the DC component and thenmplified by a simple proportional amplifier to meet theequirements of the mixer at the RF input. The demodu-ated output at the IF port of the mixer is then sent to the

ain block of the feedback electronics.The design of the feedback electronics is intended to

rovide a signal gain that is large at low frequencies (nearC) and decreases steadily as the frequency increases,ntil a unity gain point is reached at �200 kHz, the high-st frequency for which our transducers can introduceorrections without excessive phase lag. The goal is to ob-ain the gain transfer curve depicted in Fig. 2(b), whereach of the transducers covers a certain frequency regionnd there is a smooth transition between these regions,

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elimited by two crossover points. Given the range andharacteristics of our transducers, these two points werehosen to lie at 50 Hz and 10 kHz. As Fig. 2(b) illustrates,he slope of the gain curve is of only 20 dB/decade in thealvo and AOM regions, while it reaches 40 dB/decade inhe PZT region. The reason for these different slopes ishe need to accommodate simultaneously the two require-ents of unity gain at 200 kHz and a high gain at low fre-

uencies, to adequately compensate for the large-mplitude mechanical and acoustical noises present inhis region. A less aggressive approach, such as the obvi-us choice of a constant 20 dB/decade slope for all trans-ucers, would result in a system with poorer stability andigher residual jitter.The circuit topology used to accomplish the goal de-

cribed above is based on the use of opamp integrators.his integral amplifier approach is a well-known one: Aetailed description of a similar system adapted to a dif-erent type of laser can be found in Ref. 27. In our case,fter a first amplification stage, the signal is processed inarallel by three different subcircuits, each of which am-lifies and filters it according to the requirements of theransducer it drives. The uppermost subcircuit in Fig. 2(a)rocesses the signal that drives the galvo plate, and con-ists of a single integrator stage followed by an active low-ass filter block in order to minimize the galvo contribu-ion at frequencies above 50 Hz. The central subcircuitses two cascaded integrators to obtain the 40 dB/decadeequired for the PZT and two sets of active filters, high-nd low-pass, to reduce contributions below 50 Hz and

ig. 2. Electronic feedback system. (a) Simplified scheme of theeedback electronics. (b) Gain transfer function of the feedbacklectronics.

bove 10 kHz. Finally, the AOM signal is shaped by aingle integrator and high-pass filtered below 10 kHz. Allhe filters used (which for simplicity are not detailed inhe figure) are either first-order active filters (at the0 kHz crossover) or second-order Sallen–Key active fil-ers (at the 50 Hz crossover). Adjustable gains and polari-ies allow independent tuning of the signal level in each ofhe subcircuits. The galvo signal is applied to the commer-ial laser electronics, which provide an input for externalontrol of this transducer. The PZT signal is sent throughhigh-voltage amplifier and applied directly to the PZT in

he laser. The AOM signal is applied to the commercialOM driver.One important detail not included in Fig. 2(a) is the

resence of phase-lead circuitry in the AOM and PZT sub-ircuits: It is a known peculiarity of the PDH scheme25,31

hat because of the way in which the error signal is gen-rated, fluctuations of the laser frequency that are fasterhan the frequency corresponding to the HWHM of the in-erferometer fringe give rise to error signals that show a0° phase lag and have a smaller amplitude than whatould correspond to the frequency fluctuation of the laser

ight. The consequence is that error signals generatedhrough the PDH technique look, in phase and amplitude,s if they had crossed a low-pass filter with its 3 dB pointt the frequency of the HWHM of the cavity fringe. To ob-ain error signals that faithfully represent the behavior ofhe laser frequency, it is necessary to introduce a phase-ead correction in the electronic processing. In our par-icular case, and given that our 3 dB point is at12.5 kHz, this can be accomplished by “adding a zero” to

he transfer functions of the AOM and the first PZT inte-rator. This is done by connecting capacitors of appropri-te values in parallel with the input resistors of the inte-rators.

Another technical detail not included in Fig. 2(a) is theresence of simple circuitry for the substraction of thepurious DC offset that usually accompanies PDH errorignals and that can become a serious problem as a resultf the huge gain the system possesses at low frequencies.ne of the typical sources of DC offset cited in the litera-

ure is the offset of the operational amplifiers, but thisan be minimized at the design stage through the use ofow-noise, low-drift operational amplifiers and offset-ulling components. Our system is built around thePA27, OPA627, and OPA637 amplifier models. The sec-nd and more serious source of DC offset in a PDH signals residual amplitude modulation in the EOM. In our sys-em, this DC component is nulled with offset-substractionircuitry at the beginning of each scan. However, if itsagnitude varies during the scan, as it usually does when

ny changes in power or alignment of the laser occur, thenitial nulling is no longer valid. As has been noted byther authors,28 the best way to minimize this effect shortf complicated adaptive systems is careful alignment ofhe EOM to minimize residual amplitude modulation, sohat even if variations occur during a scan, the resultingC offset is still small and the locking system can copeith it. This solution also proved to be satisfactory in our

ase.Once built, the performance of the system was fine-

uned with the use of a spectrum analyzer, which showed

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ome noise components in the region between 3 and0 kHz. They were identified as electrical noise generatedy the commercial electronics of the Coherent 899-21 la-er and imprinted onto the laser frequency through thealvo plate and a piezo-scanned thick etalon. To eliminatehem, two low-pass filters were built and installed in theaser: a high-voltage RC filter with a 3 dB point of 4 kHzor the piezo-scanned etalon and an LC filter with a 3 dBoint of 290 Hz for the galvo plate. Once these were in-talled, the offending noise components were almost com-letely eliminated. The only remaining noise componentith a well-defined frequency and significant amplitudeppears at 2 kHz and is caused by the modulation thathe laser electronics apply to the thick etalon in order toe able to track the laser frequency during a scan. Thisodulation cannot be removed if one wishes to retain the

canning capability.With the main identifiable sources of frequency noise

liminated, the setup was found to be remarkably robust:n the absence of strong perturbations, it will retain theock for hours. Long-term thermal drift of the interferom-ter, which is small because of the design and materialssed in its construction, will have the effect of dragginglong the laser frequency, slaved to the maximum of theransmission fringe, through a change of the voltage ap-lied to the galvo plate. This is in fact the system used tocan the laser frequency for spectroscopic measurementsy changing the cavity length through the piezo elementZT2.The residual jitter between the laser and the cavity

