Differential laser absorption spectroscopy (DLAS) has been researched for decades as a means for accurate quantification of gas species in situ [1,2]. In particular, DLAS-based environmental gas sensing is increasingly applied for monitoring changes in atmospheric gas composition [3–6], particularly the increase in concentration of greenhouse gases that contributes to global warming.

Several sophisticated laser-based gas sensing instruments have been developed in recent decades, such as tunable diode laser spectroscopy, wavelength modulation spectroscopy [7,8], and cavity ringdown spectroscopy [9]. These techniques have all shown excellent performance under different conditions and for different purposes. However, system complexity has also increased correspondingly, due to advanced modulation schemes of the light source and the need for extensive postprocessing of measured signals. This imposes strict demands on the electronics and impacts the data acquisition rate as well as algorithm robustness, e.g., for rapidly varying signal strengths. Further, a fast update rate is pivotal for in situ measurements in the atmosphere or in industrial settings where unwanted air turbulence or mechanical vibrations may interfere with the measured signals.

In this study, we investigate a simple wavelength-toggled DLAS design using measurements at only two operating wavelengths of a diode laser to deduce the gas concentration. Using the Beer–Lambert absorption law, a transmission measurement at ON resonance and OFF resonance of the gas absorption line will ideally suffice to calculate the integrated gas concentration along the laser path in a calibration-free manner. The simplicity of data processing is a main feature that supports a fast update rate and provides robustness in data processing. However, the inherent thermal time constants of typical diode lasers limit the laser’s toggling rate to the ON and OFF wavelengths to typically 10–100 Hz. When excellent wavelength precision is needed, as for DLAS, this becomes a major obstacle for fast sensing as addressed in this work. Basic thermal properties of telecom diode laser tuning have been investigated intensively [10–12] as well as for quantum cascade lasers (QCLs) [13].

In Refs. [14,15], it was shown that, by either modifying the square-wave current pulse shape or exploiting an abrupt diode laser mode hop, respectively, the slow, thermally limited wavelength response of a diode laser could be overcome to increase the toggling rate between two wavelengths. One wavelength is closer to and the other is far from the phase-matched fundamental wavelength of a second-harmonic (SH) generation crystal, thus providing a means to generate SH pulses with power modulation depths above 90%. Reference [14] hinted at the use of a tailored current waveform to compensate for the wavelength chirp throughout an individual pulse; however, the achieved toggling rate is only up to 50 Hz for a small wavelength step of 37 pm. In Ref. [15], the first wavelength is set at the phase-matched wavelength, while the second was separated by 120 pm to match the first zero of the phase-match curve. By using a pure square-wave current pulse and modulating around a mode-hop operating region of the diode laser, a 10 kHz (square) intensity modulated SH light source was realized. However, both presented results of Refs. [14,15] are by far too noisy, have been optimized for power stability instead of wavelength stability, and lack a theoretical framework to hint at its applicability for sensitive gas sensing, i.e., the focus of this work.

We demonstrate and characterize a diode laser system using modified square-wave current pulses that can toggle reliably and precisely between two wavelengths separated by 90 pm at 8 kHz, supporting sensitive DLAS measurements. The diode laser operated mode-hop free at all times. A peak-to-peak chirp as low as 0.6 pm was obtained during one toggling cycle. Adding a novel wavelength locking scheme, we demonstrate 1.4 pm peak-to-peak wavelength toggling precision at 8 kHz rate over 20 h. The wavelength-toggled light source is coupled to an all-fiber setup, measuring the volumetric ratio (VMR) of HCN gas (H13C14N isotopologue) concealed in a fiber-coupled gas cell. By averaging the 8 kHz VMR measurements every 25 ms, the drift of the DLAS system is shown to be smaller than 0.2% peak-to-peak over a full 20 h campaign at 40 Hz update rate. Using square-wave current pulses, by contrast, would have limited the toggling rate to approximately ∼10Hz only. A best sensitivity of 8×10−6 at 25 ms in measured HCN gas VMR is achieved based on the Allan deviation analysis. These results match the sensitivity of relatively more complex state-of-the-art alternatives [16,17]. We cover design considerations as well as an experimental verification of the system performance.

We anticipate that the proposed modified square-wave current pulse approach is beneficial for several applications, including DLAS as demonstrated here (closed-path), injection seeding of OPOs [4,5], stand-off gas detection (open-path) [5], and wavelength modulation based beam steering [18,19].

