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We present a novel strategy for suppressing mode structure which often degrades off-axis cavity enhanced absorption spectra. This strategy relies on promoting small, random fluctuations in the optical frequency by perturbing the injection current of the diode laser source with radio frequency (RF) bandwidth-limited white noise. A fast and compact oxygen sensor, constructed from a 764 nm vertical-cavity surface-emitting laser (VCSEL) and an optical cavity with re-entrant configuration, is employed to demonstrate the potential of this scheme for improving the sensitivity and robustness of a field-deployable cavity spectrometer. The RF spectral density of the current noise injected into the VCSEL has been measured, and correlated to the effects on the optical spectral signal-to-noise ratio (SNR) and laser linewidth for a range of re-entrant geometries. A fourfold gain in the SNR has been achieved using the RF noise perturbation for the optimal off-axis alignment, which led to a minimum detectable absorption (MDA) predicted from an Allan variance study as low as 4.3 × 10−5 at 1 s averaging. For the optically forbidden oxygen transition under investigation, a limit of detection (SNR = 1) of 810 ppm was achieved for a 10 ms acquisition time. This performance level paves the way for a fast, sensitive, in-line oxygen spectrometer that lends itself to a range of applications in respiratory medicine.
© 2014 Optical Society of America
1. Introduction
The growing interest in the use of laser absorption spectroscopy as core technology for trace gas sensors is corroborated by the considerable effort expended by the research community in developing strategies that meet the demands of ruggedness, compactness, high sensitivity, and low cost. Among the most mature sensitivity-enhancing schemes are those making use of high-finesse optical cavities for extending the interaction length of the radiation through the gas sample, largely in the form of cavity ring-down spectroscopy (CRDS) and cavity enhanced absorption spectroscopy (CEAS) [1,2]. Despite the general consensus that higher levels of sensitivity can be achieved by the time-domain variant (CRDS), the extraction of absorption information from time-integrated intensity measurements (CEAS) is often preferred when designing field instrumentation, as it poses fewer engineering challenges. Indeed, CEAS does not require sophisticated optical and electronic components, rigorous mechanical stability, or strong spatial and temporal coherence between the laser and the cavity. The need for selective, resonant coupling of the laser to a single longitudinal cavity mode is abandoned, and CEAS benefits from excitation of an extremely dense cavity mode spectrum [3]. Typically, this is achieved by a reentrant cavity configuration featuring an off-axis light injection, which can exhibit a significant reduction in the apparent free spectral range (FSR) of the cavity, and concomitant excitation of many transverse-longitudinal modes of different order. The objective is to obtain a FSR approaching the laser linewidth (ΔνFSR ∼ ΔνDL), i.e. the re-entrant round-trip time greater than the coherence time of the laser. In this regime, wavelength-dependent resonant properties of the cavity are suppressed, and for an empty cavity the transmission spectrum becomes essentially independent of the laser frequency [4–7].
However, this condition is rarely met in practice, particularly for short cavities, and the observed residual mode structure is often the sensitivity-limiting factor. Common strategies for promoting the removal of residual mode structure include dithering the cavity length, and modulating the laser injection current. Both routes have proven to randomize to some degree the cavity mode structure, and consequently improve the measured spectral signal-to-noise ratio (SNR), but this benefit is often muted by concurring detrimental effects. Indeed, piezoelectric modulation of the cavity length requires moving mechanical components, and it has been shown to promote fringing effects due to periodic resonant coupling at the turning points of the modulation [8, 9]. Dithering the frequency space of the laser drive via a discrete current modulation (typically high kHz) is simpler to implement, but it inevitably introduces frequency and amplitude modulation, which in turn could contribute to additional signal noise and spectral broadening [8, 10, 11].
