We report the first distributed optical fibre trace-gas detection system based on photothermal interferometry (PTI) in a hollow-core photonic bandgap fibre (HC-PBF). Absorption of a modulated pump propagating in the gas-filled HC-PBF generates distributed phase modulation along the fibre, which is detected by a dual-pulse heterodyne phase-sensitive optical time-domain reflectometry (OTDR) system. Quasi-distributed sensing experiment with two 28-meter-long HC-PBF sensing sections connected by single-mode transmission fibres demonstrated a limit of detection (LOD) of ∼10 ppb acetylene with a pump power level of 55 mW and an effective noise bandwidth (ENBW) of 0.01 Hz, corresponding to a normalized detection limit of . Distributed sensing experiment over a 200-meter-long sensing cable made of serially connected HC-PBFs demonstrated a LOD of ∼ 5 ppm with 62.5 mW peak pump power and 11.8 Hz ENBW, or a normalized detection limit of . The spatial resolution of the current distributed detection system is limited to ∼ 30 m, but it is possible to reduce down to 1 meter or smaller by optimizing the phase detection system.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Detection of trace gases sensitively and selectively is important for a range of applications in environmental, safety and industrial process monitoring . In some applications such as surveillances of natural gas pipelines and oil wellbores, distributed detection of gas concentration over a long distance or an extended area is often required. The capability of detecting events in arbitrary locations along an optical fibre is a unique and overwhelming advantage of fibre-optic sensors. Distributed strain and temperature sensing systems have been well developed by exploiting Raman, Brillouin and Rayleigh scattering process in optical fibres [2, 3]. However, little work has been reported on distributed gas detection with optical fibres.
Sumida et al reported a distributed hydrogen sensor by use of a silica-core fibre coated with Pt/WO3 thin film as the hydrogen sensitive cladding . The complex fabrication process and propagation loss caused by Pt/WO3 cladding however limit the sensing distance to tens of centimeters. Jin et al studied a distributed gas detection based on the optical time-domain reflectometry (OTDR) with a hollow-core photonic bandgap fibre (HC-PBF) and demonstrated the detection of acetylene gas over ∼75-m-long HC-PBF. However, even with a very large number of averages (up to 64,000 times), the limit of detection (LOD) achieved is around 1% acetylene .
Recently, distributed gas detection based on photothermal (PT) interferometry was proposed . The PT interferometry in HC-PBF adapts a pump-probe configuration, as illustrated in Fig. 1. A periodically modulated pump beam is absorbed by gas molecules to produce distributed phase modulation along a HC-PBF, and a probe beam with its nominal wavelength away from gas absorption is used to detect the PT phase modulation by use of a phase-sensitive OTDR. However, no experiment has ever been conducted so far. Garcia-Ruiz et al demonstrated a distributed gas sensor based on PT effect in a solid-core photonic crystal fibre (PCF) . Evanescent wave absorption of gas molecules raises the local temperature of the PCF, which was detected via a chirped-pulse phase-sensitive OTDR system. However, only a qualitative demonstration of gas presence was reported with no claims made on the LOD and spatial resolution. The length of sensing PCF is ~10 m.
Here we demonstrate experimentally the first distributed spectroscopic gas detection system based on PT interferometry. The system uses a modulated pump to generate periodic PT phase modulation along the fibre and a dual-pulse heterodyne OTDR to detect the distributed phase modulation. The system is capable of detecting low concentration of trace gas along a long length of HC-PBF. The basic principles of operation are outlined in Section 2, followed by a description of the experimental setup and signal processing technique in Sections 3 and 4, respectively. The experimental results of quasi-distributed and distributed gas detection are presented respectively in Sections 5 and 6, the potentials of the technique and the problems existing in the current systems are discussed in Section 7.
2. Basic principles
2.1. Distributed PT phase modulation along a HC-PBF
An intensity-modulated pump beam and a probe beam are propagating in the same gas-filled HC-PBF, as shown in Fig. 1 and Fig. 2(a). If the nominal wavelength of the pump is tuned to an absorption line of a trace gas contained within the HC-PBF, the pump absorption will heat up the gas, change the distribution of gas temperature, pressure and density within the HC-PBF, modulate the effective refractive index (RI) and hence the accumulated phase of the probe beam [6, 8]. Assuming weak absorption, the magnitude of PT phase modulation over a section [z, z + dz] along the gas-filled HC-PBF may be expressed as :Eq. (1) is independent of the strength of the absorption lines, which could be significantly different for different absorption lines and gas species.
