1. Introduction

Noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS) is a laser based absorption technique that has an extraordinary potential for ultrasensitive detection of species in gas phase [1–7]. The high detectability is achieved by performing frequency modulation spectrometry (FMS) inside an optical cavity. This is made possible by locking the frequency of the laser to a longitudinal mode of the cavity, while keeping the modulation frequency equal to the free-spectral-range (FSR) of the cavity. The three components of the FM-triplet are then transmitted through the resonator in exactly the same way, which provides immunity to residual laser-to-cavity frequency noise. However, the requirement for a robust laser-to-cavity lock is also the major hurdle for a practical implementation of NICE-OHMS.

As a first step towards making the NICE-OHMS technique more applicable to trace species detection, we have recently developed a NICE-OHMS spectrometer based upon a narrowband fiber laser [7]. It was shown that the narrow linewidth of the fiber laser (1 kHz over 120 ms) considerably simplifies the locking of the laser to a narrow mode of a high-finesse cavity. The same work also demonstrated that a sensitive fiber-laser-based NICE-OHMS (FLB-NICE-OHMS) spectrometer can be built in a compact way using fiber coupled and integrated optics devices, few bulk optical components, and without features such as intensity stabilization and balanced detection. In that first study of FLB-NICE-OHMS, utilizing Doppler-broadened detection, acetylene was detected down to concentrations of 130 ppt, corresponding to an absorption coefficient of 2.4×10^-9 cm^-1.

To further strengthen the applicability of the technique, a theoretical model for Doppler-broadened NICE-OHMS was developed, with which the concentration of an analyte can be found by a fit to the experimental data. This model includes expressions for the signals from both the frequency-modulated (fm-NICE-OHMS) and the wavelength-modulated (wm-NICE-OHMS) mode of detection for an arbitrary FM detection phase. Lineshape fitting facilitates the accurate assessment of the analyte concentration in an unknown sample, particularly in the presence of spectral interference or a drifting background, but can also be used to obtain additional information such as the line center position, the transition width and the FM detection phase.

Despite this, the results of the first demonstration of FLB-NICE-OHMS did not reflect the full potential of the technique because of technical constraints: The detectability was limited by a large background signal (originating from an etalon inadvertently created in one of the cavity mirrors) that drifted primarily due to intensity variations, which, in turn, were caused by a malfunctioning polarization stabilization of the fiber laser.

The present work reports on an improved FLB-NICE-OHMS system that does not suffer from such shortcomings and hence provides significantly better detectability. The major modifications were a reconstructed cavity and a repaired fiber laser. In fact, the detectability increased to such an extent that the lowest C₂H₂ pressure that could be reliably controlled by the gas system was more than 3 orders of magnitude above the detection limit of the instrumentation. Measurements on a substantially weaker CO₂ transition were therefore also performed to illustrate the quality of the signal closer to the detection limit and to demonstrate the linearity of the system over a wider range of relative absorption.

2. Experimental setup

The experimental setup, which is schematically shown in Fig. 1, is based on that described in [7], but with two major changes. First, the mirrors and the piezoelectric crystals (PZTs) of the cavity have been replaced, which eliminated the large etalon that had been created in one of the mirrors by an accidental arcing in the PZT. The new mirrors (Layertec) and PZTs (Physik Instrumente) were of the same kind as in [7]. Both the flat and the concave mirror were made from parallel glass substrates, had no anti-reflection coating and their reflectivity was ~0.9994. Second, the erbium-doped fiber laser (Koheras, Adjustik E15) has been repaired, which provided an increased polarization extinction ratio and stability. As is shown by the results below, these improvements significantly reduced the drifting background signal that limited the detection sensitivity of the previous setup.