In this letter, we present the first realization of a strategy to increase the sensitivity of an off-axis cavity enhanced absorption spectrometer via injection of radio frequency (RF), white, bandwidth-limited (1–1500 MHz), current noise into the diode laser source. The operating principle lies in generating statistically uncorrelated, random fluctuations in the injection current, which are then translated into optical frequency noise. The net result is an apparent reduction in the coherence time of the laser, which promotes a more efficient minimization of residual mode structure, and thus increases the spectral signal-to-noise ratio (SNR). To achieve a similar effect, Engel et al. [12] have suggested the possibility of using laser modulation with white noise filtered to have a Gaussian envelope with a maximum at 0 Hz as a tool for controlling the laser linewidth.
The benefits of the RF noise (RFN) current perturbation are investigated here using a compact, rapid (10 ms response time), and sensitive oxygen absorption spectrometer developed in our laboratory for use in respiratory medicine. The call for an O2 analyzer that offers high accuracy (better than 2000 ppm at 1 atm), fast response (< 50 ms), large dynamic range (0–100%), and operates directly within the airways, is prompted by the potential impact of monitoring ongoing oxygen consumption in a range of clinical settings (e.g. anaesthesia, intensive care units), where current side-stream technology is not wholly applicable [13–15].
Initial measurements on the spectral characteristics of the RF current noise injected into, and experienced by the laser diode are followed by a comparison between the effects of wideband noise versus a more conventional, single-frequency, current modulation. The effectiveness in suppressing residual cavity mode structure is investigated under a range of re-entrant alignments, along with the effects of various RF power levels and frequency windows on the laser linewidth and CEAS performance.
2. Experiments and results
A schematic of the experimental set-up is illustrated in Fig. 1. The oxygen spectrometer makes use of a 764 nm, low-power (300 μW), single-mode, vertical-cavity surface-emitting laser (VCSEL) with a quoted spectral linewidth of ∼100 MHz (ULM Photonics, ULM764-01-TN-S46FTT). The laser output was launched into a 27 mm long (ΔνFSR = 5.6 GHz), medium-finesse (∼700) optical cavity in an off-axis manner to achieve re-entrant mode excitation. The short separation between the cavity mirrors was determined by the diameter of standard ventilation tubes. The choice of a modest cavity finesse was driven by the use of a low power laser source and the desire for high accuracy and precision over a large dynamic range of O2 concentrations. Indeed, for the case of high levels of oxygen, a higher finesse would result in a larger extinction ratio across the absorption line, which in turn would reduce the measurement precision. The transmitted intensity was detected by a Si photodiode coupled with a current amplifier (G = 106 V/A, BW = 10 kHz), and subsequently acquired by an analog-to-digital converter (ADC, 80 kS/s). A 200 Hz, sawtooth current ramp was applied on top of the DC bias current (1.1 mA) through the laser driver unit for repeatedly scanning the optical wavelength across the P(11)Q(10) rovibrational transition within the A(0,0) band of molecular oxygen (line position, λ = 764.17 nm; integrated absorption cross-section, σint = 6.68 × 10−24 cm2 cm−1 at 296 K) [16]. The wavelength tuning rate to detector bandwidth relationship was optimized on the basis of a FFT spectrum of the cavity transmission signal, with a view of reducing the detector output noise without removing absorption spectral information.
Fig. 1 Schematic of the experimental set-up. A bias-T network (Bias-T) combines the triangularly ramped laser current (Driver) with the pre-conditioned output (AMP, broadband RF amplifier; LP, low-pass filter) of the RF current noise source (RFN). The 764 nm VC-SEL radiation is injected onto the optical cavity in an off-axis manner (OA-CEAS). The cavity transmission is detected by a Si photodiode (PD), and the amplified signal is acquired by an analog-to-digital converter (ADC). The voltage across a 50 Ω probe placed in series with the VCSEL is measured by a spectrum analyzer (SA).
The flat, Gaussian noise current output (−174 dBm/Hz over 1–1500 MHz) generated by the RFN (RF Design, BBGen) was amplified and coupled into the laser via a bias-T network. The spectral density of the current noise injected into the VCSEL junction was derived from frequency-domain measurements of the voltage across a 50 Ω probe placed in series with the laser diode by means of a spectrum analyzer (HP, 4395A).