Due to the intrinsic fibre loss and pump absorption,the pump power level reduces with increasing propagation distance, resulting in a reduction in the magnitude of PT phase modulation per meter down the sensing HC-PBF. Taking the P(9) absorption line of C2H2 at 1530.37 nm as an example, α0 = 1.165 cm−1. For the HC-1550-02 fibre, if pump beam is intensity-modulated sinusoidally with a frequency < 330 kHz  and the probe wavelength is around 1550 nm, has been determined to be . Assuming a fibre attenuation of 24 dB/km , a peak pump power level of 100 mW, and 10 ppm C2H2 balanced by N2 is uniformly distributed along the fibre. The magnitude of PT phase modulation per unit length at z = 0 is calculated to be 1.8 mrad/m accounting for round-trip phase modulation, and reduces down to 0.4 mrad/m at the end of 200 m length of HC-PBF. If the fibre attenuation could be reduced down to 1.2 dB/km, which is the currently reported lowest loss for HC-PBF , the magnitude of PT phase modulation would be 1.3 mrad/m after 200 m and 0.11 mrad/m at the end of 2 km.
The same principle can be applied to quasi-distributed sensing (Fig. 2(b)) in which discrete sensing HC-PBF sections are connected in series by single-mode fibres (SMFs) for light transmission. In such a case, the magnitude of PT phase modulation over a length (Lt) of gas-filled HC-PBF can still be estimated with Eq. (1) by replacing dz with Lt, and with the peak pump power inputting into the particular section of the sensing HC-PBF (assuming weak absorption and negligible fibre loss for the relatively short length of the sensing HC-PBF). For multiple sensing sections (HC-PBF sensors) serially connected by SMFs, the pump power into the sensors down the fibre cable would reduce considerably due to the connection loss between the HC-PBF and SMF . Assuming the length of each HC-PBF sensor is 28 m (the length used in our experiments in Section 5) and it is filled with 10 ppm C2H2 balanced by N2, the magnitude of PT phase modulation (round-trip) for first sensing section is estimated to be 49.6 mrad with 100 mW peak input pump power. Considering the state-of-the-art splicing loss achieved between the SMF and HC-PBF, we may assume a 4-dB loss for each sensor (mainly from the two HC-PBF/SMF splicing joints ), and the PT phase modulation would then be reduced down to 19.7 mrad at the 2nd sensor and 5 µrad at the 11th sensor. If the loss per sensor could be reduced down to ∼2 dB, the PT phase modulation would be ∼0.78 mrad at the 10th sensor and ∼7.8 µrad at the 20th sensor.
2.2. Detection of PT phase modulation
The distributed phase modulation may be detected by exploiting backscattering of the HC-PBF (Fig. 2(a)) in combination with the phase-sensitive OTDR or time-resolved optical frequency domain reflectometry (OFDR) [14, 15]. The backscattering in a HC-PBF is mainly caused by surface scattering due to random fluctuations of the core dimensions and has a value of ∼ 1.5 × 10−6 m−1 . A variety of phase-sensitive OTDR configurations have been reported for acoustic/vibraion detection, including interferometry-assisted OTDR , heterodyne phase-sensitive OTDR  and chirped pulse phase sensitive OTDR . They all in principle could be used to detect the distributed PT phase modulation. However, to our knowledge, most of the previous reports were concentrated on the detection of events like intrusions and did not focus much on the quantification of phase modulation along the fibre, and little or no information is available on the minimum detectable phase modulation.
For quasi-distributed sensing, the accumulated phase modulation of probe beam over each of the sensing sections (sensors) may be determined by examining the interference between the reflected probe waves occurring at the HC-PBF/SMF splicing joints (Fig. 2(b)). The optical power reflections (∼ 4%) are much stronger than the backscattered signals and this allows the use of the various techniques developed for multiplexed acoustic sensor (hydrophone) arrays to perform de-multiplexing and de-modulation [20–24]. These techniques are well developed with phase detection resolution down to the level of 10−5 to .
We here use a dual-pulse heterodyne phase sensitive OTDR technique / [25, 26] to detect the PT phase modulation. The system is capable of detecting distributed phase modulation along a sensing HC-PBF via backscattered probe beam or quasi-distributed phase modulation at multiple sensors by utilizing the reflections at HC-PBF/SMF joints. The phase detection resolutions for the two scenarios are on the order of 10−3 and , respectively. Based on the calculated magnitude of PT phase modulation in Section 2.1, such a phase detection resolution would enable distributed detection of trace-gas over a distance of kilometers or quasi-distributed gas detection with tens of sensors with a pump power of hundreds of mW.
