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Abstract
A fiber temperature sensor based on four-wave mixing (FWM) with an oil-filled photonic crystal fiber (PCF) is proposed in this study, and a multipoint measurement based on the wavelength multiplexing of such sensors is constructed for the first time. The sensing performance and signal spectral characteristics of the temperature sensor are theoretically and experimentally studied. The maximum temperature sensitivity of the signal light of 0.207 nm/°C is achieved using a FWM sensing fiber with a length of 10 cm. The signal wavelength response to excitation power is also explored in this experiment. Results showed that the temperature sensor is relatively insensitive to the fluctuation of power change. The wavelength multiplexing of a FWM-based PCF temperature sensor also presents the possibility of multiplexing measurement and multipoint sensing, and high multiplexed capability is theoretically predicted to be obtainable with optimized sensitivity and splicing loss.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber four-wave mixing (FWM) effect is nonlinear and optical with interaction of four waves in fiber. FWM is regarded as degenerated if two pump photons have equal frequency. Phase-matching condition must be satisfied to produce Stokes and anti-Stokes waves, also called signal and idler waves, respectively. When a pump wavelength is near the zero-dispersion wavelength (ZDW) of the fiber, the signal gain is high, resulting in the easy realization of the FWM. At present, it is comprehensively used in frequency conversion [1,2], super-continuum generation [3,4], pulse amplification [5], lasers [6], entangled photon pairs [7] and so on.
Photonic crystal fiber (PCF) is an excellent platform for FWM due to its unique characteristics such as a flexible structure [8] and high nonlinearity [9], which conventional fiber does not possess. After the FWM phenomenon was first observed in microstructure fibers [10], many theoretical and experimental studies were conducted on the mechanisms and influencing conditions of FWM in PCFs. When the fiber structure (such as refractive index) or external environment (e.g., temperature, pressure, tension, and stress) exhibits a slight variation, the Stokes and anti-Stokes wavelengths will drift dramatically due to the change in fiber ZDW, which is the basic principle of FWM-based fiber sensing. Frosz et al. [11] conducted a preliminary refractive index sensing experiment by using the FWM in PCFs, and the shift in the Stokes wave was observed after the air holes were filled with methanol and water. Gu et al. [12] realized strain sensing based on the FWM effect in high-nonlinearity PCF; the obtained strain sensitivity was 0.11 pm/με. Bang et al. [13] designed a FWM-based fiber biosensor with a 1.2 cm tapered As2S3 chalcogenide fiber. Nallusamy et al. [14] developed a FWM-based temperature sensor with a high-nonlinearity CS2-filled PCF. The temperature sensitivity was − 82 nm/°C when the sensing fiber was shortened to 13 cm. Recently, Velazquez−Ibarra et al. reported a temperature-tuned wideband FWM with an ethanol-filled solid-core PCF in their experiment, results showed that the sensitivity of an ethanol-filled PCF to temperature is around 4.4 and 12.3 nm/°C for the signal and idler wavelengths, respectively [15].
Existing theoretical and experimental reports proved that the FWM effect has great potential in the field of PCF sensing. To the best of our knowledge, this study is the first to propose wavelength multiplexing of FWM-based PCF temperature sensors. In addition, the possibility of multiplexing measurement and multipoint sensing for FWM-based fiber sensors is explored. A long sensing fiber used in the FWM would limit its practical applications. Therefore, an FWM-based inline PCF temperature sensor with a length of 10 cm is fabricated in the experiment, thereby achieving a maximum temperature sensitivity of 0.207 nm/°C. Other essential issues of FWM-based sensors, such as instability-induced measurement error, are also studied thoroughly. Experiments prove that this temperature sensor is relatively insensitive to the fluctuation of excited power.
2. Theoretical analysis
PCF was purchased from Yangtze Optical Fiber and Cable (YOFC, China) company, and its cross-section image is shown in Fig. 1. It has a fiber diameter of 125 μm and a core diameter of 7.20 μm. The average diameter d and the pitch Λ of the hexagonally arranged air holes are 3.42 and 5.50 μm, respectively.
The propagation constants and group velocity dispersion (GVD) coefficients of the PCF are calculated using the frequency-domain finite difference method. Three types of refractive index matching oils, namely, no = 1.32, no = 1.34 and no = 1.36, are selected and filled into the air holes of the PCFs. The material dispersion of the silica background and the dispersion of the refractive index matching oils are incorporated into the simulation [16,17]. The coefficients of the Cauchy dispersion equation for the index matching oil are shown in Table 1. Figure 2(a) shows the theoretical GVD curves for the oil-filled and unfilled PCFs. The ZDW of the unfilled PCF is 1116.8 nm, and the ZDWs are slightly red-shift with the higher-refractive-index oils filled.
