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Abstract
The temperature sensor is the core part of the temperature measurement instrument, and its performance directly determines the temperature measurement accuracy. Photonic crystal fiber (PCF) is a new type of temperature sensor with extremely high potential. In this paper, we propose a high-performance, structurally simple, liquid-filled PCF temperature sensor, which is based on a SMF-PCF-SMF (single mode fiber, SMF) sandwich structure. By adjusting the structural parameters of the the PCF, it is possible to obtain optical properties that are superior to those of ordinary optical fibers. This allows for more obvious responsive changes of the fiber transmission mode under small external temperature changes. By optimizing the basic structure parameters, a new PCF structure with a central air hole is designed, and its temperature sensitivity is -0.04696 nm/°C. When filling the air holes of PCFs with temperature-sensitive liquid materials, the response of the optical field against the temperature fluctuations can be effectively enhanced. The Chloroform solution is used to selectively infiltrate the resulting PCF owing to its large thermo-optical coefficient. After comparing various filling schemes, the calculation results show that the highest temperature sensitivity of -15.8 nm/°C is finally realized. The designed PCF sensor has a simple structure, high-temperature sensitivity, and good linearity showing great application potential.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Owing to its high sensitivity, small size, light weight, corrosion resistance, and resistance to electromagnetic interference, the optical sensor is widely utilized in sensing areas such as temperature sensing [1–8], liquid sensing [9,10], stress-strain sensing [11], humidity detection [12], heavy metal detection [13], gas sensing [14,15], biochemical sensing [16], and so on. The use of optical sensors to measure temperature is one of the most effective ways to improve measurement accuracy. As one of the fundamental physical quantities, temperature plays a pivotal role in many practical applications, such as health monitoring [3], aerial mapping [5], clean energy development [6], fire detection, and pipeline leak detection [8]. In cutting-edge scientific research, such as the detection of gravitational waves [17,18], the accuracy requirements for temperature control are increasing, reaching up to the micro-Kelvin level. In the space environment, conventional electrical sensors are affected by strong electromagnetic interference [19]. This can lead to inaccurate or even jumpy measurement results. While fiber optic temperature sensing has the immunity to electromagnetic interference and the potential for ultra-high accuracy measurement, high-sensitivity optical fiber temperature sensors have become a hot research topic in the past decade. Due to the periodic air hole arrays, photonic crystal fibers (PCFs) can obtain many more excellent properties than conventional step-index fibers by designing the hole size and arrangement, including lower confinement loss, endless single-mode, and other adjustable optical properties [20–23]. The presence of air holes in photonic crystal fibers not only improves sensing sensitivity by optimizing their structural configuration but also provides an excellent platform for filling with functional materials to obtain higher temperature sensitivity. Most of the studies on the sensitization of photonic crystal fiber temperature sensors have also been carried out from these two aspects.
According to previous studies, different PCF structures, filling materials, and filling positions have been proposed and experimentally demonstrated. And almost all of them can improve the sensitivity of PCF sensors more or less. In 2015, Naeem K et al. [24] chose a dual-core photonic crystal fiber with 3.2µm hole diameter and filled the hole next to its core with a polymer material of high thermo-optical coefficient. The temperature sensitivity of -1.595 nm/°C was obtained. In 2017, Ma J et al. [25] designed two types of photonic crystal fibers with slightly different structural parameters and selected six symmetrical air holes in the cladding for filling with toluene. The highest temperature sensitivity of -6.02 nm/°C was finally achieved. In 2018, Shi M et al. [26] removed two air holes near the core in a standard photonic crystal fiber structure. Then, the alcohol was filled with three different schemes respectively. Temperature sensitivities of -0.121 nm/°C, -4.83 nm/°C, and -4.621 nm/°C were correspondingly obtained for the three structures. Compared to the unfilled SMF-PCF-SMF sensor [2], the temperature sensitivity has been improved by two orders of magnitude from -0.0083 nm/°C to several nanometers per Kelvin.
In this paper, in order to obtain high temperature sensitivity PCF, we will start with its structural feature parameters. By optimizing the corresponding structural parameters one by one, a better PCF structure will be achieved. Comparing the different filling solutions, its performance should be further improved. In addition, we proposed a complex random filling method to maximize the temperature sensitivity of the filling PCF.
