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Abstract
In this work, a method of photothermal spectroscopic signal extraction is presented. The refractive index modulation readout is realized in a purely frequency detection-based approach, by demodulating the beatnotes of a mode-locked fiber laser operating at 1.56 µm. A unique and non-complex self-heterodyne harmonic amplification technique is employed, yielding an increase in the limit of detection by a factor of 22. The sensor’s performance was evaluated by detecting nitric oxide at 5.26 µm, confirming the feasibility of separating the pump and probe sections of the device. The sensor reached a detection limit of 9.6 parts-per-billion by volume for an integration time of 136 s, with only a 20 cm-long laser-gas molecules interaction path length.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Precise analysis of gas composition and concentration is crucial for various applications, e.g., in chemistry, production, environmental protection, and human safety [1]. To address this problem, numerous techniques allowing precise and selective gas analysis have been developed, and this area of research is continuously attracting attention among researchers worldwide. The laser-based gas detection methods have proven their selectiveness, excellent sensitivity, and the possibility of conducting in situ measurements. Over the years, laser spectroscopy techniques have branched-out into numerous methods [2]. In this paper, I explore the photothermal spectroscopy (PTS) technique, which has attracted considerable attention over the past decade [3].
PTS relies on probing the refractive index - n (RI) changes induced in the gas sample by an external excitation source – called the pump. Matching their absorption spectra, the pump energy is absorbed by the targeted molecules, locally heating the gas along the path-length of the propagating excitation beam. The resulting gas density change can be observed as a RI modulation. The modulation effect is intrinsically small (Δn∼10−7), thus clever methods for probing this parameter of the gas sample had to be developed, usually relying on an optical readout with an auxiliary laser – called the probe. The unique feature of the PTS detection technique allows for noncomplex separation of the pump and probe sections of the sensor, thus each can be optimized for the particular task, e.g., by choosing mid-infrared (mid-IR) sources as the pump lasers, while the RI modulation probe is realized based on the inexpensive and well-developed near-infrared (near-IR) technology. This enabled the development of numerous interesting gas sensors that depend on the PTS effect, with detectivities consistently outperforming ‘classical’ techniques [4].
Although the PTS-aided sensors have been shown to provide good gas sensing capability, this approach is not free from several drawbacks, which limit the ultimate performance of such detectors. The main limitations of this technique include the tight pump-probe beam overlap requirements and the purely amplitude-based spectroscopic signal readout, which is used in most of the developed varieties of the PTS sensors [5–9]. The problem of optimizing the pump-probe overlap has been recently mitigated with the incorporation of hollow-core fibers (HCF). Appropriately designed HCFs promote low-loss transmission of the laser beams required to conduct PTS measurements and simultaneously acts as a low-volume gas cell. This approach to PTS has been experimentally verified in several configurations, yielding astonishingly good results [4,6–13]. Although HCFs emerged as an adequate solution for PTS gas sensing, several significant problems still await a solution. There are a limited number of commercially available HCFs suitable for this unique task, most of them having low-loss transmission bands in the 2 µm wavelength region, which is lacking the strong ro-vibrational molecule transitions found in the mid-IR. Furthermore, the small core sizes of the HCFs presuppose additional coupling optics and inferior filling times compared to bulk multipass cells [14]. Additionally, great care has to be taken when developing HCF-based gas sensors, as multimode transmission of the laser beam in the waveguide usually leads to high background noise, limiting the overall detectivity of the sensor.
Although several dissimilar PTS gas sensor configurations have been proposed, the majority relies on an amplitude-based interferometric readout of the signal. This requires employing clever signal processing techniques enabling proper long-term compensation, or adding complexity to the sensor configuration, which originates from an unavoidable necessity of employing advanced stabilization techniques of, i.e., emission of the used lasers or the interferometer cavity. In [15], a sensor using a Fabry-Perot (FP) signal readout was proposed. The steep transmission characteristic of the cavity was utilized to probe the PT-induced shift in the RI of the gas. However, monitoring the amplitude of the beam exiting the cavity poses several limitations, which were minimized in the improved, biased version of the sensors [16].
The FP-based RI modulation readout was also combined with an antiresonant hollow-core fiber- based gas cell in [9]. The custom-developed fiber allowed detecting a gas with strong mid-IR transitions, while the RI probing was realized using standard, near-IR telecom fiber components. This simple configuration reached a detection limit of 11 ppbv for 144 s integration time, which is currently state-of-the-art for fiber-based PTS sensors capable of detecting gases with mid-IR absorption spectra. However, the limitations of purely amplitude-based signal readout are still affecting the performance of such sensors.
