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Abstract
A two-core photonic crystal fiber (TC-PCF) based highly-sensitive temperature sensor was proposed and demonstrated. By selectively infiltrating the central airhole with refractive index liquid (RIL), a three-parallel-waveguide structure was formed. A dual-component interference pattern, consisting of a large spectrum envelope and fine interference fringes, was observed in the transmission spectrum. The simulation results confirmed that the interference was arising from a few hybrid supermodes in the fiber coupler structure. They were in good agreement with the experimental observation on the discrete temperature windows with different temperature sensitivities due to couplings between different hybrid supermodes in respective temperature windows. By tracing the wavelength shifts of the large spectrum envelope, high sensitivities were achieved at 42.621 nm/°C in the temperature range from 54.2 °C to 55 °C and 32.159 nm/°C from 51.8 °C to 52.6 °C.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber optic temperature sensors have been developed and widely used owing to their compact structure, lightweight, electromagnetic interference immunity, large transmission capacity, and ease in implementing multiplexed or distributed measurement [1–3]. Various types and configurations of optical fiber sensors for temperature measurement have been developed, such as fiber Bragg gratings (FBGs), interferometric optical structures, and distributed temperature sensors [2]. However, the sensitivity of the temperature sensor formed by conventional optic fiber is limited due to the weak temperature response of pure silica [4].
In comparison with conventional optical fibers, photonic crystal fibers (PCFs) demonstrate unique characteristics, including high design flexibility, controllable effective area, and adjustable dispersion [4–7]. In particular, the periodically arranged air holes running through the fiber length support a variety of novel post-processing potentials for additional functionality, such as the liquid infiltration by capillary effect [5–9]. The ease of infiltrating liquid with high thermo-optic coefficient into air holes enables optofluidic PCF a natural candidate for temperature measurement with better sensitivities [10–16]. Moreover, most evanescent-wave-based optofluidic PCF sensors for temperature measurement at present, are based on configurations to infiltrate airholes at the innermost cladding layer selectively [11–13]. By this means, high-temperature sensitivity can be achieved with an enlarged overlap of the optic field with the liquid rod [9,15]. PCF sensor with high temperature sensitivity was achieved at −3.86 $nm/^\circ \textrm{C}$ by infiltrating single void next to the solid core of PCF with nematic liquid crystal [11], 7.3 $nm/^\circ \textrm{C}$ by selective filling two adjacent airholes of the innermost layer with high RI liquid [12], 14.72 $nm/^\circ \textrm{C}$ with RI liquid filled into three adjacent airholes surrounded the solid core [13]. Numerical analysis of selectively filled PCF based temperature sensor shows good promise to achieve high sensitivities, such as infiltrating six airholes in the second inner layer with toluene to achieve −6.02$\; nm/^\circ \textrm{C}$ [14]. Precise control of the selective toluene infiltration into the six airholes at targeted positions is required and can be challenging in the experiment. In addition, the main drawback of liquid-infiltrated solid-core PCF is the relatively weak interaction of the solid core guided light with the liquid rod since evanescent field penetration depth is limited [9].
Higher light-matter-interaction and thus, better sensing performance can be achieved by guiding the light directly inside the liquid rod [7,9,10]. Therefore, in this study, a high thermo-optic coefficient refractive index liquid (RIL) with selected RI was introduced in the central airhole of a TC-PCF. A numerical analysis using a similar TC-PCF structure was reported in our previous study, showing simulated temperature sensitivity up to −6.91$\; nm/^\circ \textrm{C}$ based on the direct tracking of resonance wavelengths [10]. In this work, both numerical and experimental investigation of the liquid-filled TC-PCF are carried out. The central liquid waveguide acted as the central liquid core, ensuring strong interaction between the guided light and the liquid inside the liquid rod. Besides, the high-temperature-dependent RI of proposed RIL is modulating the directional coupling of the two solid cores and forming a three-core in-fiber coupler structure with efficient power transfer among a few hybrid supermodes. A dual-component interference pattern was observed with a large envelope spectrum and fine fringe interference pattern over the temperature range from 50 $^\circ \textrm{C}$ to 58.2 $^\circ \textrm{C}$. The numerical simulation revealed that the large envelope pattern resulted from the interference between different hybrid supermodes of the three-parallel-waveguide structure. By tracing the peak wavelength shift of large envelope spectrum with the variation of temperature, the largest sensitivity obtained by the sensor was achieved at 42.621 $nm/^\circ \textrm{C}\; $in the temperature range from 54.2 $^\circ \textrm{C}$ to 55 $^\circ \textrm{C}$.
