Optical cavity enhanced real-time absorption spectroscopy of CO 2 using laser amplitude modulation

We present a spectrometer based on the cavity enhanced amplitude modulated laser absorption spectroscopy (CEAMLAS) technique for measuring molecular gas absorption. This CEAMLAS spectrometer accurately measured a CO2 absorption line at 1572.992 nm with effectively 100% measurement duty cycle. It achieved an absorption sensitivity of 5.2 × 10−9 Hz−1∕2 using a linear Fabry-Perot cavity with a modest finesse of ≈1000. We also used the spectrometer to perform preliminary measurements of the 13C/12C isotopic ratio in CO2, yielding an isotopic signature δ13C of −83±9‰ for our CO2 sample.

Measurement of trace gases and their isotopic ratios are of interest in a diverse range of applications.These include the monitoring of atmospheric greenhouse gases; 1 geological, ecological, and biochemical research; 2,3 illicit drug testing; 4,5 and natural gas detection in the mining industry. 6][5] However, with advances in optical technologies, similar or surpassing levels of precision can be achieved using laser absorption spectroscopy (LAS) techniques. 1,2,6These techniques can significantly reduce instrument cost while their compactness enables in-situ measurements.One of the leading optical techniques is cavity ring-down spectroscopy (CRDS), which was first demonstrated by O'Keefe et al. in 1988. 7This method has been used in many field-deployable spectrometers to date.The state-of-the-art absorption sensitivity of a CRDS spectrometer is approximately 2 Â 10 À10 Hz À1=2 . 8,9Another notable technique is noiseimmune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) developed by Ma et al., which holds the record sensitivity of 5 Â 10 À13 Hz À1=2 . 10However, due to the complexity and high cost, portable NICE-OHMS spectrometers are still under development. 11he high sensitivity of these LAS spectrometers is a result of using a high quality Fabry-Perot cavity, where the finesse F is usually larger than 10 4 .This increases the effective light-gas interaction length by the effective bounce number b ¼ 2 Â F =p.The sensitivity in NICE-OHMS systems is further improved by using frequency modulation of the laser, and results in a continuous and zero-background absorption signal with technical noises significantly suppressed.In 2008, Chow et al. demonstrated a proof of concept experiment involving cavity enhanced amplitude modulated laser absorption spectroscopy (CEAMLAS). 12Like NICE-OHMS, the CEAMLAS method also provides a real-time, zero-background absorption signal.At optimal operating condition, the CEAMLAS signal was immune to laser intensity noise, and a quantum shot-noise limited sensitivity was achieved in a fiber cavity with finesse of 60, 12 with less complicated setup than NICE-OHMS.This result offers a new architecture for building a highly sensitivity, field deployable optical spectrometer using CEAMLAS.In this Letter, we report the construction and spectroscopic result for a CEAMLAS spectrometer, achieving an initial absorption sensitivity of 5.2 Â 10 À9 Hz À1=2 with a cavity finesse of F % 1000.This initial result is already on par with or even surpassing the sensitivity of many existing NICE-OHMS 11 and CRDS systems. 13EAMLAS uses radio frequency (RF) amplitude modulation (AM) of the laser to interrogate the resonant reflection response of the cavity. 12The modulation frequency x m is chosen to be much higher than the cavity linewidth.When the laser carrier is on resonance, the reflected optical field E r consists of the reflected carrier and the off-resonance AM sidebands, given by In Eq. ( 1), E 0 is the amplitude of the input beam, with optical power P 0 ¼ jE 0 j 2 .The first term in the bracket is the resonant reflection response of the cavity, which characterizes the impedance matching condition.r 1 and r 2 are the amplitude reflection coefficients of the input and output cavity mirrors respectively; a is the absorption coefficient of the intra-cavity gas medium; and L is the length of the cavity.
The other two terms in the bracket correspond to the reflected AM sidebands with small modulation depth of b.
