1. Introduction

Temperature sensors are ubiquitous devices that permeate our daily lives. Conventional electronic-based thermometers are the most popular sensing devices due to their technological maturity. However, electromagnetic interference is identified as one of the main limiting factors that restrict their use. Furthermore, many applications that require large area of coverage with high localization accuracy, e.g. monitoring the temperature of soils [1], atmosphere [2], power transmission cables [3], mines [4], gas pipelines [5], or dam surveillance [6], require a network of many individual electronic-based sensors, making them expensive, bulky and potentially high power consumption.

An optoelectronic temperature sensor is an alternative approach which offers various advantages over conventional methods, including electromagnetic interference immunity, compactness, large temperature range, high sensitivity reliability [7], and multiple spatially-separated sensors configured as a sensing network. A number of temperature sensing approaches have been demonstrated, ranging from monolithic sensors, namely silicon ring resonator-based temperature sensors [8], plasmonic temperature sensors based on photonic crystal surface plasmon waveguides [9], and integrated temperature sensors based on an enhanced pyroelectric photonic crystals [10], to fiber-based sensors such as high-sensitivity temperature sensors based on an alcohol-filled photonic crystal fiber loop mirrors [11], fiber-optic Raman spectra temperature sensors [12], and a multi-wavelength Raman fiber laser based on fiber Bragg grating embedded in a quartz tube [13]. These fiber-based sensors usually rely on either optical time-domain reflectometry (OTDR) [14] or optical frequency domain reflectometry (OFDR) [15] technologies, which are two important classes of distributed temperature sensors. Although OTDR-based sensors can operate over a long distance of 40 km, a small temperature resolution of 5 °C and a low spatial resolution of 17 m limit their practicality [16]. OFDR-based sensors, on the other hand, offer a much higher spatial resolution of a couple of millimeters, however their maximum sensing range is restricted to only tens of meters [15].

Recently Tanner et al. proposed a distributed temperature sensor using a superconducting nanowire single photon detector [17]. This scheme offered various advantages over other approaches, including high spatial resolution and potentially a long detection range of a few kilometers. The technique exploited the backscattered photons via the spontaneous Raman scattering (SpRS) effect [18] when short optical pulses propagate along a standard single mode silica fiber (SMF). Based on the time-of-flight and the number of Stokes and anti-Stokes photons that were backscattered from a fiber under test, location and temperature information would be retrieved [17, 19]. Because the Raman coefficient of a silica fiber is relatively small, this method required a long integration time to achieve a measurement uncertainty within 3 °C [19], which made the scheme impractical for many applications.

In this paper we experimentally demonstrate a sub-centimeter spatial resolution distributed temperature sensor using a chalcogenide (ChG) As₂S₃ fiber with enhanced measurement accuracy and reduced acquisition time. The key component of this sensing scheme is an As₂S₃ fiber [20–22], whose Raman gain coefficient (~5 × 10⁻¹² m/W) is two orders of magnitude higher than that of a silica fiber [23]. This enables shorter measurement time, higher detection accuracy, and better spatial resolution (due to the higher refractive index n_ChG of a ChG fiber) than the method reported in [17, 19]. Furthermore, this scheme operates in the commonly used telecommunication C-band and its setup leverages off robust off-the-shelf components, all of which would make it an ideal candidate for various civilian and defense applications [24]. For instance, a temperature sensing network could monitor the operating temperature at multiple points on an engine, a weapon system, and the cryogenic temperature of various ultrahigh sensitivity sensing devices, or replace thermistor strings used to measure the temperature profile of the water column. Additionally, our theoretical study shows that a small detuning frequency regime from a pump is more suitable for rapid measurements while a large detuning regime provides higher temperature resolution, but requires longer integration time.

2. Working principle and experiment

The technique is principally based on SpRS. When an optical pulse propagates through a medium, the interaction of a pump photon with the molecular lattice vibrations, i.e. optical phonons, allows the absorption of a pump photon and the emission of either a lower energy photon, named Stokes, or a higher energy photon, anti-Stokes, than the energy of the absorbed photon [18]. These SpRS photons scatter in all directions and some of them travel in the backward direction. Here we exploit the time delay of the backscattered photons to identify the location of a target. Moreover, the intensity of the SpRS is temperature dependent; it is therefore employed for temperature characterization.