The new optical cavity had a finesse of 4800 and was well balanced, with a transmission of ~85% under locked conditions. The length of the resonator was 39.45 cm, yielding an FSR of 379.9 MHz, wherefore the cavity mode half-width-half-maximum (HWHM) was 40 kHz. The scan signal and the wavelength modulation (WM) dither were sent to separate cavity PZTs. Due to a discontinuity at one of the turning points of the piezo scan, presumably of mechanical origin, the frequency with which the wavelength could be scanned by a triangular ramp over the entire tuning range of the laser (~3 GHz) without unlocking was limited to 0.7 Hz, resulting in a maximum scanning rate of ~4 GHz/s. What is more, for higher scanning frequencies the maximum scanning rate was smaller. This implied that WM could not be performed with modulation amplitudes and at frequencies that are optimum for WM spectrometry.

 

Fig. 1. A detailed schematic of the experimental setup. ‘EDFL’ denotes the erbium doped fiber laser, ‘OI’ an optical isolator and ‘DBM’ a double balanced mixer. ‘PBS’ represents a polarizing beam splitter, ‘PD’ a photodetector, and ‘Phase’ a phase shifter, whereas ‘Gain’ is a separate gain stage. The nodes (∙) stand for power splitters (or power combiners, depending on the direction of the arrows). The dotted lines indicate the free-space laser beam path.

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A fiber-coupled electro-optic modulator (fiber EOM) was again used to create the sidebands for FM detection (this time at 379.9 MHz with a modulation index of 0.39) and for the Pound-Drever-Hall laser frequency lock (at 20 MHz with a smaller modulation index). For FM modulation indices above ~0.4, the second order sidebands start to influence the signal lineshapes.

As before, a custom-made, narrowband voltage controlled oscillator (VCO) created the FM modulation frequency, which was locked to the cavity FSR by the deVoe and Brewer method [8]. It should be emphasized that the condition for noise-immunity of NICE-OHMS is fulfilled only for a precise match of these two frequencies. A small frequency offset in the FSR locking system or a noisy frequency source will inevitably lead to increased noise in the detected signal. Therefore, a narrowband VCO (HWHM of ~10 Hz) together with a sensitive offset control were used, and the FSR lock was carefully optimized before each measurement.

It was found that a VCO linewidth of ~10 Hz was suitable for the present setup. This was verified by comparison with another frequency generator (Anritsu, MG3690A) that can be run in two modes of operation: one with lower and one with higher short-term frequency stability (~1 kHz and ~0.01 Hz, respectively) than the custom-made VCO. In the first case, a dramatic increase in the noise in the FM signal channel was observed, whereas in the second case the noise remained the same.

A fiber polarizer was inserted in front of the fiber EOM since a varying polarization of the light entering an EOM gives rise to a drifting FM background signal. However, the system was still affected by a remaining polarization drift of unknown origin. One possible cause could be the polarization maintaining fibers, since they inherently lead to a polarization variation of a few degrees [9]. To stabilize and optimize the state of polarization after the fiber, a polarizer and a half-wave plate were placed between the fiber collimator and the freespace polarizing beam splitter cube that picked off the cavity reflected light.

The system was optimized for minimum etalon fringes by careful alignment of the optical components. The fiber and free-space optical isolators that were used in Ref. [7] between the cavity and the laser were not found to further reduce etalons and were therefore removed. It is worth to note that the lack of such isolation did not cause laser instabilities due to optical feedback, which implies that the internal isolation of the fiber laser was sufficient. However, multiple reflections did occur between the cavity mirrors and the detectors for cavity reflection and transmission but could efficiently be reduced with free-space optical isolators in front of the detectors. No etalon fringes from the cavity mirrors were observed.

As in the previous work, the strong acetylene transition at 1531.588 nm, with a molecular line strength of 1.165×10^-20 cm^-1/(molecule cm^-2) (corresponding to a gas line strength of 0.29 cm^-2/atm at room temperature), was used. For the CO₂ measurements, the laser was tuned to a five orders of magnitude weaker transition at 1531.19 nm, with a line strength of 8.438×10^-26 cm^-1/(molecule cm^-2) (corresponding to a gas line strength of 2.1×10^-6 cm^-2/atm at room temperature) [10].