In real applications, gas concentration would not be uniform along the sensing HC-PBF and the required detection limit could vary significantly for different applications. However, the formulation and discussion provided here would provide useful references to the design of different PT distributed gas sensing systems.
3. Experimental set-up
The setups for the distributed and quasi-distributed sensing experiments are similar and shown schematically in Fig. 3. The system comprises three main blocks: the pump, probe and sensing blocks. The pump block provides a modulated pump beam that is fed into the sensing fibre to produce distributed PT phase modulation along the gas-filled HC-PBF. Here we use a distributed-feedback laser (DFB) with a nominal central wavelength at 1530.37 nm, corresponding to the P(9) absorption line of C2H2. The pump is amplified by an erbium-doped amplifier (EDFA 2) and the accompanying ASE noise is filtered out by an optical filter (Filter 2) centered at the pump wavelength with a 3-dB pass-band of ∼1 nm. The amplified pump is modulated in intensity by an acoustic-optic modulator (AOM 3).
The probe block is a dual-pulse heterodyne phase-sensitive OTDR, and the details can be found in [25, 26]. A narrow linewidth probe laser with wavelength around 1550 nm is used. The wavelength of the probe is selected to be away from the gas absorption line and its optical frequency is denoted as f0. The probe beam is separated into two by an optical fibre coupler, and the two beams are then pulsed and frequency-shifted by the amount of f1 and f2, respectively, by AOM 1 and AOM 2. Subsequently, the probe pulses with frequency difference Δf = f1 − f2 are temporally offset by τd = Ld/v through a fibre delay line of length Ld (v is light speed in the delay fibre), and combined by a second optical fibre coupler. The pair of probe pulses are then combined with the modulated pump by a wavelength-division multiplexer (WDM) and launched into the sensing fibre. The operating windows of the WDM are centered at 1550 nm and 1531 nm, respectively, both with 3-dB bandwidth of ∼15 nm. The same WDM is also used to separate the backscattered/reflected pump and probe, and the residual pump beam is removed by an optical filter (Filter 1) before the photo-detector (PD).
The backscattered or reflected signals of the two probe pulses would interfere with each other and generate a heterodyne signal at the PD. The frequency of this signal equals to the beat frequency Δf, and the phase of the signal contains the information of PT phase modulation with its magnitude proportional to the gas concentration and the pump power level. The information about the spatial location, magnitude and frequency of PT phase modulation are recovered by post-processing the heterodyne signals, which will be described in Section 4.
For distributed sensing based on backscattered probe beams, the heterodyne signal at the PD output is the result of interference between the pair of the backscattered probe waves with a time delay of ∼ τd. The spatial resolution of the dual pulse OTDR system may be estimated by (τd + wp)vPBF/2 with wp representing the probe pulse width and vPBF is the light speed in the HC-PBF. Considering the relatively weak backscattered power level, an optical amplifier and filter module (the dashed-line rectangular box in the Fig. 3) may need to be used to boost the signal level before the PD.
For quasi-distributed sensing, the heterodyne signal is the result of interference between the two back-reflected pulses at the HC-PBF/SMF joints, and the length of the sensing HC-PBF needs to match with that of the temporal offset of the probe pulses to observe the interference signals. Since the reflected signals are considerably larger than the backscattering signals, the amplifier and filter module before the PD may not be necessary.
It should be pointed out that, for both distributed and quasi-distributed sensing systems, the pump and probe could be either co-propagating or counter-propagating. Since the magnitude of PT phase modulation depends on the pump power level, a variety of pumping schemes such as co-, counter-, or even bi-direction pumping could also be used to enhance the magnitude and uniformity of PT phase modulation along the sensing fibre [27–29].