In simple terms, the current modulation induces a temperature change of the waveguide, which in turn changes the refractive index and the length of the diode laser cavity, thus varying the center wavelength of the laser. Hereby, wavelength tuning can be obtained. In practice, the wavelength response as a function of modulation current is associated with several time constants reflecting the heat dissipating characteristics of the chip itself (10 to 100 ns scale), submount (10 μs), and heat sink (100 μs to few ms), respectively [10–13]. In our study, the laser driver itself has a small signal 3 dB bandwidth of 150 kHz limiting the response (i.e., rise and fall) time.

When our diode laser is driven by a small current step, it was experimentally observed that it takes at least 27 ms to reach 99% of the maximal wavelength change of 3.2 pm. Hence, for our target wavelength change of 90 pm, which requires a larger current step, it takes at least 27 ms for the laser wavelength to be within 1 pm deviation from its final value. This is characteristic of a thermal time constant of the diode laser in the order of a few ms, which severely limits the toggling frequency between two fixed wavelengths with a given precision. Two shorter time constants of our diode laser, τb=3μs and τc=22μs, were also experimentally measured. In this study, we aim for a toggling transition time in the 14 μs range and with a full toggling period of τp=128μs corresponding to an 8 kHz update rate with 75% duty cycle. On a 10 μs scale, the longer (ms level) time constant is, for simplicity, excluded in the model since its influence is negligible due to the fast toggling. The objective in the following is to generate a precompensated current pulse iC(t) using the sum of a step function and an exponential decay function that, by a suitable amplitude ratio p (i.e., ratio of the amplitude of the exponential term to the peak-to-peak amplitude of the step function) and time constant τm, minimize the toggling transition time by compensating the thermal time constants, τb and τc. Our approach is based on determining the system impulse response h(t) from the measured output wavelength change in response to an input step current. Assuming linearity and time-invariance properties of the system, the wavelength change y(t) is given by the convolution of h(t) with the input current function i(t), y(t)=h(t)⊗i(t),(1)where ⊗ represents the convolution operation. For a unit step current function iSTEP(t), the measured output wavelength-change ySTEP(t) is modeled as ySTEP(t)=h(t)⊗iSTEP(t)=a+b·e−tτb+c·e−tτc,(2)where a=−(b+c) to ensure a value of ySTEP=0 at t=0. ySTEP(t) is approximated by the sum of a constant and two exponential functions, as described in Eq. (2). The values of b and c and time constants τb and τc are derived by a least-squares fit to an experimental data.

In the following, we assume that the time constants are much shorter than the toggling period, τp, i.e., τp/2≫τm, τb, τc. This approximation allows us to consider each ON/OFF section of the current toggling pulse separately, leading to a simple analytical solution. In the presented system, τp=128μs, while τm, τb, τc≤22μs. Using the Laplace transformation of Eq. (2) and the assumption that iSTEP(t) is an ideal unit step function, the transfer function H(s), which is the Laplace transform of h(t), can then be expressed as H(s)=sYSTEP(s).(3)

Instead of applying an ideal step input to the system, we apply the precompensated current iC(t)=iSTEP(t)+p·exp(−t/τm), so the output YC(s) is given by YC(s)=H(s)(1s+p1s+1τm)=(1+p)YSTEP(s)−p(1τms+1τm)YSTEP(s).(4)

After insertion of YSTEP(s) in the second term of the right-hand side of Eq. (4) and explicit calculation, $$\begin{gathered} YC(s)=(1+p)YSTEP(s)+p[−a(1s−1s+1τm)+bτbτm−τb(1s+1τb−1s+1τm) \\ +cτcτm−τc(1s+1τc−1s+1τm)]. \end{gathered}$$(5)

The inverse Laplace transform of Eq. (5) yields a corresponding system response to the precompensated current as $$\begin{gathered} yC(t)=(1+p)ySTEP(t)+p[−a(iSTEP(t)−e−tτm)+bτbτm−τb(e−tτb−e−tτm) \\ +cτcτm−τc(e−tτc−e−tτm)]. \end{gathered}$$(6)

In summary, b, c, τb, and τc are experimentally found from the step response, while p and τm are determined by optimizing for a fast toggling response.