2. Sensor design and fabrication
2.1 Sensor fabrication and experiment setup
The TC-PCF (commercially available from YOFC) used in the experiment has a cross-section as shown in Fig. 1(a). The airhole diameter d equals to 2.3 $\mu m$, solid core diameter d1 is 4 $\mu m$, and hole to hole pitch Λ is 4 $\mu m$. The microscope image of the proposed TC-PCF with a liquid-infiltrated central core is presented in Fig. 1(b), where the airhole between two solid cores was filled with RIL (Cargille Labs, Series A, product 1809, see dataset. Ref. 17). Selective infiltration of the TC-PCF was done by the direct manual gluing method [6]. The TC-PCF, with clean and well-cleaved fiber ends, was first fixed under a microscope. A tapered single mode fiber (SMF) with the fiber tip dipped with UV glue (NOA81, Norland) was then fixed on a three-dimensional (3D) stage. By adjusting the 3D stage, the UV glue was transferred onto the TC-PCF fiber end, covering the air holes except the central airhole. After the UV glue was solidified by exposing the fiber end under the UV light (Thorlabs, CS2010), only the central airhole was open for infiltration.
Fig. 1. (a) SEM image of the TC-PCF; (b) Microscope image of the TC-PCF with RIL-filled central core; (c) Schematic diagram of the experimental setup for temperature sensing.
The selective liquid infiltration by the capillary effect was realized by putting this selective blocked TC-PCF end into the RIL. The TC-PCF was infiltrated over 24 hours to ensure that the central airhole was fully filled with RIL (over 8 $cm$). The selective infiltration was confirmed by visually examining the cross-section view of the TC-PCF at the other fiber end. The RIL-filled central core is clearly visible in the microscope image of the infiltrated TC-PCF, as shown in Fig. 1(b). The RIL-filled central airhole illustrated as a white spot between two solid cores, and the black spots presented the un-filled airholes.
The temperature response of the central airhole filled TC-PCF was then studied experimentally. A 1.8 $cm$ RIL-filled TC-PCF was spliced with two pieces of SMF (commercially available from YOFC) at both fiber ends by using a fusion arc splicer (Fujikura, FSM-100P+) with optimized settings. The fusion splicing between the RIL-filled TC-PCF and the SMF was done with a center-to-center alignment. To minimize the airhole collapse and the RIL evaporation of the RIL-filled TC-PCF, an arc position offset at 50 $\mu m$ from TC-PCF and SMF joint. Then the sample was fixed inside the temperature-controllable oven (HC Photonics Corp., TC038-PC) with an accuracy of 0.1 $^\circ \textrm{C}$. The schematic diagram of the experimental setup was shown in Fig. 1(c). The transmission spectrum was recorded with temperature increment from 50 $^\circ \textrm{C}$ to 58.2 $^\circ \textrm{C}\; $by a step of 0.2 $^\circ \textrm{C}$. One of the SMF was connected to a broadband light source (Infinon Research, IRBL-11111-F), which wavelength range was from 1270 $nm$ to 1650 $nm.$ The connection was using an FC/PC (Ferrule Connector/Physical Contact) single mode connector, which is a fiber-optic connector with a threaded body designed for reducing the influence of environmental vibration. The other SMF was connected to the optical spectrum analyzer (Yokogawa, AQ6370C) to collect the transmission spectrum at different temperatures.