4. Signal processing
Taking a quasi-distributed system with H sensors (the ith HC-PBF sensor is labelled as Si, i = 1, 2, …, H) as an example, the sequences of the probe pulses at different locations of the system are shown in the Fig. 4 (for H = 2). For each electric pulse (trigger, as shown in Fig. 4(a)) applied to the RF driver 1 in Fig. 3, dual probe pulses with different frequencies are generated (Fig. 4(b)) and launched into the sensing fibre. For each trigger pulse n (n = 1, 2, …, N), the waveform (the reflected optical signals from the sensing block) at the output of the PD contains H groups of pulses, each corresponding to a particular sensor (for two sensors, the groups are labelled as S1, S2 in Fig. 4(c)). Under the condition that the optical path lengths of the sensors match well with the delay fibre length Ld, there will be three pulses in each of the groups, as illustrated in the Fig. 4(c). The front pulse is the first probe pulse reflected from the splicing joint R1 (see Fig. 3) with the optical frequency of f0 + f2 while the rear pulse is the second probe pulse reflected from the splicing joint R2 with the optical frequency of f0 + f1. The middle pulse is the coherent beating of the first probe pulse reflected from R2 and the second probe pulse reflected from R1. The phase of the beat signal, with frequency of Δf = |f2 − f1|, is the optical phase difference between the dual pulses, which contains the information about the PT phase modulation accumulated over the length of sensor Si. By extracting the middle pulses of the groups, the beat frequency component Δf can be obtained and then PT phase modulation can be recovered .
The PD output is then sampled at a much faster rate than the repetition rate of the probe pulses, and the sampling is triggered by a clock signal that is synchronized with the AOM-driving pulse (generated by RF driver 1) (Fig. 4(d)). For each trigger pulse, the PD output waveform is sampled M times, and the start of the sampling is signified by a positioning pulse that has a fixed time delay with respect to the trigger pulse. This positioning pulse is used to correlate the subsequent sampled time-series data to locations along the sensing fibre. For a sequence of N trigger pulses (generating N pairs of probe pulses), a matrix with dimension of A = N × M is then created. The row N indicates the number of repetitions of the probe pulses and the column M indicates the number of sampled data points within a single repetition period Trep, as shown in Fig. 4(d). However, for quasi-distributed sensing system, not all these data need to be used. We only need to select H columns at the sampling positions mi, i = 1, 2 (for H = 2), corresponding to the beat frequency component (middle pulse) of each sensor. Hence, the useful data matrix is reduced to N × H, with H representing the number of sensors, and N the total number of sampling data points for an individual sensor.
The ith column of the data matrix is then a sampled version of the analog beating signal of sensor Si, which is an interferometric signal given by:Eq. (1). The frequency of Δϕp,i(t) is the modulation frequency of the pump beam. The time t is a digitized time sequence.
The recovery of the PT phase modulation (i.e. determining Δϕp,i(t)) is implemented with an algorithm that may be briefly described as a digital lock-in detection, as shown in Fig. 5:the interferometric signal is mixed with the orthogonal components of a sinusoidal signal with frequency of Δf, followed by low pass filters to generate a pair of orthogonal signals pi(t) = sin [Δϕp,i(t) + φi] and qi(t) = cos [Δϕp,i(t) + φi]. Then, a digital arc tangent algorithm is used to determined the phase term Δϕp,i(t) + φi, which contains the information of the PT phase modulation . By applying a digital band-pass filter centered at the PT modulation frequency, the PT phase modulation Δϕp,i(t) can be recovered and its frequency spectrum can be obtained by using Fourier transform.
For distributed sensing, the signal processing is similar to that in quasi-distributed sensing. However, for each trigger pulse or sampling period Trep, there will be two backscattered OTDR traces, corresponding to two probe pulses backscattered from the sensing fibre. The traces have a frequency difference Δf and a temporal offset τd, and interference between them generates a continuous trace of beat signal with its phase containing the PT phase modulation distributed along the fibre. To recover this distributed phase modulation, all the sampled data points during each repetition period Trep need to be used and the final data matrix dimension will be A = N × M. The phase of the beat signal recovered from each column of data correlates to the gas concentration over a specific section along the sensing fibre.
The frequency resolution of the spectrum is determined by the total number of data points used to perform Fourier transform. Here we use a Kaiser-Bessel data window with parameter α ~ 1.08 as the narrow-band digital band-pass filter, the effective noise bandwidth (ENBW) would be ∼1.1 times of the frequency resolution . For the quasi-distributed experiment (Section 5), the number of data points used for Fourier transform is 1071104 with a final sampling rate of 10 kHz, giving an ENBW of ∼0.01 Hz . For the distributed experiment (Section 6), the number of data points is 16926 with a sampling rate of 20 kHz, giving an ENBW of ∼11.8 Hz.