Figure 2 (left axis) shows the amplitude spectral density of the root-mean-square current ( ) generated by the RFN source and amplified by a 40 dB gain RF amplifier (RF Design, ZKL-1R5+, red line), along with the current flowing through the 50 Ω probe when the VCSEL was zero biased (blue line) or forward biased (black line). The upper frequency limit (500 MHz) is dictated by the spectrum analyzer. By integrating the current density spectrum obtained by subtracting the data for the two biasing regimes, the net root-mean-square current (irms) through the junction diode was estimated at 12 μA. This indicates that only a small fraction (∼ 1%) of the total current noise output by the RFN source (900 μA over 1–1500 MHz) was in fact transferred to the VCSEL. This result was explained in terms of two contributing factors. Firstly and foremostly the presence of an electrostatic discharge (ESD) protection diode within the commercial laser package which sets the maximum laser modulation frequency at approximately 50 MHz. Additionally, the large differential resistance (250 Ω) exhibited by the VCSEL (much larger than that for DFB diode lasers [17]) introduced an impedance mismatch for the RF input, which in turn reduced the RF current transfer efficiency to approximately 20%. Analogous measurements by employing an RF synthesizer to sinusoidally modulate the laser injection current at discrete frequencies corroborated these findings. The results are shown in the amplitude spectrum in Fig. 2 (right axis, data markers). The current amplitude of the single frequency modulation (SFM) was chosen to reflect the total rms current delivered by the RFN source in the range 1–30 MHz.
Fig. 2 Amplitude spectral density of the RFN root-mean-square current (left axis, lines), and amplitude spectrum of the root-mean-square current output by the single frequency modulation (SFM) source (right axis, markers). The data series represent the current coupled into the bias-T (red), and flowing through the biased (black) and unbiased (blue) laser diode.
The effects of perturbing the laser current on the transmission of a non-resonant cavity were investigated by recording the off-axis CEAS spectrum of atmospheric O2 (ptot = 751 Torr, T = 295 K) under three different regimes of perturbation. These effects were quantified by the measured spectral SNR, defined as the ratio of the CEAS signal amplitude to the standard deviation (1σ) of the noise present on the absorption-free portion of the spectrum. The signals output by the spectrometer were analysed by making use of the following equation [1–3]
where I and I0 are is the transmitted intensity signals in the presence and absence of the absorber exhibiting a frequency-dependent absorption coefficient α. The 1/(1 − R) ≃ F/π factor encapsulates the effective increase in the pathlength introduced by the non-resonant cavity of physical length L, with F and R representing the cavity finesse and the geometric mean of the mirror reflectivities, respectively.Examples of experimental cavity enhanced absorption spectra are shown is Fig. 3 (grey markers) along with the Voigt profiles returned by a non-linear regression algorithm (red lines). Each spectrum is the result of averaging and processing, according to Eq. (1), two consecutive cavity transmission signals in order to return an O2 concentration value every 10 ms, in accordance with the sampling requirements imposed by the application. The frequency range swept by the laser was calibrated by making use of an optical spectrum analyzer with a nominal free spectral range of 7.5 GHz.
Fig. 3 Cavity enhanced absorption spectra of atmospheric oxygen (ptot = 751 Torr, T = 295 K) in the absence of any laser current perturbation (left), and when RF noise (centre) or a 2 MHz modulation (right) are superimposed on the current ramp. The best fitting Voigt profiles (red) are shown along with the experimental data points (markers). The insets show the power modulation invoked by the two current perturbation regimes.