2.2 Theories and simulation
In the modified TC-PCF, the RI of the central liquid rod was slightly higher than the value of silica, resulting in a three-parallel-waveguide structure formed by central liquid rod and two solid cores with narrow waveguide separation, leading to strong coupling between the silica core modes and the liquid core modes [6,15,16,18]. Besides, the central liquid core in the three-parallel-waveguide structure ensures significant light-matter interaction, which is beneficial in leveraging the high thermo-optic coefficient of the liquid to achieve high temperature sensitivity. The proposed waveguide structure with a central core filled with RIL enabled mode energy beating and resulted in a dual-component interference pattern over a wide wavelength range [19–21].
To have a more in-depth insight into the proposed RIL-filled TC-PCF, we firstly consider the mode properties in a single liquid core PCF and an unfilled TC-PCF, which consists of the same cladding structure as that in Fig. 1(b) The mode analysis of both PCF structures was using the finite element method (COMSOL Multiphysics). The RIL used in the experiment has the thermo-optic coefficient $dn/dT\; = \; - \; 0.000389\; RIU/^\circ \textrm{C}$ (where RIU stands for refractive index unit) [17,22,23]. The Cauchy equation of the RIL is given by:
The RI of background silica was calculated by taking consideration of both temperature and wavelength dependence [24]. The dispersion curves of the fundamental mode LP01 and the LP11 mode of both PCF structures were plotted in Fig. 2(a) and Fig. 2(b), respectively. The LP11 mode in the single liquid core PCF is degenerate and denoted as TE01, TM01, and HE21 mode. The mode properties of the unfilled TC-PCF and the single liquid core PCF were analyzed at 50 $^\circ \textrm{C}$, 1500 $nm$ for illustration purpose. Only x component of the electric field distribution of the modes were plotted in Fig. 2 as inset figures. White arrows represent the direction of electric field distribution where even modes are always symmetric in the two solid cores, while the directions of odd modes in two solid cores are antisymmetric [25].
Fig. 2. Dispersion curves of the unfilled TC-PCF and the single liquid core PCF with the mode distribution; (a) The LP01 mode (inset figure) of single liquid core PCF and the fundamental supermodes of the unfilled TC-PCF (inset figure). (b) The LP11 mode (inset figure) of single liquid core PCF and the LP11 supermodes of the unfilled TC-PCF (inset figure); all mode profiles are plotted at 50 $^\circ \textrm{C}$, 1500 $nm$ with only x polarization for simplification, the white arrow indicates the direction of electric field distribution.
At the point of intersection corresponding to the phase matching wavelength, the associated modes in two structures have the same effective index, where the coupling occurs around the resonance wavelengths. It is shown in Fig. 2(a) and Fig. 2(b) that the mode couplings can occur between the fundamental modes or among higher order modes in these two coupled waveguide structures. Previous studies have shown that the coupling between solid cores and the liquid core only occurs when the supermodes of the unfilled TC-PCF have substantial overlap with the central liquid rod, including Even LP01_x, Odd LP11_a_x, and Even LP11_b_x as shown in Fig. 2. So, only the intersection regions of central liquid mode and above mentioned supermodes of the unfilled TC-PCF were circulated by the dashed circle in Fig. 2(a) and Fig. 2(b) [26].
It should be noted in Fig. 2(b), one of the supermodes denoted as Even LP11_b_x in the unfilled PCF structure is very close to the TE01, TM01, and HE21 curves in a broadband window, e.g., from 1500 $nm$ to 1700 $nm$ in Fig. 2(b). The close proximity of the mode dispersion curves in these two PCF structures in a broad wavelength range means the mode coupling will occur in a broad wavelength window between the two coupled waveguides. This is different from the previously reported optofluidic PCF-based temperature sensors, which sensing characteristic was derived from the critical phase matching condition, leading to a sharp resonance dip within only a small wavelength range for light energy coupling [16,26]. Moreover, the neighboring cores were sufficiently close for evanescent wave coupling between optical modes, supporting the transfer of power from one core to another.