hen the system is locked is difficult to quantify preciselyithout a direct measurement, for example, by beating

he laser frequency against that of another laser locked tocontiguous mode of the cavity as demonstrated by

rever and coworkers.25 However, since our work isimed at the application of the locked system to CRDSnd not the development or deep characterization of theocking technique itself, we saw no reason to embark onuch a time-consuming and complex measurement andontented ourselves with a gross, upper-limit estimate ofhe jitter. The simplest way of doing this is by measuringhe amplitude fluctuations of the light transmittedhrough the cavity when the laser is locked. It is impor-ant to emphasize that not only is this a very rough esti-ate, but also that it is only correct if the main noise com-

onents are of low frequency (long period) compared tohe ringdown time of the cavity: If such is not the case,he “light integrator” effect of the cavity will filter high-requency fluctuations and mislead us into thinking thathe jitter is smaller than it is. Since the spectrum ana-yzer reveals no relevant residual noise components in therror signal above 2 kHz, the estimate is safe to make inur case and provides worst-case amplitude fluctuationsf approximately 0.25% of the total amplitude of the sig-al. Given the width of our interferometer fringes, thislaces an upper limit of 150 Hz on the jitter between lasernd cavity. This value is not surprising considering thatitter lower than 1 Hz has been obtained through the usef the PDH scheme. It is in fact a conservative estimate:n important contribution to the amplitude noise we ob-erve after the interferometer certainly comes from am-litude fluctuations of the laser itself, especially that due

o the 2 kHz modulation whose frequency pattern can beeen after the interferometer as the main component inhe amplitude noise. The magnitude of the PDH error sig-als as measured by the spectrum analyzer also confirms50 Hz as a conservative upper limit. While this measure-ent could be improved, the figure determined as upper

imit is good enough for our purposes.

. Cavity Ringdown Experiment

. Ringdown Generation and Repetitive Locking andnlocking

n the experimental setup depicted in Fig. 1 for CRDS,he injection of light into the cavity has to be stopped inrder to start an exponential decay. This is accomplishedhrough the use of a square modulation signal applied tohe gate of the AOM driver that starts and stops the gen-ration of the first-order radiation and thus effectivelyswitches off” the laser beam being sent to the interferom-ter. The downside of this approach, which is relativelytandard in most nonlocked CRDS experiments, is thathen the injection of light is switched off, the generationf the PDH error signal also stops, and the laser is un-ocked from the cavity. This approach is sustainable onlyf, after a short interval—just enough to monitor and reg-ster the exponential decay—the injection of light is re-umed. In the time scale in which the exponential decayakes place in our experiment, tens of microseconds, thiss not enough time for the laser frequency to drift far fromhe center of the interferometer fringe; the system reac-uires the lock and starts the ringup cycle typically in lesshan a microsecond. After a certain level of light intensityas been reached inside the cavity, the process can be re-eated again. This is what van Leeuwen et al.28 call “pe-iodically locked continuous wave CRDS.” Figure 3 pre-ents an oscilloscope trace of the transmission throughhe interferometer as registered by photodiode PD2 withhe system working at a repetition rate of 10 kHz. In thisxample, which shows five full unlock/relock cycles, thexponential decay is monitored for 28 �s before the AOMate is opened again and the ringup transient starts.

The timing settings depicted in Fig. 3 (10 kHz repeti-ion rate and 28 �s of exponential decay) are the typicalnes we have used for all the spectroscopic measurementseported in this work. These settings are the result of aumber of compromises for both the ON (ringup) andFF (ringdown) parts of the cycle. Regarding the ring-own part, in a CRDS experiment it is desirable to moni-or the exponential decay for as long as possible, or ateast until the signal is very close to zero, in order to in-rease the sensitivity to small changes in the decay time.ut in a repetitively locked setup like ours monitoring

imes too long translate into a reduced repetition rate. Af-er a number of tests, it was observed that there was aoticeable increase in sensitivity as the monitoring timef the exponential decay was extended from 1 to 4 or 5avity decay times, while beyond this point a regime of di-inishing returns was entered. Therefore, typical moni-

oring times used in our experiments have been between5 and 30 �s.Regarding the ringup part of the cycle, it is also desir-

ble to keep it as short as possible in order to increase the

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epetition rate of the experiment. If the system is able toeep the unlock/relock cycle at higher repetition rates,hen the only foreseeable consequence of this would be aeduced level of light injected into the cavity. This is not aroblem with our system, since the amount of light sento the cavity can be increased by a factor of up to 50 timesf necessary.32 The setup was tested at repetition rates upo 25 kHz, and while the locking system was able to main-ain stability without trouble, it was discovered after re-ording and analyzing a large number of exponential de-ays that the dispersion of the measured decay times waslso greatly increased, as indicated by the standard devia-ion of a representative sample. We attribute this to theynamics of the relocking: It would seem that the laserrequency “jitters” around the center of the interferometerringe at the beginning of the ringup transient and stabi-izes only when the system approaches a certain level ofntracavity power. In view of this behavior, repetitionates above �12 kHz are not advisable in our setup.

The stability of the repetitively locked setup was testednd compared with that of the cw-locked system. As ex-ected, the repetitively locked system showed poorer tol-rance to perturbations, since any perturbations thatake place during the OFF (decay) time of the cycle mayush the laser out of resonance without opposition fromhe locking system. If the perturbation is not largenough to drag the laser frequency out of the captureange of the PDH system (±10 MHz, as delimited by theidebands), then the lock will be reacquired without diffi-ulty, with perhaps the only ill effect a few ringup/ingdown cycles lost. If on the other hand the perturba-ion pushes the laser frequency out of the capture range,he lock will not be reacquired and the CRDS experimentill be interrupted. It was experimentally verified that

ome perturbations that were not strong enough to unlockhe laser in the cw-locked mode (such as, for example,oud noise in close proximity to the laser, which is the el-ment of the setup most sensitive to external perturba-ions) would unlock it when working in repetitively lockedode. The probability of this happening also increaseshen the OFF time of the laser is increased. Given the

elatively short times during which we follow the decays,nd observing a few basic precautions, such as minimiz-

ig. 3. Oscilloscope trace of the repetitive locking/unlockingrocess.

ng loud noises in the laboratory and especially near theaser, the system will stay locked in repetitive mode forong periods of time (hours are usual); this means the sys-em is perfectly usable for CRDS.