5. Quasi-distributed sensing experiment
A quasi-distributed system with two sensors was tested with the dual-pulse heterodyne phase detection system. As shown in Fig. 3 (Case 2, quasi-distributed), two sections of the HC-PBFs are connected via SMFs to form the sensing cable. The length of each HC-PBF section (sensor) is about Lt ∼ 28 m. The SMF between the two HC-PBF sensing sections is sufficiently long so that the reflected pulses from the different sensors are separated in time domain. The pump beam is square-wave modulated in intensity with an AOM at the frequency of 630 Hz and is launched into the sensing fibre from the opposite direction with respect to the probe beam.
The probe beam is a low noise fibre laser (NKT Koheras Basik E15) with narrow linewidth (< 0.1 kHz). It is pulsed by the two AOMs with frequency shifts of f1 = 100.05MHz (AOM 1) and f2 = 100MHz (AOM 2), respectively, giving an optical frequency difference of Δf = 50 kHz. The pulse widths of the probe pulses are wp ∼ 140 ns and the repetition rate is frep = 200 kHz. The length of the delay SMF in unbalanced Mach-Zehnder interferometer (MZI) is ~ Ld = 38 m, approximately twice of the optical path length of the sensing HC-PBF. This ensures that the dual pulses overlap at the PD after experiencing reflections at the front and rear ends of the HC-PBF sensors, generating the beat signals.
In preparation of HC-PBF gas cells, both ends of HC-PBF were mechanically spliced to SMF and the C2H2 were pressured into the HC-PBFs by applying a pressure difference on one end of the HC-PBFs. The mechanical splicing method will be described in the following sections. For proof-of-concept purpose, we use 28-m-long HC-PBFs gas cell and it is necessary to pressure the gas over 2 days to make ensure that the HC-PBFs could be sufficiently filled by C2H2. However, uniformity of gas distribution may still exist along the HC-PBFs. For a fast response and practical gas cell, the micro-holes could be drilled along the HC-PBF, which will be discussed in Section 7. The light-gas interaction length (i.e., 28-m-long HC-PBF here) should be matched with the time delay τd between the two probe pulses. Smaller τd enables a shorter HC-PBF gas cell.
The measured output from the PD is shown in Fig. 6, which agrees with the expected pulse waveform as shown in Fig. 4(c). The 1.28 µs time delay between the two groups of pulses corresponds to the length of the SMF (i.e., L0 ∼ 128 m as shown in Fig. 3) between the two HC-PBF sensors.
By following the signal processing procedures outlined in Section 4, the phase modulation corresponding to the two HC-PBF sensors can be obtained. Figs. 7(a) and 7(b) show respectively the frequency spectrums of HC-PBF 1 filled with ∼ 2700 ppm C2H2 and HC-PBF 2 filled with ~ 44 ppm C2H2, both buffered with N2. The signal-to-noise ratio (SNR) are 65 dB and 73 dB for HC-PBF 1 and HC-PBF 2, respectively. The noise floor is measured when the pump beam is turned off. The pump and probe beams are counter-propagating in the sensing fibre, and the peak pump power delivered to HC-PBF 2 and HC-PBF 1 are estimated to be ∼ 55 mW and ∼ 7.8 mW, respectively. For HC-PBF 2, the LOD in terms of noise-equivalent gas concentration for SNR = 1 is ∼ 10 ppb with an ENBW of 0.01 Hz or when normalized to 1 W peak pump power and 1 Hz ENBW. For HC-PBF 1, it is ~1.5 ppm or . It should be mentioned that since HC-PBF 1 is filled with higher concentration of C2H2 gas, the pump light is heavily absorbed and the effective absorption length is only Leff ∼ 3.2 m, as estimated by using Leff = [1 − exp (−α0CLt)]/(α0C) .
The spectrums frequency of the recovered phase modulation for HC-PBF 2 with different pump settings are shown in Fig. 7(c) in a linear scale. As can be seen, tuning the wavelength of pump away from the absorption line does not reduce the signal down to the noise floor. This could result from the residual Kerr-induced cross-phase modulation, due to the mismatch between the length of the sensing HC-PBF Lt and the delay fibre Ld, as well as background absorption. However, the magnitude of undesired phase modulation is considerably smaller (at least 5 times smaller for the case shown in Fig. 7(c)) than that of PT phase modulation, and it would not seriously affect the estimation of the LOD.