The applicable pressure range of our system was restricted; it had an upper limit of 1 Torr, given by the recommended working range of the cavity piezos, and a lower limit of ~10 mTorr, determined by the long-term leak-tightness of the gas system.

Due to the large dipole moment of the C₂H₂ transition and the high power amplification inside the cavity, optical saturation was observed at the lowest pressures. To reduce the influence of nonlinearities due to saturation, a rather modest input power of 0.64 mW was fed to the cavity, which resulted in a cavity transmitted power of 0.54 mW and, after the optical isolator, a power of 0.49 mW incident on the detector.

3. Evaluation procedure

As a part of adopting the NICE-OHMS technique to practical trace species detection, theoretical expressions were fitted to the measured spectra. Parameters obtained from such fits were then used to obtain information about the analytical sensitivity of the instrumentation and to calculate the limit of detection (LOD).

As was shown in [7], for a laser carrier center frequency v_c, an FM modulation frequency v_m, and an FM detection phase θ_fm, the Doppler-broadened fm-NICE-OHMS signal, S^fm-no, can be written as

where χ^-abs_G (v_c±v_m) are peak-normalized Gaussian absorption profiles with center frequency v₀, χ^-dispG (v_c) and χ^-disp_G (v_c±v_m) are the corresponding Gaussian dispersion lineshape functions and S^fm-no0 is the fm-NICE-OHMS signal strength. The latter entity is defined as (2F/π) η_fmJ₀(β)J₁(β)P₀αc₀Lc_rel, where, in turn, F is the cavity finesse, η_fm an instrumentation factor, J_i Bessel functions of the first kind, β the FM modulation index, P₀ the optical power impinging onto the detector, α^c₀ the absorption coefficient on resonance for a relative analyte concentration of 100%, L the cavity length, and c_rel the analyte concentration relative to atmospheric pressure.

The corresponding wm-NICE-OHMS signal for 1f-detection, S^wm-no₁, can be expressed as

where v_a is the WM modulation amplitude and χ^-abs,evenG,₁ (v_c±v_m,v_a), χ^-disp,evenG,1 (v_c±v_m,v_a) and χ^-disp,evenG,₁ (v_c±v_m,v_a) are the even components of the first order Fourier coefficients of the peak normalized Gaussian absorption lineshape function for the sidebands and the corresponding dispersion lineshape function for the sidebands as well as the carrier, respectively. The wm-NICE-OHMS signal strength, S^wm-no₀, is defined as η_wmS^fm-no₀, where η_wm is the instrumentation factor for WM detection.

4. Results and discussion

The panels (a) and (b) in Fig. 2 show background-corrected fm-NICE-OHMS and wm-NICE-OHMS dispersion signals from 10 µTorr of C₂H₂ in 10 mTorr of N₂ (corresponding to a relative C₂H₂ concentration of 13 ppb), respectively. The solid markers represent the experimental data (only every 10th data point is displayed for clarity), whereas the solid curves display the corresponding fits, whose residuals are shown in the separate windows below the panels.

 

Fig. 2. (a). Doppler-broadened fm-NICE-OHMS dispersion signal from 13 ppb (10 µTorr) of C₂H₂ (solid markers), a fitted lineshape (curve), and the residual to the fit (separate window). (b) wm-NICE-OHMS dispersion signal from 13 ppb (10 µTorr) of C₂H₂ (solid markers), a fitted lineshape (curve), and the residual to the fit (separate window).

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The fm-NICE-OHMS lineshape was acquired over 0.7 s with a scanning rate of 4 GHz/s and low-pass filtered with a cut-off frequency of 320 Hz (high enough not to distort the lineshape). For wm-NICE-OHMS, a dither frequency of 10 Hz and a modulation amplitude of 76 MHz were found to be a reasonable compromise between possible modulation frequency and amplitude combinations. The detection bandwidth of the lock-in amplifier was set to 5.3 Hz (30 ms integration time) and the lineshape was recorded over 50 s with a scanning rate of 56 MHz/s.