Table 1. Cauchy dispersion equation of the refractive index matching oils at 25 °C. no = A + B/λ2 + C/λ4 (λ is the wavelength in nm)
Fig. 2 (a) Theoretical GVD dispersion curves and (b) tuning curves of signal wavelengths for the PCFs unfilled and filled with oils with refractive indices of 1.32, 1.34, and 1.36 when P0 = 5 kW. (c) Theoretical temperature sensitivity of signal wave for the PCFs filled with various oils when P0 = 5 kW and λP = 1064 nm. (d) The shift of the signal wavelength with the decreasing excitation power at a step of 10% when λP = 1064 nm.
According to the conservation of energy and momentum, the phase-matching condition for FWM is defined as
where κ is the value of phase mismatch, is the m-order propagation constant at frequency of the pump laser ωp, β is its propagation constant. The maximum gain of gmax = γP0 can be obtained as κ = 0; Ω = ωs − ωp = ωp − ωi is the frequency shift, where ωs and ωi represent the frequencies of the signal wave and idler wave, respectively, and γ is the nonlinear coefficient of PCFs and can be expressed by, where n2 = 2.6 × 10−20 m2 W−1 represents the nonlinear refractive index of silica and Aeff is the effective mode area at a pump wavelength of λp.The wavelengths of the signal and idler wave at various pump wavelengths could be identified by using Eq. (1). The nonlinear coefficient γ is approximately 7.7 × 10−3 W−1 m−1 with λP = 1064 nm and P0 = 5 kW. Figure 2(b) shows the tuning curves of the signal wavelength versus pump wavelengths for the PCFs unfilled and filled with oils with refractive indices of 1.32, 1.34, and 1.36. When λP = 1064 nm and P0 = 5 kW, the corresponding signal wavelengths locate at 743.2, 681.4, 671.1, and 661.1 nm, indicating that the FWM signal wavelength decreases with the increase in the oil refractive index.
As the refractive index of the filled oil changes, the ZDW of the PCF will change due to the thermo-optic effect and then correspondingly result in the shift of the signal wavelength in accordance with the FWM principle, which explains the basic sensing principle of the FWM-based PCF sensor for measuring the refractive index or the environment temperature. Here, the thermo-optic coefficients are 3.36 × 10−4, −3.38 × 10−4, and −3.41 × 10−4 RIU/°C for the 1.32, 1.34, and 1.36 oils, respectively [16]. With the use of the dispersion curves of the filled PCFs at various temperatures, the responses of signal wavelength to the temperature can be determined, as shown in Fig. 2(c). As indicated in the figure, the signal wavelength is red-shift with the increasing temperature, and the PCF filled with high refractive index oil obtains a high temperature sensitivity. When no = 1.36, the temperature sensitivity increases up to 0.236 nm/°C.
In accordance with Eq. (1), the fluctuation of excited power gives the main contribution to the instability of the wavelength-coded sensor. Therefore, the stability of the signal wavelength with excitation power fluctuation of λP = 1064 nm at 25 °C is also simulated theoretically. Figure 2(d) shows the shift of the signal wavelength as the excitation power decreases with a step of 10%. As shown in the figure, the signal wave shifts slightly to a long wavelength as the power decreases and it becomes increasingly stable when filled with high refractive index oil. Although 50% decreases of pump power may induce an error of approximately 1 °C for a temperature sensitivity of 0.236 nm/°C, the deviation of signal wavelength is only 0.045 nm considering that the stability of most commercial LD-pumped lasers is below ± 5%. The Eq. (1) also suggests that, if the excited power is reduced greatly, its impact on the generated signal wavelength would be negligible, and the stability could be further optimized by reducing the excited power. Moreover, if the temperature sensitivity could be improved by more than one order of magnitude, the power-induced measurement error may also be reduced remarkably.