The minimum detectable phase modulation of the dual-pulse detection system may be determined from the noise floor when the pump is switched off. From Figs. 7(a) and 7(b), this noise floor is ∼−91 dB re rad (with respect to 1 rad) with a ENBW of 0.01 Hz, corresponding to a phase sensitivity of , for both HC-PBF sensors. Assuming that the 28-m-long HC-PBF is filled with low concentration C2H2 uniformly and the pump power levels delivered to HC-PBF 1 and HC-PBF 2 are respectively 7.8 mW and 55 mW, the theoretical LODs may be determined by comparing the magnitude of PT phase modulation calculated from Eq. (1) with that noise floor, giving for HC-PBF 1 and for HC-PBF 2, or for both sensors. The theoretical LOD is close to that experimentally measured result for HC-PBF 2 but deviates from that measured in HC-PBF 1. The discrepancy may be resulted from the inhomogeneous gas distribution along the HC-PBF.
By using a reference interferometer to minimize the common mode noise from the laser sources and external disturbance , it is possible to achieve a ~20 dB reduction in noise floor within the frequency range of 20 Hz to 1 kHz . This would improve the phase detection limit down to and could significantly improve LOD for gas detection.
6. Distributed sensing experiment
Distributed gas detection system was performed with a similar experimental setup. The pump beam is, however, modulated at 500 Hz and made to co-propagate with probe beam along the sensing fibre (see Fig. 3, Case 1, distributed). The peak pump power delivered to the sensing HC-PBF is ∼ 62.5 mW. The probe source is a single frequency laser source (RIO ORION laser module) with wavelength centered at 1550 nm. The two independent backscattered traces, corresponding to the two probe pulses, interfere with each other to generate beat frequency components . An EDFA and an optical filter are used before PD to amplify the weak backscattered signals as shown in the dashed-box in Fig. 3. The pulse widths of probe beams are wp ∼ 50 ns and the length of delay SMF is Ld ∼ 36 m, corresponding to a spatial resolution ~30 m in HC-PBF. Other parameters are the same as the quasi-distributed experiments.
The sensing fibre comprises five segments of HC-PBFs with respective lengths of ~116, ~1.7,∼ 1.7, ∼ 80 and ∼ 4.2 meters, as shown at the top of Figs. 8 and 9. These segments are connected in series by mechanical splicers, giving a total sensing distance ~200 meters. At the splicing joint, a small gap (less than 4 µm) is left between the two HC-PBFs, and the details about the mechanical splicing can be found in . The back-reflections from the joints between the HC-PBFs are measured to be on the order of 10−6, comparable with the magnitude of backscattering coefficient from the HC-PBF [16, 35]. The sensing HC-PBF is mechanically spliced to ~131-m-long SMF for connection to the detection system. The end of SMF is angle-cleaved to minimize Fresnel reflection back into SMF while the end of HC-PBF is normal-cleaved with a flat end face . The power reflection from the SMF/HC-PBF joint is measured to be ∼−35 dB.
Figure 8 shows signal trace detected at the PD output before signal processing, when the pump is off and the HC-PBF is not filled with C2H2. The large signal due to Fresnel reflection can be clearly observed at around P1, which is the joint between SMF and HC-PBF and at the spatial location of 131 m, followed by the backscattered signals from HC-PBFs.
Gas detection experiments were conducted by filling ∼498 ppm of C2H2 gas balanced by N2 into short sections of HC-PBFs around spatial location P2 (251 m) and P3 (335 m), as shown in Fig. 9. At P2, the gas was pressurized (with ∼3 atm pressure difference) into the HC-PBF via the gap of the middle splicing joint, while the gaps of the other two joints were open to atmosphere. At P3, the gas was pressurized into the HC-PBF via the far end of the fibre with the gap at the splicing joint left open to atmosphere. With such a setup, we believe that the gas would mainly be filled into the short-lengths (i.e., 2 × 1.7 = 3.4 m around P2 and 4.2 m around P3) of the HC-PBFs. According to , the pressure-pumped gas-filling process could take ~0.5 min and ∼3.5 min to fill 1.7-m-long and 4.2-m-long HC-PBF, respectively. For other sections of HC-PBFs, since there is no pressure difference, the self-diffusion processes would take ~16 hrs for filling 1-m HC-PBF . Hence the sensing lengths could be determined by the lengths of the HC-PBFs around P2 and P3 where the gas pressure differences are applied and the magnitude of PT phase modulation within these sections of HC-PBFs can be calculated by use of Eq. (1).