In both modes of detection the background signals (from an empty cavity) were much smaller than those presented in Figs 6(a) and 7(a) in Ref. [7]. In fact, the directly measured analytical signals were virtually indistinguishable from the background-corrected analytical signals shown in Fig. 2.

Equations (1) and (2) were fitted to the fm-NICE-OHMS and wm-NICE-OHMS signals in Fig. 2, respectively, with v₀, θf_m and S^no₀ as fitting parameters, while the width of the transition was held fixed at the FWHM of the Doppler profile (473 MHz). A small linear background was included in the fit to account for electronic offsets and drifts in the background signal between scans. As can be seen from Fig. 2, the theoretical lineshapes fit very well to the experimental data. The fits to the fm- and wm-NICE-OHMS signals returned phases of 90.5° and 87.7°, respectively, which verified that the dispersion phase was detected. In the residuals one can see sharp features at frequency detunings of 0, ±190 and ±380 MHz. These constitute the Doppler-free signals that alternatively could be used for NICE-OHMS detection. Although the NICE-OHMS lineshapes are visibly distorted by the Doppler-free signals, which are not included in the fitting expressions, the parameters returned by the fits are not influenced.

Figure 3 presents fm-NICE-OHMS signal strengths, S^fm-no0, for both C₂H₂ (panel a) and CO₂ (panel b) as a function of relative absorption. In each panel the data from measurements at absorption phase is represented by open markers, whereas the dispersion phase is depicted by solid markers. Fits to these data indicate a linear pressure dependence (in the relative absorption range displayed) for three of these curves, i.e. for C₂H₂ detected at dispersion phase and the two CO₂ curves, whereas the C₂H₂ curve detected at absorption phase shows a nonlinear dependence for low pressures.

 

Fig. 3. (a). Signal strengths, S^fm-no0, of absorption (open markers) and dispersion (solid markers) fm-NICE-OHMS signals from C₂H₂ as a function of relative absorption. The solid line shows a linear fit to the dispersion phase data. A relative absorption of 10^-6 cm^-1 corresponds to ~45 µTorr of acetylene. (b) Signal strengths, S^fm-no0, of absorption (open markers) and dispersion (solid markers) fm-NICE-OHMS signals from CO₂ as a function of relative absorption and their linear fits (solid lines). Here, a relative absorption of 2×10^-7 cm^-1 corresponds to ~800 mTorr of carbon dioxide.

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According to theory, the NICE-OHMS signal strength from a given analyte concentration should be independent of the FM detection phase. However, as clearly can be seen in panel (b), the slope of the absorption curve was slightly larger than that of the dispersion curve, indicating a weak phase dependence of the sensitivity of the instrumentation. This is an artifact of technical origin caused by a phase-dependent transmission of the phase shifter, which, in turn, resulted in a power variation of the electrical reference signal used for demodulation of the FM signal. It is also possible that reflections and standing waves in the electrical cables contributed to this phase dependence.

The slightly nonlinear dependence of the C2H2 absorption curve at low relative absorption is attributed to optical saturation. The influence of saturation becomes larger for decreasing total pressure because of a decreased quenching. The measurements indicate, however, that the dispersion signal is significantly less affected by optical saturation than the absorption signal. This phenomenon has been predicted previously [11] and will be scrutinized in a separate work [12]. This suggests that dispersion is the most suitable phase for detection of Doppler-broadened NICE-OHMS signals whenever optical saturation is present.

For relative absorptions higher than 10^-6 cm^-1 two other phenomena will affect the linearity of the pressure dependence (as well as the signal shapes) at both absorption and dispersion phase. Firstly, the approximation made to linearize the absorption response from the medium, which requires that (2F/π)α^c₀c_relL≪1, will no longer hold. Secondly, the cavity finesse will decrease if the single-pass absorption becomes comparable to the intracavity losses, i.e. if α^c₀c_relL≪12π/F is no longer a valid assumption. A linear pressure dependence for large absorption requires that these effects are properly taken into account in the expressions that are fitted to the data.