Subsequently, the hybrid supermodes in the proposed RIL-filled TC-PCF structure were investigated to confirm the mode coupling between the silica core and the liquid core. The mode profiles were calculated at 50 $^\circ \textrm{C}$, 1500$\; nm$, and plotted in Fig. 3. Only x-polarized state was shown for illustration purpose.
Fig. 3. Simulation of the first eight supermodes field distribution of the RIL-filled TC-PCF at 1500 $nm$; (a)–(c) The fundamental supermodes, (a) symmetric mode, (b) decoupling mode, and (c) antisymmetric mode; (d)–(h) The higher-order supermodes; all mode profiles are plotted at 50 $^\circ \textrm{C}$, 1500 $nm$, only the x-polarization state was plotted, and the white arrows indicate the direction of the electric field distribution.
The first three dominant hybrid supermodes of the proposed RIL-filled TC-PCF can be treated as the fundamental supermodes of the three-parallel-waveguide, as shown in Figs. 3(a)–3(c), labeled as symmetric mode(a), decoupling mode(b) and antisymmetric mode(c) [16,27]. Since both the single liquid core PCF and the unfilled TC-PCF structure support higher-order modes, it was confirmed in Figs. 3(d)–3(h) that the higher-order supermodes were superposition of LP11 mode of the central liquid-core with LP11 supermodes of two-solid-core.
3. Experimental result and discussion
Transmission spectra of the RIL-filled TC-PCF at 54 $^\circ \textrm{C}$ (solid purple line) and 54.4 $^\circ \textrm{C}$ (solid green line) were given in Fig. 4(a), respectively. Two interference components were observed in the transmission spectrum with a large envelope and fine fringe interference pattern [19–21]. The fitted curves of each spectrum were extracted by a low pass filter (cutoff frequency at 0.0208 $\textrm{Hz}$) shown as the purple (54 $^\circ \textrm{C}$) and the green dash lines (54.4 $^\circ \textrm{C}$) in Fig. 4(a). The dots on each large envelope spectrum corresponding to the peak wavelength, respectively. In the meantime, the simulated interference transmission spectrum (dashed red curve) between x polarized mode(g) and mode(h) of a 1.8 $cm$ RIL-filled TC-PCF at 54 $^\circ \textrm{C}$ was compared with the experimental result (solid black curve). The simulated spectrum was in good agreement with the experimental result, as shown in Fig. 4(b). With the increase of temperature, the RI of the RI-filled liquid waveguide kept decreasing, according to Eq. (2), modulating the RI of the hybrid supermodes that were involved in the interference and leading to a redshift of the resonance wavelength peak.
Fig. 4. (a) Transmission spectra of the proposed dual-component interference at 54 $^\circ \textrm{C}$ and 54.4 $^\circ \textrm{C},$ with a RIL-filled TC-PCF length at 1.8 $cm$; (b) Comparison of experimental results (solid black curve) and the simulated result (red dash curve) of a 1.8 $cm$ RIL-filled TC-PCF at 54 $^\circ \textrm{C}$; (c) Peak wavelength shifts as a function of temperature ranges from 50 $^\circ \textrm{C}$ to 58.2 $^\circ \textrm{C}$, the inset figure represents the temperature sensitivity of proposed sensor with temperature increase (solid black square) and temperature decrease (red open circle) in the temperature range from 50 $^\circ \textrm{C}$ to 58.2 $^\circ \textrm{C}$;
The wavelength shifts of resonance peak within the temperature range from 50 $^\circ \textrm{C}$ to 58.2 $^\circ \textrm{C}$ were shown in Fig. 4(c). The temperature sensitivities are approximated by linear fitting the measurements in six temperature ranges. The highest sensitivity is up to 42.621 $nm/^\circ \textrm{C}$ in the temperature range from 54.2 $^\circ \textrm{C}$ to 55 $^\circ \textrm{C}$. In addition, the measurement was also carried out by reducing the temperature from 58.2 $^\circ \textrm{C}$ to 50 $^\circ \textrm{C}$. The temperature sensitivity of the cooling process (red open circle) has good agreement with the sensitivity measured during the heating process (solid black square), as shown in the inset figure of Fig. 4(c). The reason for having different sensitivities in each temperature range could be attributed to the presence of different supermodes that have different temperature sensitivities in each temperature range. The analysis is presented in Fig. 5–7. The comparison of the experimental results of the proposed sensor with previously reported liquid-infiltrated PCF based temperature sensors is presented in Table 1.
