1. Introduction

Highly birefringent (HiBi) fiber Sagnac interferometers (SI) have been widely applied in optical sensing and communication [1]. Owing to a high thermo-optic coefficient of a conventional HiBi fiber, a SI based sensor shows high temperature sensitivity (0.94 nm/°C) [2]. Some SIs consisting of pure silica HiBi photonic crystal fibers (PCFs) have been reported as temperature insensitive sensors due to the low thermo-optic coefficients of these HiBi PCFs [3, 4]. In addition, due to the air-hole structure of the PCFs which can provide more convenience for the infusion of active functional materials, a new class of HiBi PCFs based on material filling have been realized [5, 6]. As a result of higher thermo-optic coefficient of the infusion, sensors based on the SI with ultrahigh temperature sensitivity can be achieved. For example, a compact temperature sensor based on an alcohol-filled index-guiding HiBi PCF SI with a sensitivity of 6.6 nm/°C has been demonstrated by Qian et al. [6]. In addition to the index-guiding HiBi-PCFs in [3–6], the HiBi photonic bandgap fibers (PBGFs) possess diverse birefringence characteristics and usually result from some aspects, such as the core [7,8] or cladding holes [9] with different diameters along the two orthogonal axes, circular asymmetrical designs around fiber core [10, 11], full or selectively filling functional materials with higher index than silica glass [12, 13]. And diverse birefringence features of these PBGFs different from that of index-guiding HiBi PCFs have been achieved, such as strong wavelength dependence of model birefringence [7–9], diverse modal birefringence features affected by the anti-crossing events in a bandgap range [10], and weak wavelength dependence of group birefringence [11]. Thus, the HiBi PBGFs based SIs for sensing physical parameters also have unique features, for example, interference dips have opposite shift direction [12, 13], and the temperature sensitivity is very much dependent upon the wavelength [14]. Among the HiBi PBGFs above mentioned, the PBGFs based on full or selectively filling have especially high potential in high-sensitivity sensors due to the flexibility in the filled area and higher thermal-optical coefficient of the infusion. By selectively filling air holes of an original index-guiding HiBi PCF with a high index liquid, a high temperature sensitivity of 0.4 nm/°C has been achieved [13], which is 100 times the sensitivity of 3.97 pm/°C based on a hollow-core PBGF [14]. Another kind of HiBi PCFs which guide light by a combination of both index-guiding and bandgap-guiding have also been reported [15, 16]. And the new guiding mechanism may result in new birefringence characteristics. However, few reports have focused on the hybrid HiBi PCFs and SIs realized by filling functional materials into part holes of PCFs.

In this paper, we realize a selective-filling photonic crystal fiber (SF-PCF) which guides light by a combination of both index-guiding and bandgap-guiding by only infiltrating two adjacent air holes of the innermost layer with a high refractive index liquid. Light is guided in the solid core at wavelengths for which the high index inclusions are anti-resonant. The modal birefringence of SF-PCF is decidedly dependent on wavelength, including the modal phase birefringence having higher value at middle of the anti-resonant area, and the group birefringence having higher values near the anti-resonant area boundaries and a null value at middle of the anti-resonant area. Meanwhile, the modal birefringence is also acutely dependent on temperature because the resonant area of the high index inclusions is highly sensitive to temperature. Then, we further investigate the detailed temperature responses of the SF-PCF based SI. They are fully related to the temperature responses of the modal birefringence, and the sensitivities of the interference dips are nonlinear variation to temperature. An ultrahigh even theoretically infinite sensitivity can be achieved at a certain temperature by choosing proper fiber length. And a temperature sensitivity of −26.0 nm/°C (63,882 nm/RIU) at 50.0 °C is experimentally achieved.