It is worth mentioning here that a variation of the al-ernative approach to AOM switching proposed by Fox etl.27 based on introducing a sudden change of frequencyn the carrier was also tested. In our case, the advantagef this approach would be that even when the laser car-ier is pushed out of resonance, the system keeps receiv-ng error signal information as long as the cavity fringetays between the frequencies of the carrier and the side-ands. Technically speaking, the system never loses lock,o that higher stability can be expected. We investigatedhis possibility, which in our setup can be easily accom-lished by using a square-wave signal to periodicallyhange the sound frequency in the AOM. We discovered,owever, that in our case it is not especially practical be-ause it is necessary to push the laser frequency morehan 5 MHz away from resonance to avoid injecting lightf a different frequency in the cavity and generating beatsetween the two frequency components. At 5 MHz, one ofhe sidebands starts getting closer to the interferometerringe than the carrier, and mode beating is again visible.

successful implementation would require either work-ng with higher modulation frequencies or switching offhe sidebands temporarily, as proposed by Fox et al.

. Acquisition and Analysis of Exponential Decaysight emerging from the interferometer (for these experi-ents, typically 0.5 mW at the beginning of the exponen-

ial decays) is monitored by photodiode PD2 (Hamamatsu1223, battery biased). The photodiode is coupled to aomemade, low-noise transimpendance amplifier with aain of 10 000 V/A and a bandwidth limitation adapted tohe requirements of this experiment ��10 MHz� to avoidhe introduction of unwanted high-frequency noise. Fromhe amplifier, the signals are sent to a fast data acquisi-ion (DAQ) card (Strategic Test UF.4021) installed in aC. The DAQ card is a 20 MHz digitizer with a 14 bit A/Donverter and an onboard memory of 8�106 samplesMSamples�.

Each exponential decay is digitized with a total of 128amples acquired at a clock speed of 5 MHz. At an unlock/elock repetition rate of 10 kHz, this represents.28 MSamples/s, an acquisition rate that can be sus-ained only for a little over 6 s before the card memory isull. In fact, van Leeuwen et al.28 mention that a digitiz-ng card “with a large amount of onboard memory” woulde required for an experiment like this. This statement isot totally accurate: The features available in modernigitizing cards coupled with proper programming tech-iques allow real-time acquisition of the data with littleverhead time even with modest amounts of memory suchs that present in our card. Most fast digitizing cards pro-ide a hardware-controlled recording mode (multiple re-ording) in which the card is programmed to acquire aertain number of waveforms, the beginning of each onef which is marked by an external triggering signal, andnce started does so without further interaction with theoftware. Once the desired number of waveforms haseen acquired, new instructions can be issued to the card,

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he data dumped to the PC memory (this process beinghe origin of the overhead time), and a new acquisitionycle started. The advantage of using this mode is thatince the data acquisition is not controlled by softwarence started, the card can acquire data and at the sameime the computer is free to execute other tasks.

We typically accumulate 10 000 exponential decays forach point of the spectrum in the measurements pre-ented here. The DAQ card is programmed to acquire0 000 waveforms, the acquisition of each waveform beingriggered by the same computer-generated signal thatloses the gate of the AOM. After 1 s, when the desiredumber of waveforms have been acquired, the card trans-ers the data to the PC memory and is immediately in-tructed to start a new acquisition. The transfer processf the data takes approximately 50 ms, which amounts tonly a 5% overhead time added to the total acquisitionime of the spectrum. Other operations (like the lasercan) are also performed during this time interval. Whilehe card is again performing a new acquisition run, thereshly received data from the previous run are written tohe hard disk and an initial fit of the exponentials is per-ormed, for which 1 s is ample time. In this way, real-timeata acquisition and storage as well as preliminary analy-is and plotting of the CRD spectrum are possible withittle overhead.

Once the scan has been finished, a second analysis ofhe stored data can be performed (typically with a secondomputer while the first one performs a new scan). Vari-us reasons make this advisable if one wants to reach theaximum possible sensitivity. First, the fact that the ac-

uisition of the waveforms is controlled by an externalrigger means that if the PDH system briefly loses andhen recovers lock a few exponential decays can beissed, and the data acquired during the periods of timehen the exponential decays should have occurred will beeaningless (the baseline noise of the photodiode/

mplifier system). These bad data points (outliers) addoise to the spectrum if not rejected, but can be filteredut through a statistical analysis of the distribution of de-ay times, which is not currently implemented in the real-ime fit of the exponential decays. Second, it is possible toerform a more accurate (and time-consuming) two-stepxponential fit. A small sample of waveforms through thehole spectrum is first fitted with a Levenberg–Marquardlgorithm to a three-parameter exponential model to de-ermine the DC offset present in the signal. This offset ishen substracted from all the waveforms in the scan, andweighted least-squares linear fit of the logarithm of the

xponentials is performed.33 Proceeding in this way, alightly more refined spectrum than the one the acquisi-ion software presents in real time can be obtained. Whilet the time of writing this paper the analysis is being per-ormed as described here, we believe it is possible,hrough more refined programming, to integrate acquisi-ion and analysis in order to obtain truly real-time spec-ra without the need for a second analysis, at least for thecquisition rates used in this work.

. Laser Scan, Frequency Calibration, and Resolutionhe most straightforward way to scan the frequency of a

aser locked to an external interferometer is to scan the

ength of the interferometer, which will drag along the la-er frequency. In our setup this scan is executed by theZT labeled PZT2 in Fig. 1. The PZT, a high-voltage tu-ular stack (PI P-016.20H), was specifically selected toave an elongation of at least 30 �m, which, given theSR of our interferometer, represents a frequency scan ofbout 75 FSR at 800 nm, or 1.05 cm−1. The figure ofcm−1 was chosen in order to prevent PZT elongation

rom becoming the limiting factor of the maximum scanength: 1 cm−1 is the longest scan attainable with the la-er used in this experiment. The voltage applied to PZT2o control the scan is generated by the computer, low-passltered to remove high-frequency noise present in the sig-al, and amplified by a high-voltage commercial ampli-er.The possibility of scanning 1 cm−1 in a single run al-

ows the use of standard frequency calibration techniquesf widespread use in high-resolution spectroscopy to as-ign frequencies to the spectra obtained. To avoid the in-roduction of unnecessary complexity, the elements thatake care of the frequency calibration of the spectrum inur setup have not been included in Fig. 1 and will be de-cribed here only very briefly.