The experimental setup of the ChG fiber-based distributed temperature sensor is depicted in Fig. 1.A 20 MHz fiber laser created a 10 ps pulse train centered at 1550.9 nm. A 0.5 nm tunable optical band-pass filter (BPF) was used to improve the signal-to-noise ratio of the pump beam (whose average power P_ave = 2.7 mW), before being launched into the ChG fiber for Stokes and anti-Stokes photon generation via SpRS. As illustrated in Fig. 1, a higher number of Stokes and anti-Stokes photons were created within the heated part of the sensing fiber than those created in the fiber at room temperature, while a smaller number of photons were generated at the cooled section. Some of these photons were backscattered to a circulator and then separated by an arrayed waveguide grating (AWG), followed by two 0.5 nm tunable BPFs centered at 1541.3 nm and 1560.6 nm to further isolate pump noise, and conditioned by two polarization controllers (PCs) before being detected by two superconducting nanowire-based single photon detectors (SSPD, Single Quantum, ~50-70 ps timing jitter, ~10% detection efficiency with ~100 Hz dark count, polarization sensitive). A time-interval analyzer (TIA) with 27 ps time bin was used to construct a histogram that was later employed to calculate the location and the temperature of a target. Note that the electrical clock from the laser was used to trigger the TIA so that the time delay of each backscattered photon could be resolved and precisely plotted onto the histogram which is schematically shown in Fig. 1(i).

 

Fig. 1 The experimental setup of the ChG fiber-based distributed temperature sensor. (i) The histogram constructed from a time-interval analyzer (TIA) is used to determine the location and temperature of heating and cooling sources. PC, polarization controller; BPF, band-pass filter; AWG, arrayed waveguide grating; SSPD, superconducting nanowire-based single photon detector; solid line, optical path; dashed line, electronic path.

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The key device of this approach is a 2.7 m multimode As₂S₃ fiber. One end of the fiber was tapered through a resistive heating and drawing process [25] to reduce its cladding diameter from ~170 µm to ~80 µm so that the ChG fiber core became single mode at a wavelength of 1550 nm with a mode field diameter of ~5 µm. The uniform waist section of this initial taper was cleaved, butt-coupled to high numerical aperture (NA) silica fiber and then secured with ultraviolet (UV) cured epoxy. The other end of the ChG fiber was tapered down to ~2 µm, then cleaved to reduce Fresnel reflection caused by refractive index mismatch between the ChG fiber and air. The total insertion loss of the fiber was ~3.5 dB that consisted of a coupling loss of ~0.8 dB and a propagation loss of ~1 dB/m, which limits the sensing range of the approach to a couple of tens of meters in the working conditions of this experiment.

As previously explained, the sensing approach exploits SpRS inside a ChG fiber to construct the histograms of the time delays between the launch of a laser pulse and backscattered photons. The number of Stokes and anti-Stokes photons inside a waveguide I_S/aS is given by [26]

The location of a hot/cool spot is determined via the histogram’s time delay and its temperature can be calculated using Eqs. (1), (2) and (3)

3. Experimental results

Figure 2 presents the histograms of the location of heating and cooling sources. First, a 2 cm heater was used to gradually heat a ChG sensing fiber to ~100 °C at four different locations. This resulted in four peaks at four different positions in the histograms plotted in Fig. 2(a). Additionally, this approach could simultaneously resolve multiple heated (100 °C) and cooled (5 °C and −196 °C) spots along the fiber as shown in Fig. 2(b). These experimental results proved that the method could determine the length, temperature and location of any external heating and cooling sources. A spatial resolution L_res is defined as

 

Fig. 2 Locations of (a) a heat source at different positions with (a1) a zoom-in heating section, and (b) multiple heating and cooling sources vs. photon counts, which are used to calculate the temperature, are shown in the histograms constructed via a single-photon detector and a TIA. The temperature and length of (i) a heat source: 100 °C and 2 cm; (ii) first cooling source: 5 °C and 7 cm; (iii) second cooling source: 5 °C and 10 cm; and (iv) third cooling source: −196 °C and 20 cm, respectively.

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To verify the monitoring accuracy of the ChG fiber-based sensor, we compared the temperature measured via this scheme and a conventional electronic thermometer (Fig. 3). The comparison showed a good agreement between the two methods. A detection uncertainty of ± 0.65 °C was achieved with a relatively short measurement time of 5 seconds, while the uncertainty was reduced to less than ± 0.2 °C with a longer integration time of 2 minutes. In all calculations, the number of Stokes and anti-Stokes photons was determined by integrating the photon counts over an entire heating section. The temperature and uncertainty calculations were simple and they could be performed by a Field-Programmable Gate Array (FPGA) device, making this scheme practical in various applications. Note that although the whole heating section in the histogram was used, the spatial resolution of this approach remained intact. The location and the length of a heat source would be identified via the peak and the FWHM of a spike in a histogram, respectively.