2. Simulation model
Figure 1(a) and Fig. 1(b) show the SMF-PCF-SMF sandwich structure and the photonic crystal fiber structure, respectively. The diameter of cladding holes is d1 and the diameter of central hole is d2, the spacing between holes is Λ and the offset distance from the center point to the first layer hole is r. To explore the effect of the cladding hole shape on the sensing characteristics, we defined the relative area ratio R to characterize the cladding hole shape, as shown in Fig. 1(c). The area of the circumcircle is defined as S1, which has the same diameter as the cladding hole d1, and the area of the n-sided polygon is S2. Then the relative area ratio R can be expressed as:
Fig. 1. (a) Schematic diagram of the sensor based on SMF-PCF-SMF structure; (b) Cross-sectional view of the designed PCF; (c) Diagram of the relative area ratio R.
The mode field, effective refractive index Δneff and propagation constant β are calculated by the finite element method. The perfectly matched layer (PML) is used as the boundary condition of the model to absorb the evanescent wave energy along the fiber axis. In the simulation process, the substrate material of the fiber is set as fused silica, and the refractive index can be expressed by the Sellmeier equation [27]:
Compared with several different liquid materials in Table 1, chloroform, which has the largest thermo-optical coefficient among them, was chosen to fill the designed PCF. Its refractive index at different temperatures can be expressed as:
where n0 = 1.4467, α=-6.328 × 10−4, T0 = 20°C. Compared with chloroform, the thermo-optical and thermal expansion coefficients of silica are minor and can be neglected in the simulation.
Table 1. Several kinds of liquid material properties
The mode loss can be obtained from equation [28]:
3. Results and discussions
Due to the small thermo-optical coefficient of air, the change of refractive index of air hole is not obvious for small temperature fluctuation. In order to visualize the effective refractive index variation of PCF with different air hole parameters, we replaced the refractive index of air at different temperatures with nhole = 1 and nhole = 1.1 respectively. The larger effective refractive index difference Δneff = neff|n = 1.1- neff|n = 1 indicates the higher sensitivity of the structure. In the wavelength region of 1200∼1800nm, we optimize the number of hole layers m, the cladding hole diameter d1, the relative area radio R, the core diameter dcore, and the diameter of central hole d2 in turn, so as to obtain a lower confinement loss L and a higher difference of effective refractive index Δneff.
The cladding hole diameter d1 = 1 µm, the relative area radio R = 100%, the core diameter dcore = 2 µm and no central hole are set down initially. The number of layers m is set to 1∼5 respectively for finite element simulation. Figure 2 shows the two-dimensional electric field of the PCF when the number of cladding hole layers is 4. It can easily be seen that the light is well confined to the fiber core.
Figure 3 shows confinement loss and effective refractive index difference of the fiber in the wavelength range 1200 to 1800nm, when the PCF has the different number of hole layers. It can be seen that the confinement loss increases with the operating wavelength increasing and decreases with the number of layers increasing. This is because when the number of layers increases, light is more tightly bound in the fiber core, so the energy leakage is reduced, and the loss is lower. Meanwhile, the difference of effective refractive index increases with wavelength. When m turns to 4, the Δneff becomes the maximum value in the wavelength range. The reason for this phenomenon may be that when the cladding diameter and core diameter of the PCF have been determined. With fewer air holes, the air holes are farther from the external environment, and the proportion of air holes is smaller in the fiber cross section. Therefore, the influence of external temperature fluctuations on the optical field inside the fiber is reduced, the difference of the effective refractive index becomes smaller, and the temperature sensitivity becomes lower. As the number of hole layers increases to 5, the difference in effective refractive index decreases conversely. We speculate that this phenomenon is that when there are too many layers of holes, the light is firmly bound in the core, and the influence of the external environment on the evanescent light field is weakened, resulting in a smaller change in the effective refractive index when the temperature changes, and the temperature sensitivity of PCF is reduced. Therefore, considering the two indicators of PCF’s confinement loss and temperature sensitivity, we choose the number of hole layers m = 4 to continue the subsequent calculation.
Fig. 3. (a) Confinement loss changes in 1200-1800nm under different layers; (b) Δneff changes in 1200-1800nm under different layers.