To assess the analytical performance of the spectrometer, i.e. to determine the lowest detectable relative concentration for a species, c_rel, we calculate the LOD according to

where σ denotes the standard deviation of signal strengths obtained from fits of Eqs. (1) and (2) to the differences between consecutive empty cavity scans (with the signal strength as the only fitting parameter) recorded under the same conditions as the analytical signal. The NICE-OHMS sensitivity, ξ^no, is given by S^no₀/c_rel[7].

In order to find the optimum experimental conditions we studied how the LOD depended on different combinations of scanning rate and electronic detection bandwidth for absorption and dispersion phase. Some results of this investigation are presented in Table 1.

Table 1. Limits of detection (LODs) for absorption (abs) and dispersion (disp) fm-NICE-OHMS signals achieved for different combinations of acquisition time and electronic detection bandwidth.

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In order not to distort the lineshapes, the detection bandwidth was kept two orders of magnitude above the fractional slew rate of the signal, which for a 3 GHz scanning range implied that it was chosen a factor of ~500 above the scanning frequency. As can be seen from the table, the lowest LOD for absorption phase was achieved for a rather long acquisition time (5 s), whereas in the case of dispersion the detectability improved with decreasing acquisition time and the minimum LOD was obtained for the fastest possible acquisition time (0.7 s). This indicates that the absorption signal was steady over a long time with respect to the acquisition time, while the dispersion signal drifted more and on a faster time scale, which was confirmed by separate measurements of the background signals. One possible explanation for the drift observed at dispersion phase is temperature and stress dependent chromatic dispersion in the optical fiber after the fiber EOM, which unbalances the phase of the FM triplet and causes a varying offset in the FM dispersion signal. However, no conclusive explanation of the dissimilar behavior of the background signals at the two phases could be found.

As a consequence of these findings, dispersion was chosen as the preferred detection phase because (i) the influence of the drift can be reduced by a fast scan, (ii) the amplitude of the dispersion signal is larger than that of the absorption signal and (iii) the dispersion signal is virtually unaffected by optical saturation.

The fm-NICE-OHMS signal in Fig. 2(a) was, in fact, recorded under optimum conditions. An analytical signal strength of 3.4 V was obtained for a C₂H₂ concentration of 13 ppb, which yielded an FM sensitivity of 260 mV/ppb. The standard deviation from 16 background fits was 0.38 mV, which resulted in a LOD for fm-NICE-OHMS of 4.5 ppt, corresponding to 3.5 nTorr or an absorption coefficient on resonance of 8×10^-11 cm^-1. The LOD for fm-NICE-OHMS quoted in Ref. [7] was 360 ppt. This shows that an improvement by a factor of 80 could be achieved by eliminating the technical constraints that limited the first demonstration of FLB-NICE-OHMS and increasing the cavity finesse from 1400 to 4800.

For the wm-NICE-OHMS signal in Fig. 2(b) a sensitivity of 650 mV/ppb and a standard deviation of the signal strengths from the background fits of 3 mV were determined. This gave a LOD of 14 ppt (11 nTorr), which corresponds to an absorption coefficient on resonance of 2.4×10^-10 cm^-1 for an acquisition time of 50 s. The reasons why a worse detectability was obtained with wm-NICE-OHMS are that the wavelength modulation parameters were far from optimum and that a low scanning rate had to be used. The modulation amplitude (76 MHz) was only one third of the optimum, which is assumed to be around the HWHM of the transition (236 MHz). Moreover, it is clear that a modulation frequency of 10 Hz cannot efficiently reduce 1/f-noise. Ideally, one should choose a modulation frequency in a low noise region of the noise spectrum, but this was not possible with the present instrumentation. If a larger modulation amplitude and higher modulation frequency could be used, it is likely that wm-NICE-OHMS could rival fm-NICE-OHMS.