Fig. 5. X-polarized supermodes interference condition as a function of temperature; (a) Represents the interference condition from 51.8 $^\circ \textrm{C}$ to 52.6 $^\circ \textrm{C};$ (b) Represents the interference condition from 54.2 $^\circ \textrm{C}$ to 55 $^\circ \textrm{C}$; The insets are interfering modes involved.
Table 1. Comparison of experimental results of various liquid infiltrated PCF-based temperature sensors
Unlike the solid triple-core PCF, the mode field distribution, and the light intensity distribution of RIL-filled TC-PCF were temperature-tunable, leading to different interference spectra over the temperature range. The low-frequency envelope of the transmission spectrum of the RIL-filled TC-PCF was considered as a simplified case of two-mode interference [19]:
where ${I_1}$ and ${I_2}$ are the transmission intensities of two modes involved in the interference. Due to the significant thermo-optic coefficient of proposed RIL, leading to a significant RI variation of RIL-filled channel with the temperature change. Therefore, the phase change of the RIL-filled TC-PCF was mainly caused by the variation of RI difference between two modes as a function of temperature, which can be expressed as [36]:The interferences of different supermodes under specific temperature ranges are simulated, as shown in Fig. 5 to Fig. 7. Supermodes involved in different temperature ranges are identified based on the experimental results of RI differences, which are deduced from the FSR of the low-frequency envelope in the transmission spectrum. After the supermodes are identified in each temperature window, the simulated temperature sensitivity is calculated using Eq. (5) and compared with the measured sensitivities.
In Fig. 4(c), the highest temperature sensitivity can be observed within temperature ranges from 51.8 $^\circ \textrm{C}$ to 52.6 $^\circ \textrm{C}$ and 54.2 $^\circ \textrm{C}$ to 55 $^\circ \textrm{C}$, which are 32.159 $nm/^\circ \textrm{C}$ (with FSR of 75.592 $nm$) and 42.621 $nm/^\circ \textrm{C}$ (FSR of 82.640 $nm$), respectively. The deduced effective mode RI difference between two interfering modes are $\Delta n = \; 0.0013794$ from 51.8 $^\circ \textrm{C}$ to 52.6 $^\circ \textrm{C}$, and $\Delta n = \; 0.0013555$ from 54.2 $^\circ \textrm{C}\; $to 55 $^\circ \textrm{C}.$ These RI differences are corresponding to two fundamental supermodes of the three-waveguide-structure, namely symmetric mode(a) and decoupling mode(b). Fig. 5 shows the simulated mode profile of the two fundamental supermodes and the temperature dependence curve of the effective mode RI difference $\partial ({\Delta n} )/\partial T$. In temperature ranges 51.8 $^\circ \textrm{C}$ to 52.6 $^\circ \textrm{C}$, and 54.2 $^\circ \textrm{C}$ to 55 $^\circ \textrm{C}$, the simulated effective mode RI difference $\Delta n = \; 0.0013794$, and 0.00145227. The simulated temperature sensitivity is 34.921 $nm/^\circ \textrm{C}\; $and 34.499 $nm/^\circ \textrm{C},$ respectively.