The problem with amplitude-related signal errors has always baffled researchers working on gas detection systems, motivating experimental work on non-standard approaches to signal processing. One of the solutions relies on the encoding of the spectroscopic signal into the frequency deviation. This method has been successfully employed with sensors probing the gas dispersion, e.g., Chirped Laser Dispersion Spectroscopy (CLaDS) [17]. In CLaDS, the demodulated frequency shift is directly proportional to the gas concentration and the registered spectroscopic signal is inherently baseline-free, significantly simplifying the data processing and calibration [18]. Moreover, by encoding the gas concentration as frequency deviation, the sensor is highly resistant to drifts of the signal amplitude coupled to the detector.
The attempts to encode PT-induced RI modulation to frequency deviation were documented in [11,19]. Although the proposed configurations reached significant detection limits, the probe part of the sensors required using a polarization-maintaining fiber-pigtailed frequency shifters, which are expensive and require stable RF signal generators with significant power outputs (∼20 dB) to operate, which add complexity.
In this paper, I further explore the possibility of encoding the PT-induced spectroscopic signal into frequency and propose an improved version of our previous design [20]. Here, I propose and study a novel, non-complex method of extracting the induced RI modulation using a new technique called self-heterodyne harmonic amplification (SHHA). This approach to PT detection takes full advantage of the unique characteristics of a mode-locked (ML) laser used as a probe. Moreover, the main limitations of the previous sensor layout were mitigated, and several changes resulting in the improvement of the sensor’s versatility have been implemented. This includes constructing the gas absorption cell using a calcium fluoride (CaF2) window with a high-reflective coating for the probe wavelength. This permitted exciting the gas particles with a mid-IR pump laser, which are commonly selected because of the abundance of gases having strong absorption profiles in this part of the optical spectrum. This emphasizes the detection versatility of the proposed sensor. I have also implemented phase (PM) demodulation algorithms, which as presented in the manuscript, perform significantly better in comparison to frequency (FM) demodulation algorithms, which were used in the previous sensor configuration. The novel SHHA spectroscopic signal extraction yielded an increase in the detection limit by a factor of 22, which renders the designed sensor as sensitive, as more complex and less versatile, HCF-based PT gas sensors [9].
2. Sensor configuration
The sensor setup is depicted in Fig. 1. The main part of the sensor consists of a non-complex ML laser working in the 1.56 µm wavelength region, serving in this sensor as the probe for the PT-induced refractive index variations. The probe laser was constructed as a classical, linear cavity ML laser in which the mode synchronization was obtained by using a commercial, off-the-shelf semiconductor saturable absorber mirror (SESAM; BATOP, SAM-1550-30-2ps). The SESAM served as one of the mirrors and was mounted onto a ferrule of a fiber connector using UV curable glue. The gain was provided by a 30 cm-long piece of erbium-doped fiber (Liekki Er80), which was optically pumped by a single-mode laser diode (λ=976 nm) via a filter-type wavelength division multiplexer (FWDM). To achieve interaction between the excited gas particles and the resonating ML laser beam, a free-space optical path had to be formed, which included a 20 cm-long gas absorption cell (GAC). The laser beam was outcoupled from a PM fiber through a gradient-index collimator, which also collected the beam reflected from the far end of the GAC. The second mirror (M2) of the linear cavity was a calcium fluoride (CaF2) window, coated for high reflection (HR) in the wavelength of ML laser emission (99% reflection at 1560 nm and >80% transmission for wavelengths between 2 µm – 8 µm). This mirror was mounted in the GAC and was sealing its far end. The near end of the GAC was sealed with a BK7 wedged window (WW), anti-reflection (AR) coated for ∼1.56 µm wavelength range, to ensure minimum losses for the resonating ML laser beam. A distance of ∼5 mm between the WW and the fiber collimator was purposely used to minimize the influence of ambient air on the measurements. The parameters of the ML probe laser were monitored via a fast photodiode (LabBuddy, DSC2-50S, 3 dB bandwidth 30 GHz) connected to the tap of a 1% fiber coupler spliced into the resonator between the SESAM and the gain fiber. The laser center emission was located at 1560 nm and the repetition frequency was ∼23.66 MHz. The configuration of the ML laser is least complex and requires minimum number of fiber- and bulk optics, even when compared to classical gas detectors relying on the use of multipass cells. All components of the probe laser were based on polarization maintaining fibers and were spliced together using an arc fusion splicer, thus self-starting of the ML operation was achieved each time by simply delivering 120 mW optical power of the 980 nm laser to the active fiber.