The fraction of the laser beam used for frequency cali-ration is the one transmitted by beam splitter BS in Fig., which represents between 90 and 95% of the powerresent in the first order of the AOM. This beam, which isf the same frequency and has the same intensity modu-ation as the one sent to the interferometer, is split in twoy a 50% beam splitter cube. One of the two resultingeams is sent through a heated cell containing 254I2 at itsapor pressure at 500 K to obtain an absorption spec-rum. It is then detected by a photodiode and the signalemodulated by a lock-in amplifier and sent to the com-uter, where the absorption spectrum of iodine is used asreference to assign absolute frequencies to our spec-

rum. The second beam is sent through a low-finesse FPIith an FSR of 1 GHz and also detected by a photodiodend demodulated like the previous one. Approximately 30ransmission peaks of the FPI are obtained through a fullcan. The maxima of these peaks are used to linearize thecan.

For the experiments presented in this article, 500 volt-ge steps were used to cover the entire scan range ofcm−1. Given that acquisition time was 1 s for every

oint and factoring in the overhead time mentionedbove, this translates into an average scanning speed of7 MHz/s and 8.7 min for the total duration of the scan.To test the usability of the setup under different condi-

ions, faster scanning speeds were tried by keeping con-tant the number of points (voltage steps) in the spectrumnd accumulating a smaller number of exponential de-ays at each point. It was found that the system was per-ectly usable and the lock was stable up to speeds of ap-roximately 3 GHz/s, which implies the acquisition ofcm−1 in only ten seconds by accumulating 200 exponen-

ial decays per point. The price to pay is, of course, a re-uced sensitivity, but given the very high sensitivity ofhe setup even in a single-shot configuration (discussed inection 3), it is useful to be able to obtain a number ofuick survey scans of a given region and only then, if nec-ssary, repeat them in a higher-sensitivity configuration.

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The resolution of our experimental setup is the mostifficult characteristic to determine. As a consequence ofhe frequency locking of the laser, this resolution dependsn two main factors: the residual jitter between laser andavity and the frequency stability of the cavity itself. Anpper limit of 150 Hz for the jitter between laser and cav-

ty has been mentioned before. The limiting factor of theesolution is going to be, however, absolute frequency sta-ility of the cavity fringes, given by cavity jitter (shorterm) and cavity drift (long term, with a time scale of sec-nds).

As in the case of the residual jitter between laser andavity, a measurement of the absolute jitter in the cavityringes would require a complex experiment in which aore stable system would have to be used as a reference.

t is for this reason that, as we did in the previous case,e will give just a conservative upper estimate. In this

ase the estimate is based on the work carried out byther researchers with lasers locked to interferometricavities of similar, and in some cases identical, design tours for which such stability measurements were made.34

ased on these previous results, it can be establishedhat, even for a system in which fairly simple mounts aresed, the cavity will not produce a linewidth larger than00 kHz. This is the figure we will take as upper limit forur cavity jitter. It must be noted that given the mechani-al characteristics of our system (monolithic cavity, pneu-atic optical bench) this is a very conservative estimate.The long-term drift of the cavity fringes has been mea-

ured by monitoring the voltage applied by the lockingystem to the galvo plate of the laser and its evolution inime: Any changes in cavity length, most likely due toemperature changes, are detected as changes in thisoltage as the laser tracks the position of the fringes. Itas found that after 500 seconds, the typical duration ofne of our scans, the change in this voltage indicated aringe drift of less than 30 MHz. This figure is negligiblehen compared to the 60 MHz/s laser scan speed typi-

ally used for our measurements.Finally, it must be noted that the figure of 100 kHz for

he short term resolution of our system, even if conserva-ive, is still orders of magnitude better than what oureasurements require. In the region around 800 nm, theidth of the spectral lines recorded in a CRD experiment

s dominated by Doppler broadening. As an example, theoppler width of a spectral line of acetylene at 800 nm is900 MHz FWHM.

. RESULTS. Sensitivity of the Cavity Ringdown Spectroscopyetuphe absolute intensity of a spectral feature can be ex-ressed in terms of its absorption coefficient, which in aRDS experiment can be written as a function of cavityarameters and decay times in the form

� =1 − R

L

��

�. �1�

n this expression, R and L are the mirror reflectivity andavity length, respectively, and � is the decay time of the

avity with the sample. With �0 as the decay time of thempty cavity, then ��=�0−�. This equation can be re-rouped and expressed as a function of decay times onlyn the form

� =1

c�1

�−

1

�0� , �2�

here c is the speed of light.According to these expressions, the minimum detect-

ble absorption in a single shot (single exponential decay)s the one that will generate the minimum detectablehange in the time decay ��. Different criteria exist to de-ne this change. In this work, we adopt the criterion usedy previous authors who have demonstrated locked CRDSxperiments in order to compare our results with theirsn the same basis. Both Spence et al.26 and van Leeuwent al.28 define the minimum detectable change in decayime as that which has the value of the standard devia-ion 0 of a statistically significant sample of decays of thempty cavity. The minimum detectable absorption loss insingle shot �MDALshot� can thus be expressed as

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�0� . �3�

The standard deviation 0 of a distribution of decayime measurements is a characteristic of each experimen-al setup, and depends on multiple variables like laserype and linewidth, mechanical stability of the cavity mir-ors, noise in the detectors and circuitry, number of bits inhe digitization, laser noise, fluctuations of gas flow in theample cell, etc. Any factor that inserts noise in the ex-eriment will contribute to a decrease in the reproducibil-ty of the measurement and an increase in 0. Since aarge number of CRDS setups are in use around theorld, the range of typically attainable values for 0 (or,

o be more precise, for the relative error 0 /�0) is wellnown. Berden et al. in their review5 cite as typical valuesor the relative error 1% for experiments with pulsed la-ers and values as low as 0.03% for experiments per-ormed with cw lasers.