2. Theoretical analysis

Figure 1(a) illustrates the schematic diagram of the proposed SF-PCF based SI, which consists of a 3 dB optical coupler (OC) with a splitting ratio of ~50:50 at a wavelength range from 1300.0 nm to 1600.0 nm and a section of SF-PCF. The light from a supercontinuum source (SCS) (600.0 nm-1700.0 nm) propagates around the fiber loop, and the transmission interference spectrum is measured by an optical spectral analyzer (OSA) with the highest resolution of 0.02 nm. The top inset of Fig. 1 shows the microscopic image of the transverse cross-section of the original PCF used in this paper, which is fabricated by Yangtze Optical Fiber and Cable Corporation Ltd. of China. The pure silica fiber includes five rings of air holes arranged in a regular hexagonal pattern. The holes diameter and adjacent holes distance are ~3.6 μm and ~5.9 μm, respectively. The refractive index of the background silica is 1.444 at 1550 nm wavelength. The bottom inset shows the theoretical simulation model, where the white circles are air holes, and the red circles are the high index inclusions. The SF-PCF is realized by selectively infiltrating two adjacent air holes of the innermost layer of the PCF with liquid, which is produced by Cargille Laboratories Inc and possesses a refractive index of 1.52 at 589.3 nm for 25°C and a thermal-optic coefficient of −0.000407/°C. The coupling between the two high index rods produce guided modes therein at certain frequencies. And, meanwhile, the bandgaps-like core transmission spectra are formed. Hence, in this direction, light is guided in the core by bandgap-guiding. While in the other directions, light is guided in the core by index-guiding. And light is guided at solid core only when the guiding conditions of both index-guiding and bandgap-guiding are satisfied.

 

Fig. 1 (a) Schematic diagram of the proposed SF-PCF based SI. The inset is the cross-section of the PCF used in this paper (top inset) and theory model for simulation (bottom inset), where, the white circles are air holes and the red circles are high index inclusions. (b) Calculated phase birefringence B and group birefringence B_g dependence on wavelength under different temperatures.

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The SF-PCF with filling length of L is placed into the SI and a part of the SF-PCF with length of L₁ (L₁≤L) is located inside the temperature chamber. Thus, the transmission spectrum at temperature T can be expressed as the equation:

In order to discuss the temperature response of the interference dips, after taking the derivative with respect to temperature, we deduce the temperature sensitivity S of the dip wavelength as follows (the derivation process is similar to that in [13]):

Firstly, the effective refractive indices of core fundamental modes at slow ($n_{\text{slow}}$) and fast axes ($n_{\text{fast}}$) are numerically calculated by using a finite-element method (FEM) [17], and the dispersion of the background silica and high index inclusion are considered in the simulations. Then according to the equations describing modal phase birefringence B and group birefringence B_g, the B and B_g are calculated by programming in MATLAB, as shown in Fig. 1(b), The B does not exhibit monotonic variation with wavelength, but experiences an increment with wavelength followed by a decrement. This aspect is different from the HiBi PBGFs [7–9] achieved by deliberately making the core or cladding holes dimensions of the orthogonal axes unequal. The group modal birefringence B_g reaches relatively high values near the two anti-resonant area boundaries, respectively, and change its sign at a certain wavelength${\lambda }_{B_{\text{g}}\text{=}0}$. Figure 1(b) also shows the modal birefringence variation at different temperatures. Both B and B_g shift to the shorter wavelength because of the blue-shift of the anti-resonant area with temperature increasing according to the ARROW theory [18], and simultaneously, the B also decreases due to the reduction of liquid index.

According to Eq. (3), we calculate the temperature sensitivity S versus wavelength for different heated length ratio (γ) at 50.0 °C, as shown in Fig. 2 . The vertical lines stand for the zero denominators of Eq. (3), which results in theoretically infinite temperature sensitivity at this temperature. In addition, the temperature sensitivities increase with the decreasing distance between the resonant interference dip and the vertical lines. According to the phase-matching condition defined by Eq. (2), the total length L and heated length L₁ of the SF-PCF determine where the interference dips locate. Therefore, by choosing proper L and L_1, higher sensitivity at this temperature can be achieved, for example, a sensitivity of −98.3 nm/°C at wavelength of 1516.0 nm is achieved when choosing L = L₁ = 17.5 cm and −74.0 nm/°C at wavelength of 1610.0 nm is achieved when L = 25.0cm and L₁ = 12.0cm.

