1. Introduction

Photonic crystal fibers (PCFs) are specialty optical fibers with a two-dimensional periodicity of varied refractive indices over the fiber cladding region, either by introducing air-hole structures or using multi-component materials [1,2]. Such a microstructured fiber cladding enables advantageous properties for optical waveguides, dispersion management, and controllable transmission etc [1–4]. Since the optical properties of PCFs are strongly related to fiber structures, they can be easily altered through the modification of fiber structural parameters [4]. During the last two decades, PCFs have been investigated extensively for applications such as pulse compression, high harmonic generation, broadband light sources, fiber sensing and particle guidance [4–10]. Recently, fiber sensing using PCFs has attracted lots of research passions and novel sensing architectures have been well demonstrated [11–15]. A good reason using PCFs for sensing is that, due to large air channels in the fiber cladding, it is simple to infiltrate sensing liquids or gases into the fiber, and hence significantly enhances the light-mater-overlapping, so as the sensitivity. For example, to fill PCFs with temperature sensitive liquids or magnetic fluids, PCF-based temperature or magnetic field sensing can be proposed. In 2015, Dash et al. reported a Fabry-Perot interferometer based on a PCF with an inner microcavity, and the temperature sensitivity reaches 12 pm/°C [16]. Similarly, Ali et al. demonstrated a PCF Fabry-Perot temperature sensor based on fiber Bragg grating (FBG) with a sensitivity of 12.1 pm/°C [17]. Most PCF-based of interferometric and FBG temperature sensors, however, have relatively low sensitivity of tens of pm/°C. To improve the sensitivity, Yin et al. designed a PCF sensor by filling CdSe/ZnS quantum dots [18]. The fluorescence wavelength of the quantum dots shifts at different temperatures, and the sensitivity reaches 130.9 pm/°C. In 2012, Hu et al. reported another PCF-based temperature sensor [19]. By selectively filling a PCF with liquid crystal 6CHBT, mode-coupling can be excited, and the sensitivity is as high as 3.86 nm/°C. However, this sensor has a limit that the working range of temperature monitoring is restricted to 42–54 °C. Obviously this limits the real application under severe situations of extreme temperatures. Lu et al. demonstrated a PCF-based temperature sensing system by infiltrating silver nanowire and liquid into a PCF [20]. With enhanced surface plasmon resonance (SPR), this sensor offers a high sensitivity of 2.7 nm/°C. Unfortunately, the silver nanowires agglomerate with time. Consequently, the SPR peaks fluctuate irregularly, making the detection inaccurate.

In this study, to further improve the sensitivity and stability, as well as explore new sensing architectures, we proposed a novel system based on mode-coupling effect, using a selectively filled solid-core PCF with a central air-bore. The PCF was fabricated using the “stack-and-draw” procedure, and an air bore of ~2 μm was introduced into the fiber core through a careful design of the fabrication procedure. Rather than a normal solid-core PCF, using such an air-bore structure can provide enhanced efficiency of inter-modal coupling between the fundamental core mode and several higher order modes (HOMs) in the fiber cladding, and thus offers a new mechanism of monitoring the alteration of physical quantities through the conversion of optical modes. Toluene, as a temperature sensitive liquid, was filled into the six meristic holes of the fiber cladding through a multi-step filling procedure to excite several liquid-core modes, simultaneously coupled with the fundamental core mode. The mode-coupling between the fundamental mode and liquid-core modes in fiber cladding, influenced by temperature variation, is the main basis for improved performance on temperature sensing. The sensing properties were numerically verified using finite element method (FEM). To make the system practical, a probe with improved sensitivity and manipulation is proposed in the last part of this paper.

2. Fiber fabrication and theory

The solid-core PCF was drawn using the multi-step “stack-and-draw” procedure, as shown in Fig. 1. Fifty-five capillaries and six rods of ~1.5 mm in diameter were drawn from high-purity fused silica tubes/rods (Heraeus, Germany). They were stacked layer by layer in a home-made stacking rig. Note that in the center, instead of using a solid rod, we put a capillary to create a central void in the structure. In addition, for the first ring, six rods were inserted, as shown in Fig. 1(a). The whole stack was then inserted into a silica tube to avoid the stacked capillaries/rods from losing right positions. Figure 1(b) shows the first drawing step. The whole stack was drawn on our customized tower to ~2 mm canes, at a temperature of ~1950 °C. After the first drawing, the structure was proportionally scaled down to ~1/10 of its original stacking size. In order to further scale down the structure to micro-scale, another drawing was performed by inserting a cane into another jacket tube to form a final preform. This preform was then drawn again into fibers of 180 μm, at 2050 °C, as shown in Fig. 1(c). During both the cane and fiber drawing, we carefully controlled the pressures in different areas to form expected structures.