Fig. 1. Experimental setup. SESAM – fiber pigtailed semiconductor saturable absorber mirror, RF – RF spectrum analyzer, PD – photodiode, FC – fiber coupler with 1% out-coupling ratio, Er3+ - 30-cm-long erbium-doped fiber, FWDM – filter-type wavelength division multiplexer, COLL – fiber collimator, WW – wedged window, M2 – CaF2 HR coated window, GAC – 20 cm-long gas absorption cell, GM – gas mixer, FC – flow controller, GS - gas scrubber. QCL – mid-IR pump laser, LDTC – laser controller, GEN – signal generator.
The electric signal from the photodiode was amplified by 20 dB (Mini-Circuits, ZX60-83LN-S+) and coupled to a radio frequency (RF) spectrum analyzer (Rohde&Schwarz FSV3007), which was capable of performing digital demodulation. A custom, LabView based application was developed, which automated the signal demodulation, aggregation, and processing at a chosen frequency, which was essential for the operation of the sensor.
In PTS gas detection techniques, the gas under test has to be excited to produce the PT effect. In this experiment, nitric oxide (NO) molecules were used to determine the performance of the sensor and validate the versatility of the unique detection principle in the mid-IR wavelength range. An isolated absorption line located at 1900.09 cm-1 (∼5260 nm) was targeted by a distributed feedback (DFB) quantum cascade laser (QCL) (Thorlabs QD5500CM1) – called the pump laser. The source was capable of emitting collimated, continuous wave (CW) radiation with an output power of 100 mW when tuned to the center of the chosen NO absorption line. The QCL was controlled by a current and temperature driver (Thorlabs, ITC4002QCL), which enabled straightforward sweep of its wavelength by coupling a voltage signal to the modulation input port. This function was used to modulate the QCL wavelength with a sinusoidal signal, allowing us to use Wavelength Modulation Spectroscopy (WMS) [21] signal acquisition and processing of the demodulated signal. The pump beam was coupled into the GAC through the M2 and co-aligned with the 1.56 µm probe beam propagating inside it. The pump beam and the probe beam had a similar 1/e2 diameter of ∼1.5 mm, to ensure optimal overlap. The tested gas samples were prepared by a commercial gas mixer (Environix, 4020) and forwarded directly to the GAC. During the measurements, a constant flow of 2500 sccm was used to simulate continuous out-of-lab operation.
The proposed sensor is versatile and the unique configuration of the probe enables measuring any gas sample, at any wavelength, provided that an appropriate pump laser and beam-combining optics are used to induce the RI modulation via the PT effect.
3. Self-heterodyning harmonic amplification signal extraction principle
In this paper, I further explore the potential of using the unique characteristics of a ML laser probe to develop a new technique for performing precise and sensitive detection of gas particles - the SHHA. The cartoon presented in Fig. 2 explains the key principle of the SHHA technique, which allows for straightforward PT spectroscopic signal amplification by orders of magnitude.
Fig. 2. (a) RF spectrum of the ML probe laser showing the characteristic self-heterodyne beatnotes forming a comb-like structure. (b) Cartoon explaining the principle of self-heterodyne harmonic amplification of the PT-induced RI modulation.