 

Fig. 3 Temperature detected by a ChG fiber-based sensor (blue dots with error bars) and the corresponding temperature measured with a conventional thermometer (dashed line). Inset: three histograms captured after 5 seconds at three different temperature values.

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In addition to the temperature sensing application, this approach can be used to determine the refractive index of a waveguide. The working principle is based on the time-of-flight of the photons that are backscattered inside a waveguide under test. In this experiment, we characterized the refractive indices of an As₂S₃ and a silica fiber by heating two spots of the two fibers as presented in Fig. 4.The distance L (ChG fiber, 635 mm; and silica fiber, 388 mm) between two hot spots was premeasured. The group index n of a medium at a wavelength of 1550.9 nm could be calculated from L and the propagation time τ, which could be determined using a histogram in Fig. 4. The indices of the As₂S₃ and silica fibers were calculated to be 2.44 and 1.45, respectively, which agreed with their specifications. Note that it is possible to eliminate the heating process by taking advantage of Fresnel reflection at each end of a waveguide for identifying τ while L is the length of a device. Although accurate measurements of the refractive index of a medium are achievable, the resolution is not sufficient to fully resolve the group velocity dispersion of the medium due to the timing jitter of the experimental apparatus.

 

Fig. 4 The histograms of the (upper) As₂S₃ and (lower) silica fiber, which were used to calculate their refractive indices via the time delay τ between two heated spots.

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4. Discussion

We numerically investigate the optimum detuning from the pump frequency to maximize SpRS photons, thus enhancing the temperature resolution and reducing the measurement uncertainties. We observe from Eqs. (1), (2) and (3) that although the Stokes component is more intense than the anti-Stokes component, the intensity of the anti-Stokes band is more sensitive to temperature than that of the Stokes band. Under the same conditions, namely detection efficiency, operation bandwidth, and peak power, the ratios of the number of photons I at different temperature are equivalent to the ratios of the phonon populations N. Therefore we use the ratios of the phonon populations between the heating and the room temperature, N_heating/N_{T_room}, and between the room and the cooling temperature, N_{T_room}/N_cooling, at different detuning frequencies to determine optimum operating wavelengths in our analysis. The results of these calculations are plotted in Fig. 5.Here the phonon population ratio of either Stokes or anti-Stokes band, i.e. maximum theoretical temperature resolution, at 1.2 THz detuning frequency (which is the operational regime of this experiment) is always lower than that of the anti-Stokes channel at a higher detuning frequency such as 10 THz. Hence, a higher detuning frequency would be appropriate for high temperature resolution requirements. On the other hand, the small phonon population at the high detuning frequency results in higher uncertainties, thus reducing measurement accuracy. In short, the selection of the detuning frequency regime would depend on particular application. For example, the near-detuned regime should be considered for rapid measurements with high accuracy; while the further-detuned regime is more suitable for high temperature resolution measurements with a longer integration time.

 

Fig. 5 Theoretical analysis to find optimum detuning regimes for individual applications. The top two figures show the phonon population ratio N_heating/N_{T_room} while the bottom two figures present the ratio N_{T_room}/N_cooling for the (left) Stokes and (right) anti-Stokes components.

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5. Conclusion

In conclusion we have demonstrated a sub-centimeter spatial resolution As₂S₃ fiber-based distributed temperature sensor with enhanced measurement accuracy and reduced acquisition time. We achieved a measurement uncertainty of ± 0.65 °C for a rapid measurement of 5 seconds or less than ± 0.2 °C for a longer integration time of 2 minutes. The temperature uncertainty of this scheme was approximately an order of magnitude smaller than that of the device reported in [19] due to the high Raman coefficient of As₂S₃. Furthermore, we experimentally used this technique to accurately retrieve the refractive index of an optical waveguide, e.g. As₂S₃ and silica fibers. Finally, we demonstrated numerically that the current setup was suitable for rapid measurements and showed that higher temperature resolution could be achieved if the Stokes and anti-Stokes photon channels were further detuned from the pump frequency.