 

Fig. 1 Multi-step “stack and draw” procedure for capillary, rod, cane and fiber drawing

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With the above technique, we fabricated two pieces of PCFs with slight difference in structural parameters, as listed in Table 1. The two fibers have outer diameters of 180 μm. The pitch (Λ), the diameter of the central (d₁) and cladding holes (d₂), and the distance between the central hole and nearby holes (Λ’), are listed in Table 1 and marked in Fig. 2(c). Figures 2(a) and 2(b) are the scanning electron microscopic (SEM) photos of PCF1, shown as an example of the fabricated fibers. The measured structural parameters were later used for constructing a model for numerical calculations. In the fiber model used for simulation (Fig. 2(c)), a ten-micrometer-thick perfectly matched layer (PML) and scattering boundary conditions are adopted at the periphery of cladding to eliminate boundary reflections.

Table 1. Structural parameters of solid-core PCFs with a central bore.

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Fig. 2 SEM photographs of the fabricated fiber (a) and enlarged cladding area (b). (c) A simplified model for finite element calculation. Note that the six grey holes represent the ones filled with toluene. A PML (yellow region) was added to avoid fictitious reflections.

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The refractive index of fused silica glass n_silica is governed by the Sellmeier equation:

The refractive index of toluene n_toluene is calculated through the following equation [22]:

The equation used to calculate the confinement loss of mode, α_loss, in dB/m, is from [23]:

3. Results and discussion

Over the wavelength range of 0.3~2 μm, the refractive index of toluene, calculated using Eq. (2), is always higher than that of fused silica at the same temperature. So when to fill toluene into the six meristic holes in the fiber cladding (Fig. 2(c)), each of these holes forms effective waveguides through total internal reflection (TIR), which means light can be trapped and propagates through the liquid cores in the cladding, and so as stable liquid-core modes are formed. The attenuation of these individual liquid-core modes in fiber cladding, however, is wavelength dependent, and strongly relies on the absorption originated from toluene.

It is obvious that the central air bore can strongly influence the fiber core modes. The reduced mode area, for example, effectively modifies the corresponding mode indices, which provides a possibility to couple light between the core mode and the individual liquid-core modes in fiber cladding, due to similar effective indices of the two cases. The size of the central air-bore, therefore, was carefully controlled during fiber drawing, in order to fulfill the above theory. The mode profiles were calculated using FEM, using the model depicted in Fig. 2(c). Figure 3 shows the results. Due to the central air-bore, the core LP₀₁ mode (referred to the fundamental core mode later in the paper in order to be distinguished it from the liquid-core LP₀₁ mode in fiber cladding) has a null in the center. This fundamental core mode has the highest index and lowest confinement loss. However, when the six meristic holes in cladding are filled with toluene, several liquid-core modes appear as a multi-core fiber. The strongest liquid-core modes are the individual liquid-core LP₀₁ mode with two degeneracy ($H{E}_{01}^x$and$H{E}_{01}^y$) and individual liquid-core LP₁₁ mode with four degenerate states (TM₀₁, TE₀₁, $H{E}_{11}^x$and$H{E}_{11}^y$). Figure 3(d) shows the normalized electric field distribution of the fundamental core mode when it is coupled into liquid cores in cladding which are filled with toluene. If we then consider to further modify the index of toluene by varying temperature, so as to the effective indices of the liquid-core modes, the mode couplings between the fundamental core mode and liquid-core modes are either more effective, or hard to observed, due to the difference in effective indices, at specific wavelengths. This provides us the principle of temperature sensing by the observation of the coupling wavelengths.

 

Fig. 3 Normalized electric field distribution of supported mode profiles in the solid-core PCF. (a) The fundamental core mode. Note that the air-bore in the middle of the core contributes a central null of the electric field. (b) Normalized electric field distribution of the liquid-core LP₀₁ modes and (c) the liquid-core LP₁₁ modes (TM₀₁) in fiber cladding. (d) Field distributions of the hybrid mode when mode coupling occurs.