To measure 0 /�0 for our setup, we typically record andt a set of 10 000 exponential decays with the empty cav-

ty, which takes only 1 s. These measurements reveal thathe typical values for our setup show day-to-day varia-ions that are always in the range between 0.03% and.06%. As an example, a typical distribution of 10 000 de-ay times is plotted in Fig. 4 together with the bestaussian fit. The excellent agreement between them

hows that our distribution of decay times behaves like aormal distribution. The value of the standard deviation0 extracted from the particular distribution in Fig. 4 is.0034 �s, or a relative error of 0.052%. These values areeproducible on a day-to-day basis, and are routinelyhecked before starting a measurement session to guar-ntee the maximum possible sensitivity.From the best measured measured values of the rela-

ive error (0.03%) and an average decay time of the emptyavity of 7 �s, the MDALshot of our system is calculated as.43�10−9 cm−1. In the recording of the spectra presentedn this paper, we have operated the spectrometer by fit-

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ing 10 000 exponentials and averaging their decay timeso obtain a single point of the frequency spectrum. For aormal distribution of measurement errors, this averag-

ng provides an increase in sensitivity proportional to thequare root of the number of accumulated measurements,r a factor of 100. The maximum attainable sensitivity inhese conditions, which we consider the “standard” oper-ting configuration of the spectrometer, is then given byDAL=1.43�10−11 cm−1 Hz−1/2.The value of MDAL presented is, however, calculated

rom a single point of the spectrum, and as such it repre-ents only the short-term sensitivity of the spectrometer,ot the sensitivity in the real conditions under which mo-

ecular spectra are obtained. Since in the standard oper-ting configuration it takes about 45 seconds to scan overspectral line �3�FWHM�, it is to be expected that smallerturbations and environmental noises will introducedditional fluctuations and especially drift in the decayime as the scan is in progress. To illustrate the effect ofhis additional long-term noise in the overall sensitivity ofhe apparatus, Fig. 5 presents a sample of the baseline ofblank scan composed of 100 points. The horizontal solid

ine represents the average value of the decay time forhat scan, and the two dashed lines above and below de-

Fig. 4. Distribution of 10 000 decay times.

Fig. 5. Sample of baseline noise during a scan.

imit an interval centered on this average value and span-ing ±2 /100, where the value of is the 0.0034 �s usedbove to calculate the short-term MDAL and 100 is thequare root of the number of exponential decays accumu-ated to obtain each point of the spectrum. Thus, the rep-esented interval should contain 95% of the points in thepectrum if no other sources of long-term noise wereresent. It is apparent that the noise is considerablyarger than what the short-term values predict, and thathe main contribution comes not from point-to-point ran-om noise but from drift in the value of the measured de-ay time. This drift can be quite steep at times, as illus-rated by the behavior of the baseline between points 60nd 80.The long-term noise can be estimated from the stan-

ard deviation of a large sample of points taken from theaseline of the spectrum, and from here a long-term valueor the MDAL obtained. From the spectrum presented inig. 5 and other baseline samples, which have been inten-

ionally chosen to represent regions particularly affectedy noise, a standard deviation of 1.15�10−4 �s is calcu-ated, which, when introduced directly in Eq. (3), resultsn a long-term MDAL of 9.0�10−11 cm−1 Hz−1/2. This ishe figure that represents the worst-case, long-term sen-itivity of the spectrometer in its standard operating con-guration.

. 12C2H2 Spectran order to illustrate the capabilities of the spectrometer,e recorded the first lines of the Q-branch of one of theeakest overtones of 12C2H2 that had been previously ob-

erved in this wavelength range.35 The band in questions a 5-quantum combination identified by previous au-hors as corresponding to the –� transition between theround state and the �2,1,1,11,0� excited state. Figure(a) presents the first lines of this Q-branch recorded atoom temperature and a sample pressure of 5 torr. Theorizontal dashed line represents the change in decayime corresponding to an absorption coefficient of �=1.010−7 cm−1. It can be seen that almost all the spectral

ines of the Q-branch fall below this level. This illustrateshe sensitivity required to record the band with a good/N ratio. A number of water lines due to sample impuri-ies are also visible. The spectrum presented covers a re-ion of �6 cm−1, and it was composed by stitching to-ether eight independent scans that were individuallyinearized and calibrated as described in the experimen-al section. Absolute frequency accuracy is of the order of.005 cm−1, a typical figure for spectra calibrated with an2 reference. The whole recording process required ap-roximately 90 minutes for the region of the spectrumresented here.Figure 6(b) presents a Gaussian fit of J=10, one of theost isolated lines of the spectrum. It can be seen that

he S/N ratio is excellent and the fit is very satisfactory inhe central part of the line, but the experimental linehape deviates from a Gaussian profile toward the wings,here it shows a small but clear asymmetry. The reason

or this asymmetry is found in an imperfect baseline cor-ection: All our scans are affected by a smooth change inhe value of the baseline that for these spectra can be asarge as of 0.02 �s in a single scan, and that always shows

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he exact same pattern. We attribute this baseline drift tohe peculiarities of our laser, which executes therequency scan by tilting a galvo plate. The tilt producesinute changes in the output laser beam angle and

rofile, which may alter the decay time of the light insidehe interferometer. We are in the process of makinghe necessary modifications to the setup to eliminate orinimize the drift. For the spectra presented in this pa-

er, a simple substraction of the baseline has been carriedut for each scan to produce the nearly flat baseline de-icted in Fig. 6(a). The smoothness and reproducibility ofhe baseline drift allow the operation to be carried outith ease, but when the substraction is not perfect the

ine shapes can be slightly altered as illustrated by Fig.(b).As a side note, it must be mentioned that because the

aseline decay time is slightly different in different pointsf the spectrum, it is not technically correct to convert de-ay time variations to absorption coefficients after theaseline substraction. Thus, the dashed line in Fig. 6(a),hich has been calculated using an average baseline de-

ay time of 6.8 �s, can be considered as an approximateepresentation only of the �=1.0�10−7 cm−1 absorptionoefficient. The deviations are, however, small.

ig. 6. Q-branch head of the recorded 12C2H2 overtone. (a) Glo-al view of the first lines of the Q-brnach. (b) Gaussian fit of the=10 line.