To present a signal closer to the detection limit and to illustrate the improvement in detectability, the weak carbon dioxide transition was probed at a concentration that corresponds to the LOD reached in Ref. [7] with fm-NICE-OHMS (6×10^-9 cm^-1). Figure 4 shows, in panel (a), the fm-NICE-OHMS dispersion signal (solid black curve) from 30 mTorr (40 ppm) of pure CO₂, and the corresponding empty cavity scan (solid grey curve), recorded with the same scanning rate and electronic filter as the signal in Fig. 2(a). The background signal, caused by a weak etalon of unknown origin, changed its shape on the minute timescale and could therefore be subtracted from the analytical signal. Panel (b) displays the background-corrected analytical signal (solid markers, only every 10th data point is displayed) together with the fit (solid curve), whereas the residual is shown in the separate window below.

For reasons discussed above, lineshape fitting was used to determine the analytical performance of the instrument. An alternative way to evaluate the performance of the spectrometer is to measure the signal-to-noise ratio (SNR) of the signal at the peak and to compare the thereby obtained minimum detectable absorption with the absorption coefficient corresponding to the shot-noise.

The flat structure of the residual of the fit in Fig. 4(b) shows that the detectability of the instrumentation was (for an acquisition time of 0.7 s) limited by random noise. The SNR could therefore be calculated by dividing the signal amplitude with the root-mean-square of this noise. Given a signal amplitude of 0.7 V and a root-mean-square noise of 23 mV (for a detection bandwidth of 320 Hz) we estimate the SNR to be ~30, which corresponds to a minimum detectable absorption of 2×10^-10 cm^-1.

The shot-noise equivalent absorption coefficient for NICE-OHMS can be calculated according to Eq. (21) in Ref. [7]. With a cavity length of 39.45 cm, a detection bandwidth of 320 Hz, a detector responsivity of 1 A/W, an incident power on the detector of 0.49 mW, a cavity finesse of 4800 and a modulation index of 0.39, the shot-noise limited absorption (for SNR=2) becomes 3×10^-11 cm^-1. The instrumentational noise level of our spectrometer is therefore (for the given detection bandwidth) within one order of magnitude from the shot-noise limit.

 

Fig. 4. (a). Doppler-broadened fm-NICE-OHMS dispersion signal from 30 mTorr (40 ppm) of CO₂ (solid curve) together with the corresponding empty cavity scan (open markers). (b) Background corrected analytical signal (solid markers), a fitted lineshape (curve) and the residual to the fit (in the separate window).

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5. Conclusions

It has previously been shown that NICE-OHMS instrumentation can be made significantly simpler and more compact by the incorporation of various fiber components, primarily a narrowband fiber laser and a fiber-coupled electro-optic modulator [7]. This work demonstrates that FLB-NICE-OHMS can provide an exceptionally high analytical detectability for molecular species. A detection limit for C₂H₂ in the low ppt range (4.5 ppt, corresponding to 2 ppt·m) was obtained by frequency modulated Doppler-broadened detection at dispersion phase using a cavity with a finesse of 4800.

Detection at dispersion phase was found to be better than at absorption phase for a system affected by optical saturation, since it provides a signal that is larger and linear over a wider pressure range. The detectability was limited by a low frequency drift of a small background signal of unknown origin. Detection of wm-NICE-OHMS signals did not reduce the influence of the drift since the modulation could not be performed under optimum conditions. Instead, the fm-NICE-OHMS signal was detected with a scanning rate high enough to overcome the drift. The relatively fast acquisition time of fm-NICE-OHMS is also an advantage for trace species detection.

A further improvement in the detectability of FLB-NICE-OHMS is anticipated once the origin of the background signal and its drift has been identified and reduced, or WM is performed at higher frequency.