The setup is based on low-cost telecom fiber-optic components using polarization-maintaining (PM) fibers, as shown in Fig. 1. A fiber-coupled 1550 nm laser diode (from Eblana Photonics) is used as the light source. The laser has a linewidth of 100 kHz [20] and provides approximately 5 mW of stable output power. The laser is connected to a linear polarizer to eliminate any polarization crosstalk in the first section. A 50:50 fiber coupler divides the beam into a reference beam used to measure the actual output power at all times and a measurement beam to probe the wavelength selective element. Here, we include a fiber-coupled gas cell containing HCN gas to demonstrate closed-path gas sensing based on the Beer–Lambert law, PT=βP0e−αgas(λ)l,(7)where P0 is the incident power in the measurement arm, and PT is the transmitted power through the gas cell detected by the signal detector. αgas(λ) is the wavelength-dependent (and temperature-dependent) absorption coefficient of the gas in the path, l is the length of the gas cell, and β accounts for all coupling and insertion losses in the measurement arm. The fiber-coupled gas cell contains HCN (specifically, the H13C14N isotopologue) in nominally 100% volumetric concentration – a VMR of 1. For simplicity in simulation, we have assumed a fixed FWHM of 19.1 pm using a Lorentzian spectral profile, matching the FWHM of the absorption feature obtained from HITRAN database when using the gas cell manufacturer-specified VMR of 1, path length of 16.5 cm, pressure of 33.33 mbar, and temperature of 25°C. Thus, αgas(λ) has been assumed to follow a Lorentzian profile for our chosen HCN absorption line (λON=1549.73nm). Since the diode laser current is varied to change the wavelength, optical power also changes accordingly when toggling between the two wavelengths; hence, the reference detector (see Fig. 1) can be used to normalize the power at all times.

We assume that the two detectors in Fig. 1 are linear, i.e., having an optical power response of the form U(P)=BP+A, where U is the detector voltage, P is the incident power on the detector, B is the responsivity, and A is any (unwanted) offset of the detector and the associated amplifier. Using the ratio of an ON transmission measurement (TON) and an OFF measurement (TOFF), the gas VMR can be estimated by first taking the ratio TONTOFF=(UONgas−Agas)(UOFFref−Aref)(UONref−Aref)(UOFFgas−Agas)=e−[αgas(λON)−αgas(λOFF)]l,(8)where αgas(λON)l is the absorbance of the gas at λON and, likewise, αgas(λOFF)l at λOFF. UONgas is the measured detector voltage of gas detector when at ON resonance, i.e., the laser wavelength tuned to the central wavelength of a gas line and Agas is its detector offset (if any). UONref is correspondingly the ON reference detector voltage and Aref its offset. The same nomenclature is used for the OFF measurement. It is worth mentioning that the detector responsivities are divided out in the ratio TON/TOFF; thus, two detectors of identical responsivities are not required. This provides a high detector insensitivity, in part the explanation for the high gas sensitivity reported later. The setup includes a current feedback loop for the laser diode, which can be programmed to compensate for drifts (see Section 4.C).

From αgas(λON)−αgas(λOFF) obtained in Eq. (8), the actual gas VMR can then be derived using −1lln(TONTOFF)=qPgS(Tg)kBTg[g(λON)−g(λOFF)],(9)where q is the VMR, Pg is the gas pressure, Tg is the gas temperature, kB is the Boltzmann constant, S(Tg) is the temperature-dependent line intensity, and g(λ) is the spectral line shape.

In order to determine the wavelength response of the system, the laser wavelength was first tuned to be at approximately the half-width-at-half-maximum point of the gas line (negative transmittance) profile, so that a linear wavelength-to-transmittance response of the gas cell could be assumed for small current perturbations. The approximate wavelength step response is estimated at different toggling frequencies by applying a square drive current pulse and using one-half of the pulse to estimate the time constants.

With the objective of toggling swiftly and precisely between two wavelengths 90 pm apart, corresponding to ON and OFF wavelengths of the chosen HCN gas absorption line, the diode laser square current pulse was modified by adding to it an exponentially decaying current pulse. This choice was motivated by (i) current tuning of the wavelength being much faster than from the passive dissipation of heat to or from a heat sink, responsible for the long settling time, (ii) the exponential shape is heuristically chosen from the observed double exponential decay of the step response function; as shown in Figs. 2(b), and (iii) an exponential term is straightforward to produce. Experimentally, it was found that an exponential time constant, τm, of 18.75 μs and a relative amplitude (to the square current pulse peak-to-peak amplitude), p, of 0.30 were optimal for fastest stabilization of the wavelength during toggling. This was confirmed by the theoretical model in detail using the exact same parameters, except for (i) the value of p, which in the model is found to be optimal at p=0.275, (ii) a small 0.4 pm offset of the scan with respect to the gas line, equivalent to a small DC current of 130 μA, for the modified pulse, and (iii) a 2.5 pm offset of the scan with respect to the gas line, equivalent to a DC current of 0.8 mA, for the square pulse. The small differences are associated with the approximations used and the fact that the present model does not include the effects due to 150 kHz bandwidth of the laser driver (see Section 2).