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Mode-coupling happens when two modes have close/same effective indices. Figure 4(a) plots the effective indices of the fundamental core mode and the two degenerated liquid-core LP₀₁ modes, as a function of wavelength. It can be observed that the refractive indices of the liquid-core LP₀₁ modes (green curve) are always higher than that of the fundamental core mode (red curve). Such a non-cross of the two curves means that the two modes are never in phase, i.e. the fundamental core mode cannot be coupled into the liquid-core LP₀₁ mode in fiber cladding or vice versa. On the other hand, the refractive indices of the first higher order individual liquid-core mode, LP₁₁ (Fig. 3(c)), which has four degeneracy (TM₀₁, TE₀₁, $H{E}_{11}^x$ and $H{E}_{11}^y$), has same effective indices with that of the fundamental core mode, at specific wavelengths. When modal coupling happens, a hybrid mode is then co-existed in both the fiber core and the cladding holes filled with toluene. Light is no longer confined only in the central core but leaks out into the liquid core in the cladding, presented as stable liquid-core modes in fiber cladding, when a proper waveguide reaches. This is the reason that at the coupling wavelengths, there are a significantly rise (~4 to 5 orders) of the attenuation of the fundamental core mode, and hence forms a high loss peak in the loss spectrum, as shown in Fig. 4(b). It has also been verified that, when the six designated holes are selectively filled with toluene, the mode-coupling between the fundamental core mode and individual liquid core modes in the fiber cladding, is largely enhanced. On the contrary, when other holes are filled, the modes leaked from the central core, are no longer phase matched with the ones in the liquid-filled cladding cores. Consequently the coupling is reduced. In the latter case, the mode-coupling efficiency may be re-gained, when different fiber structural parameters such as the core and central bore diameters, pitch, air-filling-fraction, are carefully modified.

 

Fig. 4 (a) Calculated effective refractive indices of the fundamental core mode (red) and the liquid-core LP₀₁ mode (green) in the wavelength range 0.4 to 2.0 μm. (b) Calculated effective refractive indices of the fundamental core mode (red) and four degenerated liquid-core LP₁₁ modes between 0.86 and 0.92 μm, within which region the mode coupling happens. The confinement loss spectrum of the fundamental core mode is plotted in the same figure (magenta, right axis).

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In summary, from Fig. 4(b), when the liquid-core LP₁₁ modes in fiber cladding (more specifically, TM₀₁, TE₀₁, $H{E}_{11}^x$ and $H{E}_{11}^y$) and the fundamental core mode (fiber core LP₀₁ mode) are phase matched, the mode-coupling occurs. From Fig. 4(a), however, it can be seen the effective refractive index of liquid-core LP₀₁ mode in fiber cladding is always higher than that of fundamental core mode, so these two modes never match to each other. By monitoring the coupling wavelengths between the liquid-core LP₁₁ modes in fiber cladding and the fundamental core mode, the temperature sensing can be realized.

Figure 5(a) shows the relationship between the confinement loss and wavelength at different temperatures. At coupling wavelengths, the confinement loss of the fundamental core mode has a sharp increase and thus it is possible to determine the coupling wavelengths from the output spectra. It is clear that the coupling wavelength blue shifts from 1.02 μm to 0.86 μm when the temperature rises from 0 to 25 °C and the intervals between coupling wavelengths are approximately equal, indicating a linear change. Figures 5(b)–5(d) shows the relationship between the temperature and coupling wavelengths when both the PCF1 and PCF2 are used for calculations. The melting point and boiling point of toluene are −94.9 °C and 110.6 °C respectively, the scope of the calculation is, therefore, restricted to the above limits. However, when temperature is near the melting or boiling points of toluene, its thermo-optic coefficient becomes unstable and deviates dramatically. Due to this reason, we performed the calculation between −80 to 90 °C. Figure 5(b) shows that the coupling wavelength exhibits an obvious blue shift when the temperature increases. The results from the two fiber pieces show small difference due to the small difference in structural parameters. Using PCF1 we obtain a temperature sensitivity as high as −6.02 nm/°C, and for PCF2 this is −5.62 nm/°C. Compared to existing theoretical or experimental studies, the fiber sensitivity obtained here is about 100–1000 times higher [15–17]. Furthermore, the working range has been significantly extended to extreme temperatures, for instance, −80 °C, as a clear advance over the 42–54 °C limit in [19]. The correlation coefficients are 99.784% and 99.823%, respectively, which means the linear relationships between temperature and coupling wavelength are consistent. The spectrometer has a minimum resolution of 0.02 nm, the temperature sensing resolution can be realized as high as 3.32 × 10⁻³ °C and 3.56 × 10⁻³ °C, respectively. Note that in the low-temperature range from −80 to 0 °C (Fig. 5(c)), the linear coefficient between temperature and coupling wavelength are 99.842% and 99.857% for PCF1 and PCF2 respectively, which are slightly better than that of the full range from −80 to 90 °C, and their sensitivities are −5.41 nm/°C and −5.12 nm/°C. It is believed that such an advantageous character offers promising applications under extremely low-temperature conditions. PCF1 has a larger air-hole cladding structure than PCF2 does, and as a result, the sensitivity of using PCF1 is higher since mode-coupling starts more efficiently.

 

Fig. 5 (a) The confinement loss of PCF1 at different temperatures. At couling wavelengths the confinement loss has an obvious increase. The coupling wavelength of PCF1 and PCF2 and their fitted curves when temperature ranges from −80 to 90 °C are shown in (b), −80 to 0 °C in (c) and 0 to 90 °C in (d).