3. Sensor fabrication and experimental setup
Figure 3 shows the experimental setup for the FWM-based PCF temperature sensors. A solid-state passive Q-switched laser (Changchun New Industry Co. Ltd.) with a central wavelength of 1064.1 nm is used as the excited laser source. Its pulse width and repetition frequency are 1.3 ns and 11.8 kHz, respectively. Two polarizers (P1 and P2) are assembled as an optical power attenuator, and a half-wave plate (HWP) is utilized to change the output polarization state of the excited laser. A 1064 nm laser line filter (LF) is used to allow only the 1064 nm light to pass through. With the use of a 25 × microscope objective, the output light of the excited laser is coupled into a single-mode fiber (SMF-28, Corning), the coupling efficiency is approximately 65% and a power of approximately 102 mW is delivered to the PCF. The output leading fiber is a multimode fiber (MMF) with a core size of 40 μm, which could reduce the background spectral of FWM. A short PCF of approximately 10 cm is inserted into the SMF/MMF leading fibers and forms an in-line fiber sensor. A short-wave pass filter (SP) is used to filter out the residual 1064 nm excited laser; hence only the signal light produced by the FWM is collected. The final spectra are recorded by using a charge-coupled device (CCD) spectrometer (CCS200, Thorlabs) with an integration time of 5 s.
The two ends of the PCFs are cleaved and inserted into the refractive index matching oils, and the liquid is filled into the PCF through the air holes via capillary force. Both ends of the oil-filled PCF are treated with small liquefied petroleum gas flame before splicing with leading fibers as we used previously to reduce the splicing loss [18]. The insertion loss is approximately 1.0 dB. As shown in Fig. 4, for the PCFs unfilled and filled with the three refractive index matching oils, namely, no = 1.32, no = 1.34, and no = 1.36, the signal wavelengths occurred at 745.31, 689.71, 680.85 and 668.98 nm, respectively. Only a small deviation is present between the simulated and experimental signal wavelengths due to the measurement error of the fiber structure. The wavelength of 621.17 nm results from the background FWM spectra of the SMF-28. Given that idler wavelength is beyond the spectrometer measurement range of 200–1000 nm, the signal wavelength is used for the following temperature sensing.
Fig. 4 Signal wave output spectra for the unfilled and filled PCFs. Note that the integration time for the 745.31 nm light is 1 s.
4. Sensitivity and stability tests
The fabricated fiber sensors are placed in a temperature-controlled oven, and the signal wave spectra are recorded with a step of 10 °C from room temperature to 72 °C, which is a safe working range. Figure 5(a) shows the shift of the signal spectra with the increasing temperature for the PCFs filled with three different refractive index oils. As shown in the figure, all the signal wavelengths are red-shift due to the ZDWs of the filled PCFs moving to short wavelengths with gradually increasing temperature. The result is consistent with theoretical calculation. Figure 5(b) shows the average response of the signal wavelength to temperature after several cycles of heating and cooling. It presents good linearity of the signal wavelength to temperature from the room temperature to 72 °C, exceeding this range may lead to the degeneration of linear response or the hysteresis phenomenon in cooling process for the signal wavelength as the figure shows. From linear fitting, the obtained temperature sensitivities are 0.093, 0.124, and 0.207 nm/°C, respectively, which are slightly lower than the theoretical value. This phenomenon may be due to the existence of pressure, which makes weak elasto-optic effect slightly resistant to the thermo-optic effect during the heating process. Due to a more evanescent field penetrating into the air holes of the first layer as the PCF is filled with the high refractive index oil, the temperature sensitivity of the PCFs filled with high refractive index oil is increased. However, in this case, the excited laser wavelength is far from ZDW and experiences large transmission losses, thereby obtaining a small signal gain. Therefore, a tradeoff must be made between the sensitivity and signal gain.
Fig. 5 (a) Signal spectra shift with the increasing temperature, (b) The response of the signal wavelength to temperature for the FWM-based PCF temperature sensors, RT is the room temperature.
Unlike the Mach–Zehnder (MZ) interferometer PCF temperature sensor that we fabricated previously [18], the temperature sensitivity is relatively low because this fiber temperature sensor based on the FWM effect uses the fundamental mode and the corresponding evanescent field is relatively small. The sensitivity may be improved through two methods: 1) the use of a small-core PCF instead, where a more evanescent field distributes in the air holes of the first layer and the GVD could be changed effectively by the filled oil; 2) and the use of idler wave for sensing, which allows the improvement of the sensitivity due to its larger tuning slope than the signal wave.