The number of hole layers is selected as m = 4, keeping the relative area ratio R = 100%, the core diameter dcore = 2µm, the core hole diameter d2 = 0. The PCF structures with different hole diameters d1 between 0.6 and 1.4µm are simulated respectively. The relationship between loss and wavelength and hole diameter is shown in Fig. 4. For the same hole diameter, as the incident wavelength increases, the difference of the effective refractive index Δneff also increases. When the diameter of the air hole is small, such as the limit case d1 = 0, the structure of the obtained fiber is similar to that of a simple step-index fiber, the light is totally reflected at the fiber interface, consequently the loss is low. When the hole diameter increases to the range of 0.4∼0.8µm, the PCF's ability to constrain the propagation mode is significantly weakened and the loss increases abruptly. As the hole diameter continues to increase, the effective refractive index of the cladding is reduced by the presence of periodic air hole structures. The refractive index difference between the cladding and core becomes larger, which enhances the fiber's ability to bind light in the core, therefore the loss becomes smaller. Figure 4(b) reveals that there is a maximum value with the hole diameter of 1µm. Taking into account the confinement loss and the difference of effective refractive index, the hole diameter of 1 µm was chosen to continue the calculation.
Fig. 4. (a) Confinement loss changes in 1200-1800nm under different hole diameters; (b) Δneff changes in 1200-1800nm under different hole diameters.
Based on the above simulations, the number of hole layers and the hole diameter have been determined in the PCF’s structure. To investigate the effect of the hole shape on the sensing characteristics, we continued to run a series of simulations for different relative area ratio R. The simulation results are shown in Fig. 5. As can be seen from Fig. 5(a), the loss increases with the increase of wavelength and decreases with the increase of relative ratio. The surge of loss occurred at 1380 nm and 1600 nm is due to the fact that the shape of the orthogonal polygon cannot meet the condition of total internal reflection (TIR) at a specific wavelength, and the light cannot propagate forward for a long distance, thus causing a significant transmission loss. The light transmission performance is best when the hole shape is circular (R = 100%), and there is no sudden increase in loss at a specific wavelength. Figure 5(b) illustrates that with the same temperature variation, the difference of effective refractive index grows with the increase of the relative area radio R. Therefore, the fiber structure is most sensitive to the temperature when the cladding holes are circular. As a result, the shape of the cladding holes for the designed photonic crystal fiber is circular.
Fig. 5. (a) Confinement changes in 1200-1800nm under different hole shapes; (b) Δneff changes in 1200-1800nm under different hole shapes.
According to the above analysis, the structural parameters of the cladding hole are determined already. The structural parameters of the cores need to be further calculated, which are the core diameter dcore and the central hole diameter d2. After preliminary simulations, the selection of fiber core diameter needs to be within a specific range. When the core is over thin, light cannot be transmitted stably in the fiber core. Conversely, an excessively thick fiber can lead to a weak evanescent field. Therefore, the calculation range is selected as 1.8∼4µm, and the results are shown in Fig. 6. In the range of 2∼4µm core diameter, both the loss and the effective refractive index decrease with the increase of core diameter. Although the effective refractive index changes by a larger amount when the core diameter is 1.8um, it is still not chosen. This is because its corresponding transmission loss is also greater, potentially resulting in an insignificant decrease in the transmission spectrum. Hence the final selected core diameter dcore is 2µm.
Fig. 6. (a) Confinement loss changes in 1200-1800nm under different diameters of core; (b) Δneff changes in 1200-1800nm under different diameters of core.
The last undetermined structural parameter is the diameter d2 of the central hole in the fiber core. The core of conventional photonic crystal fibers is solid, but in previous studies special structures such as microstructure core and suspended core have been implemented in the core to achieve high sensitivity for gas [30], liquid [30,31] and temperature sensing [32]. Specializing central hole structure can improve duty cycle, increase the contact area between the filled material and the light field, and make the light field more sensitive to external temperature changes. In order to investigate whether the addition of air hole in the fiber core can enhance the sensing characteristics or not, a series of simulations were conducted and the results are shown in Fig. 7. It can be seen that the diameter of the central hole is positively correlated with fiber loss and sensitivity. The presence of a hole in the core significantly increases the amount of change in the effective refractive index. However, the diameter of the hole in the core cannot be too large, otherwise the light cannot be transmitted in the core (no case of photonic bandgap guiding is considered). Considering the confinement loss and temperature sensitivity, the core hole diameter d2 is eventually selected as 0.25µm.
Fig. 7. (a)Confinement loss vs. wavelength under different diameters of central hole(b) Δneff vs. wavelength under different diameters of central hole.
The final obtained PCF structure parameters are listed in Table 2.