. DISCUSSIONhe aim of the experimental work reported in this paperas the design and construction of a high-repetition-rate

avity-ringdown spectrometer and the evaluation of itsnitial performance. Given the large number of cavityingdown setups in operation around the world, thisvaluation requires a comparison of our results withhose of other authors in order to illustrate better theain advantages and disadvantages of the experimental

cheme we have built.The main feature of a high-repetition-rate, cavity-

ingdown spectrometer is typically its sensitivity. It ishus illustrative to begin our discussion by briefly com-aring our results with those obtained by other authorsho have built high-repetition-rate CRD setups. As men-

ioned in the introduction, the most relevant efforts inhis direction come from van Leeuwen et al.28 and fromaldus et al. and Spence et al. at Stanford.24,26

The first demonstration of a high-repetition-rate setupbuilt by Paldus et al.24) reached a sensitivity (baselineoise) of 5�10−9 cm−1. In later years, this same setupas further developed and improved to make full use of

he repetition rate,26 reaching a sensitivity (MDAL) of.8�10−12 cm−1 Hz−1/2 (with a short-term sensitivity of 110−12 cm−1 Hz−1/2) at a ringdown generation rate of

0 kHz. This is, to our knowledge, the highest sensitivityemonstrated by a standard cavity ringdownxperiment.36 The experimental setup recently built byan Leeuwen et al.28 is technically the closest to ours,ince we make use of their “periodically locked” scheme; itemonstrated a sensitivity (MDAL) of 4.7�10−9 cm−1.All these experiments make important original contri-

utions to high-repetition-rate, cavity-ringdown spectros-opy, but their main drawback (common to all of them) ishat they have limited utility as spectroscopic tools and,t least in the incarnations described in the referencedorks, fall in the category of proof-of-concept experi-ents. For example, the experiment by Paldus et al.24

uffered from limitations in the data acquisition system,amely, the data transfer rate between the oscilloscopesed for digitization and the computer, which constrainedhe effective acquisition rate to a few hundred hertz. Andditional limitation of this setup was the lack of a long-ange frequency scan capability: With the cavity fringeocked to the laser, a frequency scan of the laser largerhan 30 MHz required manual relocking of the system.he improved experiment developed in the same group,26

ith its extraordinary sensitivity, got rid of the limita-ions in the data acquisition system but used a Nd:YAGaser as light source; thus its tunability and absolute fre-uency range were constrained to the width of the laserine ��1 cm−1�. The setup described by van Leeuwen etl.28 also suffered from limitations in the data acquisitionystem that constrained the effective acquisition rate andeduced the potentially attainable sensitivity by almostn order of magnitude. This experiment constituted atep forward in terms of tunability, since it presented aontinuous scan capability of 4 GHz, but this is still aelatively small range that makes frequency calibrationroblematic and the recording of large regions of the spec-rum a difficult proposition.

The main feature of our experimental setup when com-

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ared with those just mentioned is that it combines theensitivity attainable by a high-repetition-rate, cavity-ingdown apparatus with a number of additional charac-eristics that make it a usable and reliable spectroscopicool: a broad tunability limited only by the reflectivity ofhe cavity mirrors and ultimately the range of the lasersed; a continuous scanning range of �1 cm−1; easy lin-arization and calibration of the frequency scan throughhe use of a reference interferometer and an I2 referenceell; and a stable and robust operation that allows routinese of the apparatus.While the usability of our apparatus as a spectroscopic

ool is demonstrated by the spectrum presented, it isorth analyzing possible improvements to the sensitivity.ur short-term and long-term sensitivities, while veryigh, are still an order of magnitude lower than those at-ainable with the apparatus built by Spence et al.26 Theact that this setup works at a repetition rate of 80 kHzncreases its sensitivity by a nominal factor of 2.8 with re-pect to ours, so that the single-shot MDAL of the experi-ent is 2.83�10−10 cm−1 compared with our 1.4310−9 cm−1. This higher repetition rate is not in itself the

dvantage it might initially seem, since it is a conse-uence of the use of mirrors of lower reflectivity that giveise to an empty cavity decay time of 2.8 �s. If we workith the approximation that the sensitivity of a CRDS

etup increases linearly with the empty cavity decay time,he sensitivity gain factor of 2.8 mentioned above has toe combined with a loss factor of �7 �s/2.8 �s�=2.5 com-ared with our setup, which would render an initial sen-itivity advantage factor of 1.1 for the Spence et al. setupf all other factors were equal. This indicates that the rea-ons for the difference in sensitivity between the twopectrometers does not reside in mirror reflectivity or rep-tition rate, but in the standard deviations of the distri-ution of shots that each setup manages to reach.When the single-shot MDAL figure calculated above

rom the Spence et al. data is inserted in Eq. (3) togetherith the empty cavity ringdown time of 2.8 �s, a standardeviation of 0.0024% for the equivalent distribution ofingdowns is obtained. This is a remarkably low figure:ot only is it more than an order of magnitude better

han our best standard deviations of 0.03%, but it is ob-ained with an empty cavity decay time 2.5 times shorterhan ours. Moreover, this calculation does not include theact that Spence et al. monitor the ringdown curve fornly 5 �s, a little less than twice the decay time of thempty cavity, while we monitor it for approximately fourecay times. When all these factors are taken into consid-ration, the results are nothing short of amazing.

The factor that seems to be responsible for the out-tanding sensitivity of the setup of Spence et al. is the usef an analog detection system instead of a digitizer card.his lifts the restriction imposed by the finite number ofits of the analog-to-digital converters present in digitizerards and takes full advantage of the low noise of the de-ectors the authors built for that work. The use of an ana-og detection system is not without drawbacks: For ex-mple, since the data processing is done by analoglectronic circuits, analysis and rejection of individual ex-onentials is impossible. This means that it is not feasibleo check the exponential model consistency or simply re-

ect outliers that may appear when perturbations compro-ise the stability of the lock. Still, given the sensitivity

chieved with this system, the addition of a system simi-ar to our setup, which could be operated in parallel withhe digitizer currently in use, is an avenue worth explor-ng in the future.