 

Fig. 2 Calculated temperature sensitivity S(T) versus wavelength for different heated length ratio γ at 50.0 °C.

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Next, we choose L = L₁ = 25.0 cm, and calculate the interference transmission spectrum at room temperature (25.0 °C) according to Eq. (1) also by programming in MALAB, as shown in the inset of Fig. 3(a) . It is clear seen several interference dips with unequal spacing appear. The spacing (s) between adjacent interference dips is decided by $s={\lambda }^2/\left|n_{g}L\right|$, which results in a broad spacing at the middle of anti-resonant area due to the small group birefringence magnitude shown in Fig. 1(b). Several transmission spectra of dips A and B from 45.0°C to 50.3°C is shown in Fig. 3(a). With temperature increasing, the two dips exhibit opposite trends and the spacing between the two dips reduces gradually. At 50.3°C, they both vanish completely, and a wide loss dip appears. During this changing process, the loss at 1500.0 nm increases and the contrast of the two dips reduces with increasing temperature. Then, we discuss in detail the wavelength variation of interference dips A, B, C and D under different temperatures, as shown in Fig. 3(b). The blue dotted line represents the variation of the wavelength ${\lambda }_{B_{\text{g}}\text{=}0}$satisfying $B_{\text{g}}\text{=}0$at different temperatures. We can see that the interference dips located at wavelengths $\lambda >{\lambda }_{B_g=0}$ (or $\lambda <{\lambda }_{B_g=0}$) have similar change tendency. Dips B and D will shift to shorter wavelengths with temperature increasing until they disappear. Nevertheless, dips A and C first shift to shorter wavelengths and when temperature increases to a certain value, they will shift to longer wavelengths until they disappear. Furthermore, the wavelengths of interference dips nonlinearly change with temperature, and the temperature sensitivities gradually increase with temperature increasing. Especially, nearby the wavelength ${\lambda }_{B_{\text{g}}\text{=}0}$, the sensitivities reach the maximum value, for example, dips A and B at 50.0 °C and dips C and D at 61.0 °C.

 

Fig. 3 (a) Calculated interference transmission spectra of two interference dips A and B from 45°C to 50.3°C. The inset shows the interference transmission spectrum at room temperature when L = L₁ = 25 cm. (b) The wavelength variation of interference dips A, B, C and D in (a) dependence on temperature. The red curves shows the variation of dips A and B when L = 25 cm and the heated ratio γ = 0.48 (L₁ = 12 cm). The blue doted line represents the variation of the wavelength λ_{Bg = 0} satisfying B_g = 0 at different temperatures.

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Then, we fix the filling length at 25.0 cm and change the heated length ratio γ at 0.48 (L₁ = 12.0 cm), the wavelength variation of dips A and B with temperature is also shown in Fig. 3(b) (red curves). We can see that the shift velocities of the two dips at the smaller ratio γ is slower than those at the lager ratio γ. Furthermore, the temperatures at which the sensitivities reach the highest value are different for different γ. The γ (or the length of the heated fiber L₁) can be controlled by regulating the relative location of the temperature chamber to the SF-PCF. Thus, the highest sensitivity can be achieved at different temperatures only by changing the heated fiber length (or the location of the temperature chamber) without changing the total filling length. It makes the practical application more convenient.