However, the performance of the sensor can be characterized by a figure of merit FM = S/ΔλFWHM, which is a ratio between the temperature sensitivity S and the full width at half maximum (FWHM) ΔλFWHM of the resonance dip or peak [19]. In the PCF filled with oil of no = 1.36, the FM approached 0.24 °C−1 as ΔλFWHM = 0.85 nm for the signal wavelength, which is comparable with the PCF-based Bragg grating [20], and is larger than that of the PCF-filled MZ interferometer fiber temperature sensor (S = −1.83 nm/°C, FM = 0.09 °C−1) (fabricated previously) [18], PCF-based long period grating [20] and the widely tunable FWM (0.15 °C−1) [15], but it remained smaller than that of the PCF-filled MZ with fiber ring laser demodulation (S = −1.747 nm/°C, FM = 21.83 °C−1) [21] and the theoretically designed FWM temperature sensor (S = −82 nm/°C, FM is between 4 and 8 °C−1) [14].
According to the phase-matching conditions, the signal wavelength generated by the FWM greatly depends on the excitation power. Therefore, evaluating the stability of the signal wavelength to the excitation power intensity is necessary and important for the improvement of measurement accuracy. When the angle of the first polarizer (P1) is rotated for every 10 minutes, the excitation power is manually adjusted to be 100%, 75%, and 50% of the original powers. The CCD spectrometer is used to monitor and record the central positions of the signal wavelength in real time. Figure 6 illustrates the obtained central signal wavelength versus time for the FWM-based fiber temperature sensors filled with different refractive index oils. As indicated by the three panels in the figure, when the power of the excitation laser decreases by 50%, the maximum fluctuation ranges of the signal wavelength are 0.17, 0.15, and 0.10 nm, respectively. Therefore, if the output power instability of a commercial 1064 nm laser is ± 5%, then the temperature measurement errors of are 0.7, 0.3, and 0.15 °C due to the fluctuations of the signal wavelength. When the optical fiber was filled with high refractive index oil, the signal wavelength stabilizes further and shows insensitivity to power fluctuations. In this sense, filling with the high refractive index matching oils would improve the sensitivity and stability, but the gain of the signal light will be reduced. If the excited power is reduced or the sensitivity is improved by one or two orders, the measurement error would be reduced remarkably. Note that the polarization direction of the excited wave may also induce the variation of the signal wavelength; it must be kept still in the experiment or a polarization-maintaining leading fiber should be used instead of the standard single mode leading fiber.
5. Wavelength multiplexing of sensors
The PCFs filled with different refractive index oils have different signal wavelengths, providing the feasible construction of the wavelength-multiplexed FWM fiber temperature sensors. Therefore, three such FWM-based PCF temperature sensors are cascaded to achieve multipoint temperature detection in the experiment. With the standard SMF-28 used as leading fibers between PCFs, the total insertion loss of the three sensors is 6.5 dB, which can be reduced further using a mode-field-matching leading fiber instead of the SMF-28. The lengths of the fiber are 5.5, 7.8, and 10.0 cm to balance the amplitude of signal spectra. In the experiment, only the PCF filled with the 1.32 oil is heated, whereas the others are kept at room temperature. Figure 7 shows the output spectra of the multiplexed sensors. As indicated in the figure, only the signal wavelength of the heated PCF1 shifts with the increasing temperature, whereas the other signal spectra remain constant, thereby proving the possibility of multipoint temperature detection by using this FWM-based fiber temperature sensor.
Fig. 7 Transmission spectra of the multiplexed PCF temperature sensors at different temperatures. PCF1, PCF2, PCF3 are the PCFs filled with oils with refractive indices of 1.32, 1.34, and 1.36.
Here, only three sensors are multiplexed for the large splicing loss. However, the multiplexed capability of the FWM-based sensors could be simulated and analyzed theoretically. Assuming that the number of total sensing units is N and the transmission loss is neglected, the received signal spectra of the ith sensor could be expressed by
where gi(λ) is the spectral shape of the FWM sensors, Li is the fiber length of the ith sensor, α is the experienced splicing loss for the excited and signal waves in the joint interface from SMF to PCF, and η is a conversion constant from the power to the spectrometer counts, which could be obtained from the experimental result. The first part of is the maximum amplification factor of the signal wave for the ith sensor [22]. For simplicity, the spectra of the signal wave are assumed to be of Gaussian shape, i. e., where λi is the central wavelength of the ith sensor and Δλi is its FWHM, which could be evaluated using Eq. (5) [22]. In addition, ΔTmax is the temperature measurement range, Si is the temperature sensitivity of the ith sensor, and C is the velocity of light.With the use of Eqs. (2)–(5), the output spectra of an N-sensor multiplexed network can be simulated through . Presumably, the temperature measurement range is from room temperature to 75 °C, that is, ΔTmax = 50 °C, and the available bandwidth is from 650 nm to 720 nm. Considering that the splicing loss from SMF to PCF is much larger than the transmission loss, only the splicing loss is considered in the simulation for simplicity. In the experiment, the distinguishable minimum peak value of our CCD spectrometer is approximately 0.01 for the signal wave in a normalized condition. The number of the multiplexed sensors can be determined through the available bandwidth and the detectable peak value.