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It can be seen from Figs. 4(b) and 5(a), the confinement losses of the fundamental core mode at coupling wavelengths are as high as a few tenths of dB/m, while at other wavelengths they are about 4–5 orders of magnitudes lower, well below 1 dB/km. The intrinsic loss (from materials absorption and Rayleigh scattering) is known no more than 50 dB/km in the visible (e.g. at 600 nm, α_SMF = 10 dB/km [24]) and even lower in the near infrared. Take both cases into consideration, we figured out the total losses at coupling wavelengths remain significantly higher than those at other wavelengths, mainly triggered by the mode-coupling effect. Due to this reason, a 20–30 cm PCF is sufficient for expected sensitivity. In addition, to use it practically, the cross influences by liquid-core modes to output spectrum can be eliminated. Here we propose a SMF-PCF-SMF sandwiched structure, as shown in Fig. 6. The two end faces of the solid-core PCF are both spliced with single-mode fiber (SMF), after filled with toluene. Since the mode area of SMF is small, when coupled with PCF, no liquid-core modes can be excited. This is important because liquid-core modes directly excited from the light source form the noise background which makes the sensing inaccurate. When the light propagates through the PCF, the liquid-core LP₁₁ modes will then be excited at coupling wavelengths by leaking the fundamental core mode to the liquid core. Finally, at the connection between the PCF and SMF2, the liquid-core LP₁₁ modes in cladding are coupled into the cladding of SMF2 and attenuated rapidly, while the fundamental core mode is coupled into the core of SMF2 and propagates. In this way, the separation between signals of the fundamental core mode and liquid-core modes can be improved. The splicing technique between a PCF and a conventional SMF has been intensively explored, and many publications can be found [16,17,19,20,25]. One key point is that during splicing, the microstructure of the PCF must be maintained at the splicing point, otherwise, the coupling efficiency from SMF to PCF, or from PCF to SMF, will be reduced. This is because light can directly leak to the cladding region of the PCF/SMF when the structure is missing. Both from the reference [25] and our preliminary experience, to avoid collapsing the fiber end faces, the fusion current and duration should be manually adjusted and optimized for different cases. In addition, the discharge point needs to be set on the side of the SMF, in the vicinity of the fiber end, rather than right in the middle of the two fiber ends, or the other side near the PCF end face.

 

Fig. 6 The design of the structure of temperature sensing probe that enables the separation between signals of the fundamental mode and cladding modes.

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The selectively filling of cladding holes with toluene is verified by a two-step filling technique. The filling procedure is depicted in Fig. 7. Firstly, under a microscope, a taped glass or metal tip with a diameter of ~1 μm is mounted onto a multi-axial stage, moving towards the fiber front end. The tip carries a tiny drop of UV-harden glue. All holes are then applied with the UV glue through the taped glass/metal tip, except the ones later to be filled with liquid. It is efficient by doing so as precisely locating one or several specific holes for filling is rather difficult, than spreading the glue over a large area, covering holes not to be used for liquid-filling. The applied UV glue is then sucked into these holes of a few mm due to surface tension and then cured by a UV lamp. After hardening, the glue blocks all the selected holes, and leaves the other ones open for liquid-filling. At the final step, the fiber is connected to a syringe from the other end, and liquid can be pumped into the open holes throughout the whole fiber. Depending on the fiber length and hole diameters, it can take several ten minutes to a few hours to complete the filling. After that, the filling end needs to be cleaved ~1 cm to remove the part with the UV-harden glue. As a proof-of-concept, we experimentally demonstrate the filling of one cladding hole on purpose, as shown in Fig. 8. The single hole in the right-bottom corner was not covered with UV-harden glue. After hardening, the PCF was connected with a syringe pump, and this hole was then filled with toluene through the fiber.

 

Fig. 7 Schematic diagram of the selective filling process.

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Fig. 8 Microscope image of PCF cross section. (a) Most holes were firstly sealed with UV harden glue except one in the right-bottom corner. (b) Selective filling of that one hole with toluene.

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4. Conclusions

To summarize, we have successfully fabricated a solid-core PCF with a central micro-scale air-bore, based on which, a novel temperature sensor is designed. By selectively filling toluene into the second row of six cladding holes, we created a mode-sensitivity system for temperature sensing. When the fundamental core mode is coupled into the liquid-core modes, consequently the confinement loss presents a drastic increase, providing a possibility to monitor temperature—as accurate as a few nm/°C through the shift of the coupling wavelengths. Numerical analysis shows this novel temperature sensor can achieve a sensitivity of as high as −6.02 nm/°C with a resolution of 3.32 × 10⁻³ °C. Such a high sensitivity is about 2–3 orders of magnitudes higher than most existing systems, with an extended working range from −80 to 90 °C. The filling was executed using a multi-step procedure. A SMF-PCF-SMF structure is constructed which enables practical operation. For future experiments, we are now trying to construct the system for more systematic measurements. We hope new results will appear in following publications.