Figure 3(a) shows the input square current pulse and its precompensated version with the added exponential decay term. Figure 3(b) shows the measured transmittance of the gas cell (including coupling and insertion losses) as a function of DC current together with a comparison to the HITRAN simulation. The FWHM of the gas line is 19.1 pm. Figure 3(c) shows the transmittance with the square and the modified current pulse when transitioning from the desired OFF wavelength to the ON wavelength 90 pm away. As can be clearly seen, when applying the modified current pulse, the wavelength stabilizes to the desired level in just 14 μs. When using a square current pulse, the wavelength of the diode laser never reaches the minimum transmittance, i.e., does not reach the desired ON wavelength in the allotted 64 μs ON duration. Figure 3(d) shows the toggling transmittance for one full cycle of the current pulse. From Figs. 3(c) and 3(d), it is clearly seen that the model shows close agreement with the experimental results.

Figure 4 shows a full period and zoomed-in views of the toggling process. Due to a limited sampling rate (250 kSamples/s) of our present analog-to-digital converter (ADC), a full cycle consists of only 32 data points, as shown in Fig. 4(a). Nevertheless, 75% of the transmittance data points are within 4×10−4 of the steady-state value, as shown in Figs. 4(b) and 4(c). The solid black curve represents a single data series obtained at 8 kHz toggling rate, while the dashed curve represents a 40 Hz average included for comparison. The theoretical model in solid yellow line confirms satisfactorily the same degree of variation in transmittance data values, as shown by the right-hand scale. Note that, in Fig. 4(b), the slopes of the experimental and theoretical curves appear to have opposite signs when observed on a zoomed-in transmittance scale. This merely reflects that the wavelength is dynamically reaching the steady-state wavelength, thus transmission, from opposite directions.

The use of the modified current pulse demonstrates an improved update rate of the DLAS system by ∼3 orders of magnitude over a similar system with a simple square current pulse. The exponential decay term p·exp(−t/τm) of the modified current pulse compensates for the thermal time constants, τb=3μs and τc=22μs, which allows for a toggling rate of 8 kHz.

To keep the laser locked at the ON resonance wavelength for extended measurement period, e.g., tens of hours, an active current control system was implemented. The control loop is based on the average slope calculated from the individual transmittance data during the ON portion of the pulse comprising the 20–64 μs section of Fig. 4(a) [or Fig. 4(c)] to avoid the transient period during the 14 μs transition. The wavelength locking criterion (set point) implemented by the feedback control loop was defined as the zero slope in the ON transmittance, and the control loop ran at 260 Hz update rate, correcting for any change in the ON transmittance slope by adjusting the laser DC current. The feedback loop comprises a proportional term and an integral term. The ON transmittance in Fig. 4(c) shows an instance where the wavelength is locked, corresponding to zero ON transmittance slope. From the peak-to-peak change in transmittance (of 4×10−4), the chirp in the wavelength during the ON cycle can be estimated in Fig. 4(c) to be 0.64 pm at 8 kHz rate. Figure 5 shows the measured and theoretical ON transmittance slope as the laser DC current is minutely changed. The wavelength locked case of zero ON transmittance slope in the yellow shaded region occurs approximately at a bias current of Imean=225.0mA in Fig. 5(a). When the laser wavelength drifts to either side of the ON resonance wavelength position, the slope also changes. If the laser wavelength reached is shorter than the desired value, as simulated by adding a small negative bias current, the average slopes of the ON period are positive, as shown for Imean=224.8mA and Imean=224.6mA, respectively, in Fig. 5(a). The average slopes become negative for the case when the laser wavelength reached exceeds the target ON resonance wavelength, as shown for Imean=225.2mA and Imean=225.4mA, respectively, in Fig. 5(a). Figure 5(b) shows the corresponding curves based on our theoretical model. The model predicts almost identical variation of the absolute transmittance, and qualitatively the same dynamic features, especially the sign of the slope, which is important for the wavelength control loop. We attribute some slight differences to be associated with the approximations in the model (see Section 2).