When compared with “conventional” (not high-epetition-rate) cw-CRDS experiments, our setup is typi-ally an order of magnitude more sensitive than most ofhe setups in use today, with only a few experimentshowing a sensitivity comparable with our figure. This isormally achieved through the use of mirrors of excep-ionally high reflectivity. In addition to the setups alreadyiscussed in the introduction, it is worth mentioning as aore recent example the work of Dudek et al.37 in which a

ingle-shot baseline absorbance of 9.2�10−11 cm−1 waseached through the use of mirrors with a reflectivity of9.9985% and a 130 cm-long cavity. This produced anmpty cavity decay time of �300 �s, and illustrates per-ectly the difference in philosophy with the high-epetition-rate approach, which relies on the use of mir-ors of modest reflectivity and the accumulation of a largeumber of decays. In view of these results, it is appropri-te to discuss further the relative merits of these two ap-roaches.According to Eq. (3), and assuming that the relative er-

or of the distribution remains constant, the sensitivity ofCRDS experiment increases linearly with the empty

avity decay time �0. This means that using mirrors withery high reflectivity to reach a value of �0 that is N timesarger should always be preferred to accumulating Nhorter decays in the same time interval, since in the sec-nd case the sensitivity increases only with �N. Severalactors, however, partially compensate for this initial dis-dvantage. The first is the fact, already mentioned, thatnlike a conventional setup, a high-repetition-rate setupas no dead time between the end of a ringdown and theeginning of the next ringup cycle, which translates inton optimum use of time. A second advantage, also men-ioned in the introduction, is that the power injected intohe cavity is much higher than in the conventional ap-roach. Some experiments using high-reflectivity mirrorsnject so little power into the cavity that detectors withigh gain and low noise, such as bolometers and photo-ultipliers, are required. The large powers available in

ur experiment allow us to use normal silicon photodiodess detectors and reach excellent S/N ratios, which alsoontribute to a high sensitivity. A third factor that is dif-cult to evaluate but may also have a positive impact ineducing 0 is that the spectral distribution of the lightnjected into the cavity in a locked system is narrowerhan in a conventional system where the injection typi-ally takes place by scanning the interferometer fringe orhe laser frequency. It is reasonable to assume that thisffect will be most relevant in setups in which the laser isermanently locked to the top of the interferometerringe, like that of Spence et al., than in repetitivelyocked systems like that of van Leeuwen et al. and ours.

When one weighs the advantages and disadvantagesiscussed above, it seems clear that an experimentaletup aiming to maximize sensitivity would combine ele-ents from both approaches. Ideally, a cavity with mir-

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ors of very high reflectivity would be used in a lockedystem to benefit from the high sensitivity associatedith large values of �0, the absence of dead times, and the

pectral purity of the injected radiation that are charac-eristic of locked systems. The implementation of thisetup would require a system (like that of Spence et al.) inhich the laser is permanently locked to the interferom-ter, since the long ringup times required could be enoughor the laser to drift away from the fringe. Additionally,nd depending on the width of the interferometer fringesnd the type of laser source used, extra transducers mighte needed to guarantee the stability of the lock.In exchange for the advantages mentioned above, a

ocked-high-repetition-rate approach has as its mainrawbacks the additional instrumental complexity it re-uires and the fact that it is a less robust experimenthan a conventional cw-CRDS setup. We have found ro-ustness, however, to be a smaller problem than we ini-ially anticipated: Under normal operating conditions, westimate that only one of every ten 1 cm−1 scans needs toe restarted because of the system losing lock. This is nor-ally caused by operator “error” (for example, dropping a

ool near the laser). Regarding instrumental complexity,t must be noted than the majority of the instrumentationnd key optical and electro-optical elements used in ouretup are also present in most standard cw-CRDS experi-ents. Elements specific to a high-repetition-rate setup

re the EOM and the homemade electronics, as well asome other minor elements like the additional photodiodend optics required for the locking. Of all these elements,nly the locking electronics present a certain difficulty:hey have to be built according to the system character-

stics, tested, and fine-tuned. Once these electronics areuilt and working, the system is easy to use on a regularasis.We would like to end this discussion by commenting on

ome additional possibilities of high-repetition-rate set-ps that we have not explored in our experiments buthat are worth mentioning. One of them is the possibilityf synchronizing the ringdowns with external events.ontrary to what happens in nonlocked CRDS experi-ents, in which ringdowns are initiated periodically but

t random instants determined by the coincidence of theaser frequency and the position of the interferometerringe, ringdowns in our setup are initiated by an exter-al triggering signal and thus can be synchronized withvents of interest. This could be used, for example, toonitor the kinetics of chemical reactions in which the

ariation of the concentration of a product is measured atrecise intervals in time or to study processes in whichnstable, short-lived species are generated.

CKNOWLEDGMENTSe thank S. Yang for help at the initial stages of this

roject. We are also grateful to J. Ye and J. L. Hall fromoulder, Colorado, for useful discussions, and to J. Ro-ríguez Azañedo from Madrid for his help with the designf part of the electronics used in this work. We thank thecademy of Finland, Graduate School Laskemo (Ministryf Education), and the EU (contract HPRN-CT-2000-0022 and HPRN-CT-1999-00005) for financial support.

Corresponding author L. Halonen’s e-mail address [email protected].

*Present address, Instituto de Estructura de la Mate-ia, Consejo Superior de Investigaciones Cientificas, Ser-ano 123, 28006 Madrid, Spain.

EFERENCES AND NOTES1. A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical

spectrometer for absorption measurements using pulsedlaser sources,” Rev. Sci. Instrum. 59, 2544–2551(1988).

2. A. O’Keefe, “Trace gas analysis by pulsed laser absorptionspectroscopy,” Am. Lab. (Shelton, Conn.) 21, 19–22 (1989).

3. A. O’Keefe, J. J. Scherer, A. L. Cooksy, R. Sheeks, J. Heath,and R. J. Saykally, “Cavity ring down dye laserspectroscopy of jet-cooled metal clusters: Cu2 and Cu3,”Chem. Phys. Lett. 172, 215–218 (1990).

4. M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, and M. N.R. Ashfold, “Cavity ring-down spectroscopy,” J. Chem. Soc.,Faraday Trans. 94, 337–351 (1998).

5. G. Berden, R. Peeters, and G. Meijer, “Cavity ring-downspectroscopy: Experimental schemes and applications,” Int.Rev. Phys. Chem. 19, 565–607 (2000).

6. D. Romanini and K. K. Lehmann, “Ring-down cavityabsorption spectroscopy of the very weak HCN overtonebands with six, seven and eight stretching quanta,” J.Chem. Phys. 99, 6287–6301 (1993).

7. D. Romanini and K. K. Lehmann, “Cavity ring-downovertone spectroscopy of HCN, H13CN and H15CN,” J.Chem. Phys. 102, 633–642 (1995).

8. P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopyfor quantitative absorption measurements,” J. Chem. Phys.102, 2708–2717 (1995).