Table 2. Structural parameters of designed PCF
Assuming a PCF length of 1 m, the transmittance can be calculated as
where Pout and Pin are the output intensity and the input intensity, respectively. Figure 8(a) shows the variation of transmissivity as a function of wavelength under different temperatures. There are three groups of resonance peaks in the 1550∼1560 nm band, and the resonance peaks are blue-shifted with the increase of temperature, and the temperature sensitivity is slightly different between each group of resonance peaks. The resonance wavelengths are traced in the transmission spectrum and the resulting data are linearly fitted, as shown in Fig. 8(b). The temperature sensitivities of -0.03093 nm/°C, -0.03896 nm/°C, and -0.04296 nm/°C are obtained for dip1, dip2, and dip3, respectively.Fig. 8. (a) Shift in the interference spectra for various temperature and (b) the average sensitivity of three sets of dip wavelength.
As shown in Table 3, the temperature sensitivity attained by the proposed structure in this work is greatly improved in comparison to the PCF structures without temperature-sensitive material filling in other studies [33–36].
Table 3. Comparasion of structure and performance among proposed PCF and previous work
In order to further enhance the temperature sensitivity, we proposed a new complex random filling method. The chloroform was used as the larger thermo-optical coefficient solution to selectively fill the above structure in this paper. After a variety of experiments with different filling positions, it is found that the temperature sensitivity was highest when the filling position was as shown in Fig. 9. That is, the central air hole and three cladding air holes are filled. Techniques for the selectively filling of photonic crystal fibres with liquid materials are well established in the laboratory. This can be achieved by directly blocking one by one the selected holes with polymerizable glue, or by milling a microchannel into the end facet of a PCF, and by femtosecond laser assisted drilling.
The finite element method is used to calculate the electric field pattern, and the results are shown in Fig. 10. Because the refractive index of chloroform is higher than that of quartz material, there are liquid waveguides in each liquid hole. The effective refractive index of each mode supported by the liquid rod is also different, and the waveguide far from the fiber core has a larger effective refractive index. When the light is transmitted to the fusion splice of PCF and SMF, multiple modes interfere. Although there may be many high-order modes in the fiber, they are neglected here due to their low intensity.
The length of the fused PCF was set to 1 mm. Figure 11(a) shows the relationship between transmittance and wavelength at different temperatures. It can be clearly seen that when the temperature increases, the resonance wavelength shifts to the short wavelength direction, and the shift of the resonance wavelength and the temperature change linearly. From Fig. 11(b), a linear fit to the resonant wavelength gives a temperature sensitivity of -15.8 nm/°C and a linearity of 99.5% for the proposed sensor structure after selective filling. Theoretically, the designed temperature sensor can be used in the temperature range between the freezing point and the boiling point of chloroform solution, i.e. -63.5°C to 63.3°C. In this temperature range, the thermo-optical coefficient of chloroform solution is relatively constant. In room temperature application scenarios, we can consider the designed temperature sensor is effective in a wide range of 15°C∼55°C.The ultra-high temperature sensitivity is achieved, which is more than 300 times higher compared to the unfilled one, and the linearity is quite excellent. The highest resolution of the spectrum analyzer currently available in the laboratory is 0.01 nm (YOKOGAWA, AQ6370D), thereby the proposed sensor can obtain a temperature resolution of up to 6.33 × 10−4 °C in theory. Compared to another study published in 2020 [37], our design structure is simple, the sensing system is light, and the sensitivity is comparable. If the sensor structure designed by us is also put into the Sagnac interference loop, the temperature sensitivity will be greatly improved.
Fig. 11. (a) Temperature response of the interference spectrum; (b) Temperature sensitivity around T = 20°C.
4. Conclusion
In summary, a novel PCF temperature sensor featuring a central air hole has been successfully designed with excellent temperature sensing performance by optimizing each structural parameter of the PCF in this paper. We have investigated the variation of the transmission characteristics of photonic crystal fibers with different structural parameters such as the number of hole layers, the diameter of the cladding hole, the relative area radio of the hole, the core diameter, and the central core hole diameter. A PCF structure with high sensitivity and low limiting loss has been designed. The structure can reach to a temperature sensitivity of -0.04296 nm/°C without functional material filling, which is three times higher than that of the same type of sensing structure. The temperature sensitivity of -15.8 nm/°C is achieved after selective filling with a temperature-sensitive chloroform solution. The good temperature measurement performance and high linearity make it competitive in the field of temperature sensing. In addition, the structure of the designed PCF is simple and easy to be produced. The type of SMF-PCF-SMF sandwiched structure is compact and lightweight, which is suitable for temperature measurement in various applications.
Funding
National Key Research and Development Program of China (2021YFC2202100, 2022YFC2203801, 2022YFC2203802).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
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