ML lasers have a unique feature, which originates from the mutual beating of the longitudinal optical modes being phase-locked in their cavity. If we analyze the optical signal outcoupled from the laser using a fast photodiode and an RF spectrum analyzer, we can observe a distinct comb-like spectrum – Fig. 2(a) [22]. This spectrum is composed of thousands of beatnotes, evenly spaced and separated by the repetition frequency (frep), which is directly connected to the optical path-length of the laser resonator, according to the following equation: frep = c/2Ln, where c is the vacuum light speed, L is the length of the resonator, and n is the refractive index of the resonator. The first beatnote will be located at the frep, subsequent beatnotes will be observable at harmonics of the frep – 2·frep, 3·frep, etc. If the length or the refractive index values change in time, the result will be clearly observable as a shift in the frequency of the frep and each of the self-heterodyning harmonic beatnotes. Due to the fact, that the measured gas molecules in our sensor configuration are trapped inside the resonator of the ML laser, the PT effect inducing the RI modulation of the gas will affect the laser’s optical pathlength, hence affect the frep and, consequently, the frequency of all of the harmonics. The RI of the gas will change by Δn, according to the formula [23]:
where α is the absorption coefficient of the gas, f is the pump beam modulation frequency, Cp is the specific heat of the gas mixture; ρ is the density of the gas mixture; Pexc is the pump beam power, T0 is the absolute temperature and n is the refractive index of the gas mixture; a is the pump beam radius. The value of the change in the repetition frequency of the ML can be estimated by taking the derivative of the frep function with respect to a PT-induced change in RI: Δfrep =-(c·Δn)/(2L·n2). Furthermore, the frequency change of any harmonic of the frep can be estimated as Δf_harm = -H(c·Δn)/(2L·n2), where H is the harmonic number at which the effect is observed (see Fig. 2(b)). This clearly underlines the unique feature of the new SHHA spectroscopic signal readout - the possibility of multiplying the registered amplitude of the induced RI modulation, simply by detecting the resulting frequency shift of high-harmonic beatnotes.This effect is especially evident when the RF spectrum of different harmonics of the ML laser is observed. For the purpose of illustrating the influence of the PT-induced change in the RI in the ML resonator, 1000 ppmv of NO in nitrogen (N2) was flowing through the GAC at a rate of 2500 sccm and the wavelength of the QCL laser was modulated in the vicinity of the NO absorption line using a sinewave signal with frequency f0 = 300 Hz. The measured RF spectra are depicted in Fig. 3.
Fig. 3. RF spectra of the probe laser emission showing the characteristic modulation sidebands originating from the PT-induced RI modulation occurring inside the ML laser resonator. The center frequencies of the beatnotes are listed under each graph.
The PT-induced RI modulation of the NO gas is clearly visible as characteristic sidebands observed around the beatnotes, which indicate frequency modulation. The positions of the sidebands are correlated with the QCL sinewave modulation frequency f0= 300 Hz and the harmonics of this frequency (2·f0, 3·f0, etc.). The increase in the observable Δfrep for higher harmonics of self-heterodyne beatnotes is evident, as the amplitude of the sidebands increases with the harmonics at which the measurement was performed. This feature was the basis for the novel SHHA detection technique.
To extract the spectroscopic signal containing the information about the gas concentration, the chosen beatnote has to be demodulated and subsequently analyzed as in the traditional WMS technique. For the proof-of-concept realization of the sensor, the electric signal from the fast photodiode was coupled to the RF spectrum analyzer. This apparatus was conducting demodulation of the incoming signal at a chosen frequency. Data aggregation and processing was performed on a computer running a custom LabView application. In this version, I have constructed the LabView application to enable direct extraction of the raw PM demodulated signal at a chosen frequency. The advantage of this improved method is clearly visible when comparing the same signal demodulated using two different methods, as presented in Fig. 4, depicting 100-ms-long traces acquired using frequency (FM) and phase (PM) demodulation blocks of the RF spectrum analyzer.
Fig. 4. Signals collected by the custom LabView application containing FM- and PM-demodulated traces; (a) and (b) graphs, respectively. The fdemod was set to 23.66 MHz during this measurement. 1000 ppmv NO was flowing through the sensor.
The PM demodulated signal contains significantly less noise, which directly translates to better detectivity of the constructed sensor, compared to the previous FM-demodulation-based sensor [20]. The custom LabView application collects the data from the apparatus, calculates a fast Fourier Transform (FFT) of the demodulated signals and plots the amplitude of the 2·f0 component as a function of time (this functionality of the designed software is similar to performing detection using a standard lock-in amplifier apparatus, which registers the amplitudes at chosen harmonics of the WMS signal [24]). The demodulation frequency (fdemod) can be changed in real-time, thus any beatnote of the ML laser can be chosen in the bandwidth of the RF analyzer (up to 7.5 GHz, in case of the one used in this particular experiment).