9. R. T. Jongma, M. G. H. Boogaarts, I. Holleman, and G.Meijer, “Trace gas detection with cavity ring downspectroscopy,” Rev. Sci. Instrum. 66, 2821–2828 (1995).

0. J. T. Hodges, J. P. Looney, and R. D. van Zee, “Laserbandwidth effects in quantitative cavity ring-downspectroscopy,” Appl. Opt. 35, 4112–4116 (1996).

1. J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response ofa ring-down cavity to an arbitrary excitation,” J. Chem.Phys. 105, 10278–10288 (1996).

2. J. Martin, B. A. Paldus, P. Zalicki, E. H. Wahl, T. G. Owano,J. S. Harris Jr., C. H. Kruger, and R. N. Zare, “Cavityring-down spectroscopy with Fourier-transform-limitedlaser pulses,” Chem. Phys. Lett. 258, 63–70 (1996).

3. K. K. Lehmann and D. Romanini, “The superpositionprinciple and cavity ring-down spectroscopy,” J. Chem.Phys. 105, 10263–10277 (1996).

4. K. K. Lehmann, “Ring-down cavity spectroscopy cell usingcontinuous wave excitation for trace species detection,”U.S. Patent 5,528,040, June 18, 1996.

5. D. Romanini, J. Gambogi, and K. K. Lehmann, “Cavity ringdown spectroscopy with cw diode laser excitation,”presented at the 50th Ohio State University Symposium onMolecular Spectroscopy, Columbus, Ohio, June 12–16,1995.

6. D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel,“CW cavity ring down spectroscopy,” Chem. Phys. Lett.264, 316–322 (1997).

7. D. Romanini, A. A. Kachanov, and F. Stoeckel, “Diode lasercavity ring down spectroscopy,” Chem. Phys. Lett. 270,538–545 (1997).

8. D. Romanini, A. A. Kachanov, and F. Stoeckel, “Cavityringdown spectroscopy: broad band absolute absorptionmeasurements,” Chem. Phys. Lett. 270, 546–550 (1997).

9. Li Ziyuan, R. G. T. Bennett, and G. E. Stedman, “Swept-frequency induced optical cavity ringing,” Opt. Commun.86, 51–56 (1991).

0. K. An, C. Yang, R. R. Dasari, and M. S. Feld, “Cavityring-down technique and its application to the

2

2

2

2

2

2

2

2

23

3

3

3

3

3

3

3


measurement of ultraslow velocities,” Opt. Lett. 20,1068–1070 (1995).

1. J. Poirson, F. Bretenaker, M. Vallet, and A. Le Floch,“Analytical and experimental study of ringing effects in aFabry-Perot cavity. Application to the measurement of highfinesses,” J. Opt. Soc. Am. B 14, 2811–2817 (1997).

2. M. J. Lawrence, B. Willke, M. E. Husman, E. K. Gustafson,and R. L. Byer, “Dynamic response of a Fabry-Perotinterferometer,” J. Opt. Soc. Am. B 16, 523–532 (1999).

3. J. Ye and J. L. Hall, “Cavity ringdown heterodynespectroscopy: High sensitivity with microwatt light power,”Phys. Rev. A 61, 061802 (2000).

4. B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J.S. Harris, and R. N. Zare, “Cavity-locked ring-downspectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).

5. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M.Ford, A. J. Munley, and H. Ward, “Laser phase andfrequency stabilization using an optical resonator,” Appl.Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).

6. T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Wilke,and R. L. Byer, “A laser-locked cavity ring-downspectrometer employing an analog detection scheme,” Rev.Sci. Instrum. 71, 347–353 (2000).

7. R. W. Fox, C. W. Oates, and L. W. Hollberg, “Stabilizingdiode lasers to high-finesse cavities,” in Cavity-EnhancedSpectroscopies, R. D. Van Zee and J. P. Looney, eds.(Academic, 2002).

8. N. J. van Leeuwen, J. C. Diettrich, and A. C. Wilson,“Periodically locked continuous-wave cavity ringdownspectroscopy,” Appl. Opt. 42, 3670–3677 (2003).

9. Typically, with mirror reflectivities of 99.95% and higher.0. J. A. Barnes, T. E. Gough, and M. Stoer, “Laser power

build-up cavity for high-resolution laser spectroscopy,” Rev.
Sci. Instrum. 70, 3515–3518 (1999).
1. T. Day, E. K. Gustafson, and R. L. Byer, “Sub-hertz relativefrequency stabilization of two diode-laser-pumped Nd:YAGlasers locked to a Fabry-Perot interferometer,” IEEE J.Quantum Electron. 28, 1106–1117 (1992).

2. Nominally, the sensitivity of CRDS experiments isindependent of the light intensity used, but this is true onlyas long as the intensity is large enough to stay away fromthe noise floor of the detectors. When detector noise is nolonger negligible, the sensitivity is also reduced.

3. R. J. Cvetanovic, D. L. Singleton, and G. Paraskevopoulos,“Evaluations of the mean values and standard errors ofrate constants and their temperature coefficients,” J. Phys.Chem. 83, 50–60 (1979).

4. J. Ye, Joint Institute for Laboratory Astrophysics (Space),National Institute of Standards and Technology, andUniversity of Colorado, Boulder, Colorado 80309-0440(personal communication, 2005).

5. M. Metsälä, S. Yang, O. Vaittinen, D. Permogorov, and L.Halonen, “High-resolution cavity ring-down study ofacetylene between 12 260 and 12 380 cm−1,” Chem. Phys.Lett. 346, 373–378 (2001).

6. We will confine our discussion to what we regard as“standard” cavity ringdown setups, which rely on themeasurement of the decay time of the cavity. This explicitlyexcludes the group of what nowadays are called “cavity-enhanced” techniques, which are also based on the use ofexternal interferometers but typically do not rely on themeasurement of decay times. While technically complex,some of these techniques have demonstrated exceptionalsensitivities.

7. J. B. Dudek, P. B. Tarsa, A. Velasquez, M. Wladyslawski, P.Rabinowitz, and K. K. Lehmann, “Trace moisture detectionusing continuous-wave cavity ring-down spectroscopy,”
Anal. Chem. 75, 4599–4605 (2003).

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Laser-locked, high-repetition-rate cavity ringdown spectrometer