The CEAS spectrum returned by a partially off-axis cavity configuration in the absence of any current perturbation (left) was noticeably affected by cavity mode noise. The addition of wideband, current noise (1–30 MHz, irms = 55 μA, as measured from integrating the red curve in Fig. 2 between 1 and 30 MHz) played a major role in suppressing residual cavity resonance (centre), as the spectral SNR clearly benefits from the random frequency perturbations of the laser light injected into the optical cavity. This effect was accompanied by a moderate (∼ 8%) increase in the full-width half-maximum (FWHM) of the O2 absorption profile (3.49 ± 0.03 GHz). For comparison, a less efficient suppression of the residual mode structure was accomplished when modulating the laser current at a single frequency of 2 MHz, for the same total RF power injected into the laser (right). A 6 dB increase in the amplitude of the current modulation (Arms = 105 μA) returned a gain in the SNR comparable to the RFN strategy, but at the cost of a much larger broadening of the absorption spectrum (FWHM = 4.07 ± 0.05 GHz).
In parallel, the laser power modulation resulting from these two current perturbation regimes was estimated by redirecting the laser light onto a high-speed Si photodiode (5 ns rise-time, 0.52 A/W responsivity), and using the RF spectrum analyzer to measure the photocurrent spectral density. The results are reported in the insets of Fig. 3. As expected, a single frequency component around 2 MHz was exhibited by the SFM approach, with rms amplitude of approximately 130 nW (∼ 0.7 % of the DC laser output power). Conversely, the RFN source appeared to introduce random perturbation of the optical power around a mean level of 0.06 nW. This frequency dependence mirrors the trend in the net noise current experienced by the laser over the 1–30 MHz range (see Fig. 2).
The extent to which the RF noise current suppresses intra-cavity power build-up was also evaluated for various degrees of off-axis alignment. Figure 4 presents the CEAS spectra recorded in absence (left) and presence (right) of the RF current perturbation, with the off-axis distance (defined as the distance between the input beam axis and the cavity axis) increasing from top to bottom. For an almost on-axis alignment (top, left), despite the absorption profile being hidden within the pronounced mode structure, a remarkable twentyfold improvement in the SNR was observed when the noise source was switched on (1–30 MHz, Arms = 55 μA). As the off-axis distance was increased a greater mode density was achieved [18], and a smaller gain in the SNR was brought by the noise injection. The highest sensitivity was achieved for an optimized off-axis geometry in the presence of RF current perturbation (bottom, right), at the modest price of a slightly broadened absorption spectrum.
Fig. 4 Cavity enhanced absorption spectra of atmospheric oxygen (ptot = 751 Torr, T = 295 K) for increasing off-axis distances (from top to bottom), in the absence (left) and presence (right) of the RFN current perturbation.
The improvement in the CEAS performance was correlated to the increase in the diode laser linewidth by measuring the change in the width of the oxygen absorption spectrum returned by a low-pressure sample of air (ptot = 15 Torr, T = 295 K). The physical length of the cavity was extended to 36 cm to compensate for the reduction in the absorption coefficient. The laser ramp frequency was reduced to 10 Hz while keeping the detector bandwidth at 10 kHz, in order to ensure a comparatively high spectral resolution limited by the photodiode response time. Under experimental conditions of weak, pressure-induced broadening, a more accurate assessment of the change in the spectral components of the VCSEL linewidth over a range of RF noise regimes was possible. The bar plot in Fig. 5 summarizes the Gaussian and Lorentzian contributions to the laser line shape, which were calculated by subtracting the contributions to the FWHM of the absorption spectrum [19] associated with the O2 transition from the values returned by the non-linear regression of a Voigt profile to the experimental data. In the absence of any perturbation (A), Gaussian and Lorentzian contributions with similar magnitude give a total VCSEL linewidth of approximately 140 MHz, which agrees well with the typical value reported by the manufacturer (∼ 100 MHz). Injection of current noise with components in the high RF domain (1–1500 MHz) is accompanied by an increase in the Gaussian component only (B–C), the magnitude of which appears to follow the increase in the total RF power from configuration B to C (with C being 13 dB above B). No spectral broadening was observed when high-pass filtering (250 MHz cut-off frequency) the RFN output (D), confirming the conclusions drawn from the spectral density plots in Fig. 2, where no current noise with frequency component above ∼ 100 MHz appeared to perturb the laser diode. The addition of a 30 MHz, low-pass filter to configuration C led to no appreciable reduction in the magnitude of the Gaussian broadening of the laser linewidth (E). These results are in good agreement with previous studies on the lineshape of VCSELs, according to which the Gaussian contribution to the lineshape arises from efficient translation of carrier density fluctuations into 1/ f frequency noise, due to their high current-tuning coefficient of the optical frequency [20, 21]. Conversely, the Lorentzian component appeared to be invariant under the presence of external current perturbation.