The Fig. 9 shows the recovered phase distribution map over the entire 200-m-long HC-PBF. The presence of gas absorption around P2 and P3 can be clearly observed. The signals around P1 are the result of Kerr-induced cross-phase modulation.
To verify that the phase modulation signals observed in Fig. 9 are the results of gas absorption, the phase distributions along the fibre were measured again when pump wavelength is tuned away from the absorption line and when pump is turned off. The results are shown in Figs. 10 (a) and 10(b), respectively. With the pump wavelength away from the absorption line, the phase modulation signals around P2 and P3 disappear while that around P1 remains. Turning off the pump beam results in the disappearance of all the phase modulation signals. Obviously, the phase modulation signals around P2 and P3 are due to gas-absorption-induced PT phase modulation.
The location and time-varying phase information in the presence of gas absorption can be observed simultaneously in a three dimension display. Figure 11 shows an example of demonstration for the recovered phase modulation signal around P2. The projection in the left coordinate plane shows the location information while that in the rear coordinate plane shows the time-varying phase information. The information about other locations can be also displayed in a similar way.
The recovered phase modulation signals at P2 and P3 are extracted out and further analyzed. Figs. 12(a),(c) and (b), (d) shows respectively the time waveforms and frequency spectrums of the signals for the two locations P2 and P3. The LODs can be evaluated from the spectrums by comparing the signal levels with the noise floors measured with pump tuned away from the gas absorption, which is not much different from that measured when the pump is switched off. At P2, the signal and noise floor levels are 0.35 rad (3.4-m-long HC-PBF) and 0.012 rad, giving a SNR of 29 with a ENBW of 11.8 Hz and a normalized LOD of or . Similarly, at P3, the SNR is 9.5 (4.2-m-long HC-PBF), giving a normalized LOD of or .
From Figs. 12(c) and 12(d), the minimum detectable phase modulation of the current detection system can be estimated to be and for P2 and P3, respectively. If we assume that 3.4-m-long and 4.2-m-long HC-PBFs around P2 and P3 are uniformly filled with low concentration C2H2 balanced by N2, by using Eq. (1) with peak pump power of 62.5 mW, the theoretical expected LODs are (or ) and (or) at P2 and P3, respectively. The theoretical expected LODs are close to that of the measured results and therefore we believe that the gas were mainly filled into the two short HC-PBF segments around P2 and P3, rather than other sections of HC-PBFs. This means that the lengths of our gas-filled HC-PBF are much shorter than the spatial resolution ∼30 m of phase detection system. If the length of gas-filled HC-PBF matches with the spatial resolution, the LOD of our gas detection system can be further improved.
For the further development of distributed gas detection system with PT interferometry, some important issues need to be addressed:
- Spatial resolution: the spatial resolution of the current dual-pulse heterodyne OTDR system is ∼30 m, determined by the probe pulse width and the length of the delay fibre to offset the pulses. The use of narrower pulses in combination of a shorter delay fibre would improve the spatial resolution. However, the magnitude of backscattering signal is pulse-width relevant  and a narrower probe pulse would result in a weaker backscattering signal, affecting the SNR at the PD. Since the length of the delay fibre approximately determines the sensing length over which the PT phase modulation is examined by the dual-pulse approach, the use of shorter delay fibre also reduces the magnitude of the accumulated phase modulation being detected.
- LOD: increasing the pump power can increase the magnitude of PT phase modulatoin and hence improves the SNR and LOD. By using a bi-directional pump secheme, the pump power level can be made more uniform and hence more uniform LOD over the entire sensing distance. The nonlinear threshold of HC-PBFs is significantly higher than that of the conventional SMFs [40, 41], which would enable higher pump power delivered to the HC-PBF to achieve distributed gas detection with high sensitivity over a long distance.
The SNR could be further enhanced by operating at a higher modulation frequency. It has been shown that the pump intensity could be modulated at a frequency of up to 330 kHz without compromising the efficiency of PT phase modulation . In our current distributed sensing experiment, the pump modulation frequency is 500 Hz, which lies in the low frequency region where the flicker noise or environmental noise may be dominant . The maximum detectable frequency is limited by the relatively low beat frequency (50 kHz) and the pulse repetition rate (200 kHz) of the current dual-pulse detection system. To operate at a higher modulation frequency, the beat frequency and the repetition rate need to increase correspondingly to ensure accurate recovery of the PT phase modulation. This could be at the cost of reducing sensing distance, since the maximum measurable length is inversely proportional to the repetition rate of probe pulse .