4. Sensor optimization and nitric oxide detection
As in traditional WMS-based configurations, two crucial parameters of the sensor had to be optimized, the modulation depth and f0. For this measurement, a certified mixture of 1000 ppmv NO in N2 was flowing through the GAC at a 2500 sccm rate. The pump laser was tuned to the center of the R6.5 NO transition located at 1900.09 cm-1 (no active locking was used), and the output power was set to 100 mW. The signal was demodulated at the first harmonic of the ML laser, fdemod = 23.66 MHz. Firstly, the f0 was optimized. This was achieved by setting several values of the sinusoidal frequency and simultaneously registering the maximum amplitude of the 2f PT signal. The results of the measurements are depicted in Fig. 5.
Fig. 5. Process of optimization of the sensor parameters. (a) Maximum 2f PT signal registered as a function of the sinewave modulation of the pump laser; (b) maximum 2f PT signal registered as a function of the sinewave modulation depth. The crucial parameters of the measurements are listed in the graphs.
The amplitude of the registered PT signal is inversely proportional to f0, which is consistent with the Eq. (1), and previously published publications documenting gas sensors based on this effect [5,6,9,11,25]. This is a direct result of the finite relaxation time of the excited gas molecules [26]. A significant improvement should be observed after humidification of the gas samples, similar to what is observed in photoacoustic spectroscopy, which will be investigated in future experiments [27]. PT gas sensors that are based on interferometric or ML laser-based spectroscopic signal readout are intrinsically vulnerable to mechanical vibrations, which is the main source of noise and instabilities of the systems. Therefore, choosing the optimal f0 is always a compromise between the registered PT signal amplitude and the amount of background noise that affects the long-term operation of such detectors. In case of this sensor, the optimal signal-to-noise ratio (SNR) was obtained while using f0 = 300 Hz. The second parameter requiring optimization is the modulation depth. This parameter was optimized also using a certified mixture of 1000 ppmv NO in N2 flowing through the GAC at a rate of 2500 sccm. The pump laser was tuned to the center of the NO transition (no active locking was used), and the output power was set to 100 mW. The signal was demodulated at the first harmonic of the ML laser, fdemod = 23.66 MHz, and f0 was set to the optimized value of 300 Hz. The modulation depth was changed in steps by increasing the amplitude of the sinewave signal coupled to the modulation input of the QCL driver, while simultaneously registering the maximum amplitude of the 2f PT signal. The modulation depth was calculated in GHz using a germanium (Ge) etalon with a length of 50.8 mm, based on the method described in [11].The optimum value of the modulation depth was 6.9 GHz, similar to previous articles documenting NO detection at the considered wavelength [9,11].
With the sensor optimized for detection of NO particles, I have conducted an experiment, which verified the thesis that the unique SHHA method can yield a substantial increase of the registered PT spectroscopic signal, and thus increase the detectivity of the sensor. The measurement parameters were set to the defined, optimal values and sensors was filled with a certified mixture of 1000 ppmv NO in N2 flowing through the GAC at a rate of 2500 sccm. The LabView application controlling the RF spectrum analyzer was designed to allow on-the-fly switching of the fdemod via the SCPI protocol (Standard Commands for Programmable Instruments). The graph in Fig. 6(a) shows the amplitude of the 2f PT signal plotted as a function of the harmonic of the ML laser frep, at which the PT signal was demodulated.
Fig. 6. (a) Amplitude of the 2f PT signal plotted as a function of the harmonic of the ML laser repetition frequency, at which the PT signal was demodulated (the harmonic numbers are given in the graph). During the measurement the GAC was filled with 1000 ppmv NO in N2. Graphs (b) and (c) show the full 2f spectra of the transition doublet registered for 1000 ppmv NO in the gas cell, for the 1st and the 315th harmonic. The blue trace shows the background noise registered for pure N2 in the GAC (magnified 10x for clarity reasons).
The performed experiment clearly shows an increase of the registered PT signal amplitude with respect to the harmonic on the ML laser beatnote, at which the demodulation is executed. The increase in the amplitude is consistent with the predicted value described by the equations in Section 3, and at the 315th harmonic, the registered PT signal had an amplitude 315 times higher, compared to the signal demodulated at the 1st harmonic. Graphs in Figs. 6(b) and 6(c) show the full 2f spectra, which were taken by sweeping the wavelength of the pump laser across the NO doublet. This was accomplished by combining the 300 Hz sinusoidal modulation signal with a triangular-shaped signal with a period of 60 s. Data points during the measurement were taken with a resolution of 10 Hz.