As shown in Fig. 1, the resonance between the carrier and the cavity is maintained using the Pound-Drever-Hall laser frequency stabilization technique. 14The reflected beam is fully detected on a fast photodiode by optimizing the a) orientation of the quarter wave plate.The optical power P r ¼ jE r j 2 is then converted into an electronic signal, and is subsequently mixed with the local oscillator at x m to isolate the beat between the sidebands and the resonant carrier.After passing the down-mixed signal through a low pass filter and optimizing the demodulation phase, the demodulated resonant signal V res can be extracted.In the approximation that the empty cavity is nearly impedance matched ðr 1 À r 2 ( 1Þ and the absorption is small ðaL ( 1Þ, V res becomes where k is a proportionality constant that depends on the modulation depth, photodiode response, and transimpedance gain.ðr 1 À r 2 Þ= ffiffiffiffiffiffiffiffi r 1 r 2 p quantifies the impedance mismatch of the cavity mirrors, and is represented as a DC offset in V res .As shown in Eq. ( 2), this is a zero background signal and immune to laser intensity noise when the empty cavity is impedance matched.In the presence of small impedance mismatch and small intra-cavity absorption, fluctuations in P 0 are still highly suppressed by the resonant reflection response of the cavity.When the carrier is far off resonance, it can be shown that the signal V of f % P 0 k, thus the AM readout can be normalized as Equation ( 3) shows a simple conversion between the experimental AM readout and the absorption aL.The signal processing system was digitally implemented using an analog-to-digital converter (ADC) and a field programmable gate array (FPGA).Digital signal processing enables rapid design and implementation of the low pass filters, data acquisition, and subsequent data processing.To obtain a CO 2 spectral line, an NKT Photonics Koheras Adjustik E15 fiber laser was used.It covers the wavelength from 1572.4 nm to 1573.4 nm and has less than 1 kHz linewidth as specified by the manufacturer.The cavity had a finesse of approximately 1000, and a length of 20 cm, with a stainless steel spacer for mechanical stability.The output cavity mirror was mounted on a piezo-electric transducer (PZT) which enabled cavity length tuning.The cavity was enclosed within a vacuum tank which can be evacuated and filled with CO 2 gas.
Figure 2 shows the demodulated AM readout as we scanned the laser frequency across a cavity resonance.When the laser was off resonance, the readout was normalized to 1.The central trough occured when the laser carrier and the cavity were resonant (0 frequency detuning).6][17] This impedance mismatch was treated as a DC offset in a spectral measurement.The two satellite features in Fig. 2 occured when each of the AM sidebands became resonant with the cavity.They were associated with our modulation frequency sidebands of 37.5 MHz.We used the drive voltage to the laser PZT to calibrate the frequency axis in Fig. 2, obtaining a calibration factor of 14.6 MHz/V.However, this frequency calibration was only approximate, as it is known that there can be significant nonlinearity between PZT displacement and drive voltage.This was confirmed by the unequal spacing of cavity resonance modes when we scanned the laser PZT with a linear voltage ramp.
When CO 2 is injected into a cavity and the cavity resonant mode is coincident with a molecular transition, the intra-cavity loss increases.As can be observed in the inset of Fig. 2, such intra-cavity loss resulted in the rise of the resonant AM readout shown as the red dashed line.This was a first order effect, with the resonant AM readout strongly dependent on the strength of gas absorption.One expects the cavity finesse to be slightly degraded if it was on a transition.However, this was a secondary effect for the weak absorption measurement of interest here.Hence, we assumed that finesse remained constant across the absorption spectrum when we calibrated the absorption signal.
There are three strong CO 2 rovibrational overtone transitions within the wavelength tuning range of our fibre laser.We injected 0.32 6 0.03 millibar of room temperature pure CO 2 into the evacuated gas chamber, and found an absorption line by a quick frequency scan.We then PDH locked the laser onto the cavity resonance near the line.This represents one fixed point on the absorption spectrum.The cavity length was then scanned by a sawtooth voltage at a period of 50 s to tune the cavity resonant mode.The laser wavelength closely tracked the scanning cavity resonance because it was locked, thereby mapping out the CO 2 absorption spectrum while the mirror was translated longitudinally.Figure 3 shows the absorption spectrum obtained for the R12e line in the 30012 00001 band of CO 2 , 18 with the vertical axis calibrated by Eq. ( 3) using F % 1000.The drive voltage to the laser PZT became the feedback control signal, because the laser was locked to the cavity resonance.As in Fig. 2, we used this drive voltage for calibration of our horizontal frequency axis.This CEAMLAS spectrum was measured in less than 4 min.
Figure 3 shows that the spectral line measured by the CEAMLAS spectrometer had a high signal to noise ratio (more than 1000).At 0.32 6 0.03 millibar of CO 2 pressure, Doppler broadening dominates over pressure broadening; therefore, the absorption line can be modeled by a Gaussian line shape. 18The measured profile was well fitted by this model.The full width at half maximum of the absorption line yield a gas temperature of 20 C. This was in good agreement with an independent measurement taken with a thermometer.A gas pressure of 0.29 millibar was obtained from the fitted profile, using the spectral line intensity of 1.663 Â 10 À23 cm À1 /(mol cm À2 ) for this R12e transition line. 18This was also in close agreement with an independent measurement from a pressure gauge.
The sample spacing in Fig. 3 was approximately 50 kHz, and can be further narrowed by using a slower scan and/or faster data acquisition.This spacing over a large measurement span of the order of 1 GHz implied a continuous, real-time spectral measurement, enabling effectively 100% measurement duty cycle.With an absolute frequency reference such as a frequency comb, such small frequency spacing will enable high precision measurement of the fundamental Voigt lineshapes of molecular transitions.