The error signal based on the slope is extraordinarily sensitive to drift. A 100 μA DC current change corresponds to a mere 300 fm shift of the center wavelength, which is easily detected by the proposed feedback loop. Figure 6 shows the experimentally measured (average) slope for the five DC current settings used in Fig. 5. The standard deviation error bar for the slope (horizontal black lines) at each current shows the high sensitivity of slope to change in current.

The system performance was tested during 20 h of operation using the control loop operating at 260 Hz. In the actual long-term measurement campaign, we used 12 out of 16 data points [shown by the section from 20 to 64 μs in Fig. 4(a)] to calculate the average slope. The measured absorbance of HCN in the gas cell is converted to VMR using Eq. (9), accounting for the temperature-dependent change in the line intensity S(Tg) from HITRAN. Figure 7 summarizes the results of the 20 h test. Due to the excessive amount of data over 20 h, the data were low-pass filtered and stored only at 40 Hz, even though the toggling rate during the experiment was 8 kHz. Since the reference gas cell contains pure HCN gas (VMR of 1), we associate any deviation with drift or noise in the system. Since the setup was not temperature-stabilized, we also measured the correlation of the measured gas concentration with ambient temperature (blue curve), as shown in Fig. 7(a). This sinusoidal-like correlation is likely a result of temperature-dependent fringing effects in the system. Figure 7(b) shows the derived VMR at 40 Hz as a function of time (blue curve). Removing the sinusoidal temperature dependency, using the fit from Fig. 7(a), the red curve is obtained. At 40 Hz update rate, the variation in concentration over the total 20 h was <0.2% peak-to-peak with only a minor reduction in drift due to temperature correction, thus showcasing the excellent performance of the sensor system. From the peak-to-peak change in slope at 8 kHz monitored over 20 h, the corresponding peak-to-peak fluctuation in wavelength is estimated to be within 1.4 pm.

Figure 7(c) shows the Allan deviation based on the VMR time-series data in red in Fig. 7(b). As can be observed, at an averaging time τ=1s, the sensitivity in VMR is 4.2×10−5, and the system achieves the best VMR sensitivity of 8×10−6 at τ=25ms. Unlike a typical Allan deviation curve that decreases initially due to white noise averaging, Fig. 7(c) shows an increasing trend, likely due to excess noise from the wavelength-stabilizing feedback loop. The feedback loop updates every 4 ms (260 Hz), while measurements were done at 25 ms (40 Hz). Faster measurements would likely reveal the usual white noise-dominated region in the curve. Remarkably, the reported sensitivity of our instrument is still at par with that of more sophisticated and complex implementations [16,17].

A detailed analysis of a mode-hop free, ON/OFF toggling of a 1550 nm diode laser-based DLAS system operating at 8 kHz toggling rate is presented. Thermal time constants in the wavelength step response of the diode laser source prevent fast toggling between two 90 pm spaced ON and OFF wavelengths. However, adding an exponentially decaying current component with an amplitude of ∼30% of the applied square current pulse peak-to-peak amplitude and, with an 18.75 μs time constant, allows for the wavelength to be toggled between two values 90 pm apart with a transition time of only 14 μs, meeting a criterion of being within ∼1pm of the steady-state target wavelength values. Thus, 75% useful data are available for concentration calculations at 8 kHz. A theoretical model supports the experimental data in detail. A sensitive feedback loop was implemented that allowed for precise locking to one of the operating wavelengths at the center of an absorption line of HCN gas over 20 h at 8 kHz toggling rate with less than 1.4 pm peak-to-peak fluctuation in wavelength. The peak-to-peak variation in the measured VMR (averaged to 40 Hz) of the reference HCN gas over 20 h was less than 0.2% for any time interval.

The presented DLAS system benefits from simple postprocessing of data, as the gas concentration is extracted from ratioed ON/OFF data and Beer–Lambert absorption law. This, combined with a high raw update rate of 8 kHz, will make the system useful for gas measurements in rapidly fluctuating environments, such as those found in the atmosphere or industrial settings. The authors have recently demonstrated open-path atmospheric gas sensing using similar laser diodes [21]. To adopt a wavelength toggling approach to such open-path systems, the ON/OFF wavelength range needed is comparable (or about a factor of 2) to what we have reported here (90 pm). Such a wavelength toggling range can be easily achieved by recalculating the precompensated current pulse based on the framework described in Section 2 and Section 4.A. The proposed method of precompensation of the laser modulation current can be adapted for other applications such as seeding of OPOs or pulsed lasers to generate precise and stable wavelength-spaced pulses.