The obvious advantage of using the SHHA detection method was confronted with the background N2 noise registered for both the 1st and 315th harmonics – determining the SNR of the measurements. The maximum amplitude of the 2f PT signal obtained for the 1st harmonic was 140.36 a.u., with a 1σ noise equal to 1.01 a.u. (SNR= 139), while the 315th harmonic set as the demodulation frequency yielded a maximum signal of 44214 a.u. and a 1σ noise equal to 14.4 a.u. (SNR= 3070). The sensor’s SNR increased by a factor of 22, simply by taking the advantage of the applied SHHA technique.
Worth noting is the fact that in the proposed PT signal extraction technique is baseline-free. Apart from random noise, no background signals are observable in the noise graphs (blue graph; N2 in the GAC cell), which were registered in the same measurement conditions as the signal traces (black squares and red fit; 1000 ppmv NO in the GAC). This permits the use of long integration times, if required by the application.
The performance of the proposed sensor configuration was evaluated based on measuring the noise of the sensor for 20 minutes. During this experiment, the pump laser was tuned to the center of the NO absorption line (no active locking was used), and the parameters were set, as in the previous measurements. The GAC was flushed with N2 and the flow was set at 2500 sccm. The noise was measured for two cases separately – demodulating the 1st and 315th beatnotes of the ML laser. Allan deviation plots and the registered noise are plotted in Fig. 7.
Fig. 7. (a) Allan deviation plots calculated based on sensor noise. 2f PT signal amplitudes registered for 20 minutes with N2 flowing through the GAC. (b),(c) Signal measured at the 1st and 315th harmonics of the ML laser beatnote, respectively.
Any noise source affecting the optical path-length of the ML laser resonator (with mechanical or acoustic origin), will translate to the frequency deviation observed after demodulation. The noise registered for the 315th harmonic has an overall higher average amplitude, compared to the 1st harmonic, which is consistent with the equation derived in Section 3. However, in our setup, I perform a frequency sensitive detection, by calculating the FFT of the demodulated signal and focusing only on the 2·f0,component (similar to the WMS technique aided with a lock-in amplifier). Therefore, although the signal scales linearly with increasing harmonic number (315x increase in spectroscopic signal amplitude), the noise is only 12x higher when comparing 1σ values for the 1st and 315th harmonics, which were 1.05 a.u. and 13.61 a.u., respectively. This fact is clearly evident when the calculated Allan deviation plots are compared in Fig. 7(a). Taking advantage of the unique feature of the SHHA, the sensor reached a limit of detection (LOD) equal to 90 ppbv and 6.9 ppbv for 1s and 137 s, respectively. This corresponds to a noise equivalent absorption coefficient (NEA) of 1.44·10−6 cm-1 and 1.1·10−7 cm-1, for 1 s and 137 s, respectively.
I have also experimentally verified the gas exchange time in the custom GAC. Firstly, the cell was flushed with N2 and was subsequently filled with the 1000 ppmv NO mixture. The results are plotted in Fig. 8(a).
Fig. 8. (a) Gas exchange time in the constructed sensor. Raw demodulated signal of 2 ppmv NO in the GAC registered at the 1st and 315th harmonics of the ML laser beatnote, respectively.
Due to the excellent detectivity of the proposed spectroscopic signal readout, the length of the region in which the PT effect induces the RI modulation could be confined in a 20 cm-long path, thus limiting the volume of the gas sample required for analysis. Using a 2500 sccm flow, the gas sample could be exchanged in the sensor in less than 2 seconds (the time during which the amplitude of the registered 2f PT signal change from 10% to 90% of its maximum value). The graphs presented in Figs. 8(b) and 8(c) show the difference between demodulating the PT-induced signal at the 1st and 315th harmonic of the ML laser beatnote. The advantage of using the SHHA is also clearly demonstrated in this comparison. The signal registered for the 315th harmonic is characterized by significantly greater amplitude in comparison to the 1st harmonic trace, and can be distinguished from the noise without any uncertainty.
As the proposed method of spectroscopic signal extraction is purely based on measuring frequency deviations, the method is intrinsically invulnerable (to a very wide extent) to changes in the electric signal amplitude forwarded to the demodulator by the photodiode, distinct from methods like WMS, which require additional signal processing and fitting to maintain accuracy of the readings, e.g., using the 2f/1f normalization methods [28]. This feature was verified by performing an experiment, in which the amplitude of the beatnote signal at the 315th harmonic was artificially attenuated by increasing the bending losses of the fiber delivering the optical signal to the photodiode. The results are plotted in Fig. 9.