The rest of the experiment results of temperature sensitivity within different temperature ranges can be explained by the interference of higher-order supermodes. The interference between mode(g) and mode(h) was contributed to the temperature sensitivity within temperature ranges, 53.4 $^\circ \textrm{C}$ to 54.2 $^\circ \textrm{C},$ and 55 $^\circ \textrm{C}\; $to 58.2 $^\circ \textrm{C}$, as shown in Fig. 6. The deduced $\Delta n = \; 0.0011406$ within 53.4$\; ^\circ \textrm{C}\; $to 54.2 $^\circ \textrm{C}$ (experimental FSR around 96.828 $nm$). The simulated temperature sensitivity is 16.215 $nm/^\circ \textrm{C},$ with $\Delta n = \; 0.0011280$, which accords with the experiment sensitivity of 14.648 $nm/^\circ \textrm{C}.\; $In the temperature range 55 $^\circ \textrm{C}$ to 58.2${\; }^\circ \textrm{C},$ the deduced RI difference $\Delta n$ equals to 0.0009911, corresponding to FSR around 119.490 $nm$. The experimental temperature sensitivity is 19.634 $nm/^\circ \textrm{C}.$ The numerical result of sensitivity is 17.682 $nm/^\circ \textrm{C},$ with $\Delta n\; = \; 0.0010328$.
Fig. 6. X-polarized supermodes interference condition as a function of temperature; (a) Represents the interference condition from 53.4 $^\circ \textrm{C}$ to 54.2 $^\circ \textrm{C}$; (b) Represents the interference condition from 55$\; ^\circ \textrm{C}\; $to 58.2 $^\circ \textrm{C}$; The insets are interfering modes involved.
Fig. 7. X-polarized supermodes interference condition as a function of temperature; (a) Represents the interference condition from 50 $^\circ \textrm{C}$ to 51.8 $^\circ \textrm{C}$; (b) Represents the interference condition from 52.6 $\; ^\circ \textrm{C}\; $to 53.4 $^\circ \textrm{C}$; The insets are interfering modes involved.
As shown in Fig. 7(a), two interfering mode are mode(e) and mode(f) with deduced $\Delta n\; = \; 0.0012758$ (experimental FSR is around 79.361 $nm$). Within temperature range from 50$\; ^\circ \textrm{C}\; $to 51.8 $^\circ \textrm{C},$ The experimentally measured temperature sensitivity is 14.713$\; nm/^\circ \textrm{C}$, and the simulated result is 15.098$\; nm/^\circ \textrm{C}$ with $\Delta n = \; 0.0012941.$ For temperature range from 52.6 $^\circ \textrm{C}$ to 53.4 $^\circ \textrm{C}$, mode(d), and mode(e) were identified to be the two interfering modes with deduced $\Delta n = \; 0.0011526$. The simulated sensitivity is 0.9122 $nm/^\circ \textrm{C}\; $and the corresponding $\Delta n\; = \; 0.00114288$, in good agreement with the experiment result of sensitivity 1.025 $nm/^\circ \textrm{C}$ with FSR around 93.122 $nm$. The comparison between the experimental results and the simulated results in different temperature ranges was shown in Table 2.
Table 2. The comparison between simulation and experiment results of different temperature windows
4. Conclusion
In conclusion, we have experimentally demonstrated a highly-sensitive temperature sensor with a temperature detection range from 50 $^\circ \textrm{C}\; $to 58.2 $^\circ \textrm{C}$ by infiltrating RIL with a high thermo-optic coefficient into the central airhole of TC-PCF to form a three-parallel waveguide structure. The highest sensitivity obtained by the sensor was 42.621 $nm/^\circ \textrm{C}\; $in the temperature range from 54.2 $^\circ \textrm{C}$ to 55 $^\circ \textrm{C}.$
Funding
Ministry of Education - Singapore, Academic Research Fund Tier 1 (MOE2019-T1-001-111).
Acknowledgments
This work was supported by the Ministry of Education - Singapore, Academic Research Fund Tier 1 (MOE2019-T1-001-111). We thank the Yangtze Optical Fibre and Cable Joint Stock Limited Company (YOFC) for providing the TC-PCF.
Disclosures
The authors declare no conflicts of interest.
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