To characterize the sensitivity of this first generation spectrometer, we measured the AM readout at a fixed spectral point in vacuum.The typical result of a measurement is illustrated in Fig. 4. The standard deviation for the noise was DaL ¼ 1.6 Â 10 À7 over a time span of 1 s, which agrees with the inset of Fig. 3.As in a CRDS system, the noise equivalent absorption (NEA) sensitivity of this CEAMLAS spectrometer was calculated as where r aL is the standard deviation of the absorption and f is the data acquisition rate. 9In Fig. 4, the sampling rate was 1 kHz, so the NEA of the initial CEAMLAS spectrometer was 5.2 Â 10 À9 Hz À1=2 .This was achieved with a relatively modest cavity finesse of 1000, whereas the best CRDS sensitivity of 2 Â 10 À10 Hz À1=2 was achieved with a cavity of much higher finesse (F % 20000 used by Spece et al. 8 and Hodges et al. 9 ).Our investigations suggested that this initial sensitivity of CEAMLAS spectrometer was limited by technical noise sources, such as time varying beam pointing error.This was confirmed by gently dithering the cavity alignment and observing the resultant noise increase.These technical limitations will be overcome with improved opto-mechanical design in the next generation CEAMLAS systems.
To demonstrate the potential application of the CEAMLAS spectrometer, we measured the 13 C/ 12 C isotopic ratio of our gas sample.This was achieved by changing the laser to a New Focus Vortex II external cavity tunable diode laser (ECDL).This laser has tunable wavelength from 1596.6 nm to 1597.1 nm.A transition line R60e in the 30013 00001 band of 12 CO 2 and an R30e line in the 30013 00001 band of 13 CO 2 are present within this wavelength region. 18These two absorption lines have similar absorption strengths at natural abundance.The solid line in Fig. 5 shows this pair of isotopic absorption lines measured by the CEAMLAS spectrometer at 10 millibar of pure CO 2 and room temperature.Overlaid in Fig. 5 as a dashed line is the calculated spectrum.In contrast to Fig. 3, a Voigt profile was assumed instead of a Gaussian fit, because, at 10 millibar, the effect of pressure broadening becomes observable alongside Doppler broadening. 18Using the independently measured total pressure and room temperature, we fitted the 13 CO 2 absorption line and obtained a concentration of 1.01%.From the fit residual, we estimated an uncertainty in 13 CO 2 concentration of 0.01%.The fitted 13 CO 2 profile stayed well within one standard deviation of the measured absorption data, as evident from Fig. 5.
In comparison, we note that there is observable difference in the widths between experimental and calculated Voigt line shapes for the 12 CO 2 absorption line.We attributed the width mismatch to the calibration error in wavelength.This was likely due to the laser PZT nonlinearity as previously discussed.The 12 CO 2 absorption line was obtained near the end of the laser PZT tuning range, where the most significant nonlinearity was manifested.There are various methods to calibrate for this nonlinearity if it was desired, for example, by using a wavelength meter or absolute referenced frequency comb, which is planned for the next generation of CEAMLAS spectrometer.Based on the gas mixing ratios used in the two fit, the isotopic ratio of 13 C/ 12 C was approximately 0.0103 0.0001.The sample 13 C isotopic signature d 13 C was then calculated as where 13 C/ 12 C standard is referred to an established standard of 0.0112372. 2Thus, for the CO 2 sample we tested, d 13 C was À8369& which was within the naturally occurring d 13 C value from 0& to À110&. 2 The signal to noise ratio in this isotopic ratio measurement was degraded compared to that in Fig. 3.This was because of the weaker transition and the higher frequency noise of the ECDL.Since the isotopic ratio of the CO 2 we used has not been calibrated, the accuracy of this isotopic ratio measurement awaits further confirmation.
In conclusion, this Letter reports the demonstration of molecular gas sensing with a CEAMLAS spectrometer, accurately measuring a rovibrational transition for CO 2 in real-time, with high spectral resolution.The initial noise equivalent absorption sensitivity is 5.2 Â 10 À9 Hz À1=2 , achieved using a modest finesse cavity with F % 1000.In addition, we have demonstrated that CEAMLAS can readily be adapted to measure the 13 C/ 12 C isotopic ratio of CO 2 .This research was funded by the Australian Research Council under the Project ID: LP100200604 and DE130101361.

FIG. 3 .
FIG. 3. line in the 30012 00001 band of CO 2 measured by the CEAMLAS spectrometer, fitted by a Gaussian lineshape.Inset: Noise of the CEAMLAS measurement.

FIG. 4 .
FIG. 4. Fractional measured by the CEAMLAS spectrometer at a fixed wavelength, away from any gas absorption lines.This indicates the time-varying noise of the spectral measurement.