Figure 8(a) shows the fitted temperature sensitivity and the FWHM of the signal waves obtained from Eq. (5). As the signal wavelength increased, the temperature sensitivity reduced and the FWHM broadened. Figure 8(b) shows the number of multiplexed sensors versus the splicing loss at the original temperature sensitivity and partially reduced temperature sensitivity. Figure 8(c) shows the simulated output spectra with the original temperature sensitivity for α = 0 and α = 2 dB. When α = 2 dB, only three sensing units could be multiplexed. Figure 8(d) shows the simulated output spectra for α = 0.4 dB at half of the original temperature sensitivity. In this case, up to 14 sensing units could be multiplexed. Therefore, 1) the number of multiplexed sensors remarkably reduced as the loss increased. As the splicing loss of α for each sensor exceeded 2 dB, only three sensors would be multiplexed. Meanwhile, the former and the latter number of multiplexed sensors can reach 8 and 14 when α is less than 0.5 dB. 2) The number of multiplexed sensors can be increased by reducing the temperature sensitivity due to the known tradeoff between the sensitivity and dynamic sensing range, and it can be increased to 14 if the temperature sensitivities of all sensing units are reduced by half. Notably, the multiplexed spectra from different sensing channels are unbalanced due to the existing loss. However, this issue can be addressed by using a stepwise sensing fiber length of Li = 1.07Li-1, for example, as shown in the bottom panel of Fig. 8(d). The multiplexed capability can also be improved using this method.
Fig. 8 (a) The fitted original temperature sensitivity and FWHM of the signal waves; (b) The number of the multiplexed PCF temperature sensors versus splicing loss of each unit at the original temperature sensitivity and half of it; (c) the simulated output spectra for α = 0.4 and α = 2 dB at the original temperature sensitivity; (d) simulated output spectra for Li = Li-1 and Li = 1.07Li-1 when α = 0.4 dB and S is at the original temperature sensitivity.
The wavelength multiplexing method of the FWM-based sensors is not limited to temperature sensing. It can also be expanded to the multiplex measurement of strain, pressure, and refractive index. For example, the cascaded fiber temperature sensor can be applied to multiplexed refractive index sensing. The temperature sensitivity of the sensor filled with 1.36 oil is 0.207 nm/°C, and the thermal coefficient is −3.41 × 10−4 RIU/°C. Therefore, the sensitivity of refractive index sensing can be estimated to be approximately 607.0 nm/RIU.
6. Conclusions
Wavelength multiplexing of FWM-based PCF temperature sensors is fabricated, and the possibility for multiplexing measurement and multipoint sensing of FWM-based fiber sensors is explored. The FWM-based PCF temperature sensor filled with oils with different refractive indices were designed and fabricated successfully. Moreover, the signal spectral characteristics and sensing performance of the temperature sensor were theoretically and experimentally investigated. By using the fabricated PCF temperature sensor, we achieved the maximum experimental sensitivity of 0.207 nm/°C. With an idler light sensing or a small-core PCF, the temperature sensitivity may be improved further by one or two orders of magnitude due to the excessive evanescent field that penetrates the first air-hole layer, similar to presentation in [15]. However, a tradeoff must be made between the sensitivity and the multiplexed capability. Results showed that good stability and small measurement error can be obtained with oil-filled PCFs. The sensors are cascaded using the wavelength-multiplexed method based on characteristics of the FWM-generated signal light, thereby indicating the feasibility of FWM-based fiber sensors for multipoint temperature measurement. Although only three sensors are cascaded due to the slightly large splicing loss in the experiment, high-capacity sensors are theoretically predicted to be further multiplexed with the optimized splicing and reduced temperature sensitivities.
Funding
The Basic Research Program fund of Shenzhen (JCYJ20160307145209361); National Natural Science Foundation of China (NSFC) (61505115, 61308046, 61775149); Natural Science Foundation of Guangdong Province (2018A030313376).
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