- Response time: the current sensing cable is made of several segments of HC-PBFs connected in series for the reasons that we can easily determine the locations where the trace-gas is loaded into the HC-PBF and the length of gas-filled HC-PBF. Future work would use a single long HC-PBF as the sensing fibre, with many micro-size holes drilled along the fibre by using, for example, a femtosecond laser . It is possible to drill hundreds and more holes along a HC-PBF with low loss  and the response time will be determined by the spacing between the holes . There are other types of fibres such as negative curvature hollow-core fibres  and suspended-core fibres [47,48] that would allow continuous opening of the fibre core to the outside but more research is needed to access the potential of these fibres for distributed gas detection.
- Phase detection technique: here we use a dual-pulse heterodyne phase-sensitive OTDR system to perform distributed phase detection. There are other schemes that are actively being investigated for distributed acoustic sensing (DAS) [49–52] and could be used for detecting the PT phase modulation. Similar to PT gas detection, DAS could be understood as a method to detect the dynamic phase modulation along the fibre. The only difference is that the DAS accounts for the external acoustic-wave ‘hitting’ the fibre, which induces phase modulation of probe beam. However, the PT phase modulation accounts for the internal gas-absorption-induced phase modulation. The fact that the fixed modulation waveform (e.g., pure sinusoidal wave with a known frequency) for PT gas sensing, as compared with the unpredictable ones for the DAS, would allow better performance in terms of phase detection resolution/accuracy.
- Implications of laser power levels: Currently we used a periodically modulated continuous-wave laser with peak power of 62.5 mW, corresponding to a peak light intensity of 2.5 × 105 W/cm2 in the hollow-core. With such an intensity level, the temperature rise in the central hollow-core filled with 1% concentration C2H2 is small and below 1 K. For longer distance sensing that requires higher pump power and if applications also involve higher gas concentration, the temperature rise could be significant to cause burning or even explosion. The LOD of the distributed sensing system depends on the averaged power level of the backscattered probe beam. For current system, we used a pulse probe source with ~35 mW peak power input HC-PBF, 50 ns pulse duration and 200 kHz repetition rate, and achieved satisfactory results. Increasing sensing distance will cause lower backscattered power level of the probe beam from the far end, which would require the use of a probe source with higher power or an optical receiver with higher sensitivity. These would be topics for future study.
An optical fibre distributed spectroscopic gas detection system based on PTI is described. The system uses a HC-PBF as the sensing fibre and a dual-pulse heterodyne phase-sensitive OTDR to detect the absorption-induced photothermal phase modulation along the fibre. The use of low-loss HC-PBF enables strong spectroscopic light-gas interaction within the hollow-core over a long distance, allowing label free distributed gas detection with high sensitivity and avoiding complex procedures to coat fibres with gas-sensitive materials. The use of PTI with a modulated pump beam enables zero-background gas detection with significantly higher sensitivity over the previous direct absorption-based sensors. Experiment with a two-sensor quasi-distributed system demonstrated a LOD down to ∼10 ppb acetylene with a pump power level of ~55 mW and a noise bandwidth of 0.01 Hz. Distributed sensing experiment with ~200-meter-long HC-PBF demonstrated a LOD of ∼5ppm with ∼63 mW pump power and 10∼Hz noise bandwidth. The spatial resolution of the current distributed sensing system is limited to ~30 m by the dual-pulse OTDR, but it is possible to reduce down to 1 meter or smaller by optimizing the system parameters. The PTI system operates at telecom wavelength band and could be developed for distributed gas sensing over long distances (kilometers) with high sensitivity and selectivity.
Hong Kong SAR government GRF grant (PolyU 152064/14E); National Natural Science Foundation of China (NSFC grants 61535004 and 61290313); Hong Kong Polytechnic University (4BCBE, 1-ZVG4 and 4-BCD1).
Y.C. Lin and F. Liu contributed equally to this work. W. Jin and Y.C. Lin proposed the primary idea. Y.C. Lin, F. Yang, H.L. Ho and Y.Z. Tan prepared the HC-PBF gas samples. Y.C. Lin, F. Liu and X.G. He designed and conducted the experiments. W. Jin and M. Zhang supervised the whole experimental process. Y.C. Lin and W. Jin wrote and revised the paper, with contributions from M. Zhang, F. Liu, X.G. He and L.J. Gu. We also want to express thanks to Dr. Kun Chen from Tsinghua University for providing useful discussion and laser source.
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