Fig. 5 Bar plot of the Gaussian (ΔνG) and Lorentzian (ΔνL) contributions to the VCSEL linewidth measured for a range of RFN perturbation regimes (top). A, no perturbation; B, 200 μA over 1–1500 MHz; C, 900 μA over 1–1500 MHz; D, 900 μA over 250–1500 MHz; E, 900 μA over 1–30 MHz. The Allan deviation plots of oxygen concentration for regime A (red) and E (green) are shown for comparison (bottom).
In view of these observations, the gain in the spectrometer sensitivity brought by each perturbation regime was analyzed in terms of the Allan variance by performing concentration measurements of atmospheric oxygen over a 5 s period at a frequency of 100 Hz. The nature of CEAS requires the path enhancement factor resulting from the cavity be known. This was measured using air as a calibration sample, which has a known (humidity adjusted) oxygen content. Finally, the molecular concentration was determined from the area of the Voigt profile returned by a non-linear regression analysis. The Allan deviation plots of the molecular concentration, expressed in part-per-million (ppm), for the RF noise regimes A and E are reported in Fig. 5 (bottom). It is worth noting that the two plots exhibit very similar trends, but the selective noise-induced perturbation results in an approximately fourfold improvement in the limit of detection (LOD, SNR = 1), which reduces the Allan deviation from a 3400 ppm noise-equivalent O2 concentration to approximately 810 ppm at 10 ms averaging (SNR = 258). The LOD appeared to improve by a further factor of ten when extending the integration time to 1 s, which indicates that within this time scale the performance of the O2 sensor is governed by white noise. Expressing the sensitivity of the spectrometer in terms of the minimum detectable absorption (MDA) normalized to the effective measurement bandwidth (taken as the reciprocal of the product of the acquisition period and the number of scans averaged, 1/(nTscan) = 1 Hz for n = 200 and Tscan = 5 ms) [7], this leads to a measured value as low as 4.3 × 10−5 Hz−1/2, which corresponds to a noise equivalent absorption sensitivity (NEAS) scaled to pathlength and given as a per bandwidth value of 6.7 × 10−8 cm−1 Hz−1/2.
3. Conclusion
This study demonstrates a novel, practical addition to the design of cavity enhanced absorption spectrometers which aims to improve the instrumental sensitivity by promoting the non-resonant properties of the cavity. Traditionally, this is sought by periodically modulating the laser current at a discrete frequency, although this scheme only partially succeeds in the suppressing residual mode structure, owing to the coherent nature of the interaction between frequency-amplitude modulated light and the cavity transmission function. Practically, this manifests as residual, wavelength-dependent, intensity fluctuations in the transmitted signal which are known to limit the instrumental performance.
Conversely, the bandwidth-limited, radio-frequency, white noise source perturbs the laser drive current with a packet of frequency components exhibiting random, and time-varying phase relationships. This has the net effect of greatly reducing the coherence length of the laser, and thus more efficiently disrupting intra-cavity power build-up. Additionally, this strategy has shown to allow a relaxation of cavity alignment tolerances, simplifying design, assembly and stability of a measurement system. For the case of the VCSEL-based spectrometer presented here, this contributed to a fourfold improvement in the detection limit, paving the way to the use of the in-line oxygen sensor for respiratory medicine studies.
Acknowledgments
The research was funded by the National Institute for Health Research (NIHR) Oxford Biomedical Research Centre Programme. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health. Special thanks to Philip Hurst for the invaluable help on the electronics.
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