Fig. 9. Amplitude of the 1000 ppmv NO 2f PT signal plotted as a function of the RF signal power measured on the 315th demodulated beatnote. Graphs (d), (e), (f) show the background noise registered for each case, respectively, with the GAC flushed with N2.
The experimental results show that a significant drop in the beatnote amplitude, below -55 dBm results in an observable increase in the registered noise of the sensor, which is evident for the measurement presented in Fig. 9(f). However, no influence of the RF beatnote signal power targeted for demodulation on the amplitude of the retrieved 2f PT spectroscopic signal was detected, which confirms the above-stated thesis.
5. Conclusion and discussion
In this paper, I proposed an ML-based intra-cavity gas sensor relying on the PT effect and a novel signal extraction method. The unique configuration contains minimum bulk optical elements and permits a simple separation of the pump and probe parts of the sensor. This feature allows using non-expensive near-IR photodetectors, compared to configurations based on, e.g., the WMS detection technique [9,24,29]. The proposed sensor has a unique readout to detect the PT-induced RI modulation, which does not require building dedicated interferometers, usually requiring sophisticated stabilization techniques. In this configuration, the excited gas molecules were enclosed in a cell incorporated into a ML laser resonator cavity, thus the resulting RI modulation was directly translated to the pulse repetition frequency variations, which can be easily detected and correlated with the gas analyte concentration. The sensor layout is non-complex, built using off-the-shelf fibers and components. Apart from the open-path section, the entire ML laser resonator, including all fiber components, was enclosed in a 17.5 × 10.5 × 1.5 cm3 fiber tray, which gives perspective for further miniaturization of the proposed sensor configuration.
Arthur Schawlow, the Noble Prize winner advised his students to “Never measure anything but frequency!” [30]. This advice is grounded in the digital nature of frequency measurements and the inherent noise immunity, which lead to the highest precision and accuracy. This motivated me to further explore the unique technique of encoding the spectroscopic signal into frequency. My further investigation of the ML-laser-based PT signal extraction led to the development of the SHHA technique, which yields a significant increase of the sensor detectivity. What is most important, the harmonic amplification of the signal is directly originating from the unique feature of the ML lasers, thus no auxiliary equipment is required in order to take full advantage of the proposed method. As presented theoretically and verified experimentally, the frequency deviation in which the spectroscopic signal is encoded increases with the index of the demodulated beatnote. In this experiment the 315th beatnote of the ML laser was targeted to show confirm the improvement in comparison with the signal registered while demodulating the 1st, fundamental beatnote. It should be noted, that the 315th harmonic was chosen only due to the limitations of the apparatus used to demodulated the signal (7.5 GHz bandwidth of the RF spectrum analyzer). The incorporation of commercial demodulator electronics (e.g., from cellular technology) is of course possible, which would allow accessing higher harmonics and thus yielding and additional increase in the detector sensitivity. Moreover, the apparatus required for executing gas measurements using the SHHA technique can be based on Field-Programmable Gate Array (FPGA) modules, which can be programmed to perform all the required tasks, including demodulation, FFT and signal aggregation, eliminating the need of using e.g., multi-purpose RF spectrum analyzers. In its current form, the sensor reached an LOD of 9.6 ppbv for 136 s integration time. This result is comparable with PT sensors that rely on interferometric signal retrieval, which usually have more complex layouts based on bulk optics or require adding advanced stabilization of the interferometer setup [9,11]. A comparison of several selected PT gas sensors is presented in Table 1, below.
Table 1. Performance of selected PT gas sensors
Furthermore, by modifying the GAC construction, the sensor in its current form allows detecting molecules having absorption spectrum also in the mid-IR wavelength range without the need of using expensive mid-IR detectors, making it a versatile platform.
Further work will involve the integration of the ML PT sensor into a configuration incorporating antiresonant hollow-core fibers (ARHCFs), which enables simultaneously transmitting light in the near- and mid-IR spectral bands. This will result in improved robustness and compactness. Moreover, the optimized overlap between the pump and probe beams achievable in the ARHCFs will significantly boost the PT signal, yielding higher SNR ratios. FPGA-based signal processing will be investigated in order to reduce the sensors complexity and cost.
Funding
Narodowe Centrum Nauki (2019/01/Y/ST7/00088, 2019/35/D/ST7/04436).
Disclosures
The author declares no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the author upon reasonable request.
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