3. Experimental results

In the experiment, the two adjacent air holes located at the innermost layer of the PCF are selectively infiltrated with the high index liquid by the direct manual gluing method described in detail in [18]. The filling length L is ~25.0 cm. Two ends of the SF-PCF are infiltrated into a bit of air to avoid high loss when fusion splicing with infiltrated fluid. Then SF-PCF is splicing fusion to SMFs and put into the SI as shown in Fig. 1(a) and 12.0 cm length of the SF-PCF is located inside the temperature chamber with temperature stability of ± 0.1°C. Figure 4(a) shows the transmission spectra of the SI from 46.4°C to 71.3°C. Interference dips A and B shift to the opposite direction with temperature increasing, and the wavelength space between the two dips decreases gradually, accompanying the interference contrast reducing. Until 50.5°C, the two dips disappear, and a wide loss dip appears. With temperature increasing, the dip becomes shallower, and finally disappears at 58.3°C. Interference dips C and D have the similar change tendency as dips A and B.

 

Fig. 4 (a) The experimental transmission spectra of the SI from 46.4°C to 71.3°C when L = 25 cm and L₁ = 12 cm. (b) (top) The experimental wavelength variation (the circles) A_EX-D_EX and theoretical wavelength variation (the solid curves) A_THE-D_THE of dips A, B, C and D dependence on temperature. The blue solid curves are the nonlinear fitting curves of the experimental results. (bottom) The temperature sensitivity of dips A, B, C and D dependence on temperature.

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Then the specific temperature sensitivities of interference dips A, B, C and D are further discussed. Figure 4(b) (top) shows the wavelength variation of dips A, B, C and D (A_EX-D_EX) dependence on temperature (the circles). And the theoretical results are shown with the solid curves (A_THE-D_THE), which have different wavelength scales compared to experimental results. This is because, in PBGFs, the diameter and index of high index rods greatly affect the bandgap wavelengths based on the ARROW theory [18]. Hence, small derivation in the diameter and index of high index rods between theoretical model and actual experimental measurement can lead to mismatched wavelength scales. But, the total discussed wavelength ranges in theory and experiment are both 500nm, from 1430nm to 1930nm and from 1350nm to 1850nm, respectively. Furthermore, the variation tendencies of experimental results basically match with that of theoretical results. Then, the experimental results are analyzed and fitted with 6-order polynomial, as shown with the blue solid curves. We use the first-order derivative of the fitting curves, and get the temperature sensitivity, as shown in Fig. 4(b) (bottom). It is clearly seen that the sensitivities change nonlinearly with temperature, and increase with temperature increasing. Dips B and D have sensitivities higher than −10.0 nm/°C from 44°C to 50°C and from 56.7°C to 66.5°C, and the sensitivities reaches up to −26.0 nm/°C at 50.0 °C and −23.0 nm/°C at 66.5°C, respectively. This can be adopted for sensitively detecting tiny temperature variation at a certain temperature. In practice, this valid sensing temperature ranges can be changed and even wider by choosing proper fiber length.

In addition, the change in temperature essentially brings about the variation in the refractive index of the filled liquid analyte, so this device also can be used for optical detection of small change in refractive index within liquid analyte. The refractive index sensitivity corresponding to −26nm/°C is 63882.1 nm/RIU.

4. Conclusion

In conclusion, the characteristics and temperature response of a SI based on a HiBi SF-PCF are theoretically and experimentally investigated. The selective filling pattern affects the guiding mechanism of the SF-PCF which guides light by a combination of both index-guiding and bandgap-guiding. The birefringence characteristics are different from the traditional index guiding HiBi PCF [5] and HiBi PBGFs [7–9]. Based on the unique birefringence features, the temperature response of the SI based on the SF-PCF presents a temperature sensitivity of higher than ~-10.0 nm/°C, and the highest sensitivity of ~-26.0 nm/°C at 50.0 °C is experimentally achieved. Furthermore, the highest sensitivity can be achieved at different temperatures only by changing the heated fiber length (or the location of the temperature chamber) without changing the total filling length. This device can be adopted for sensitively detecting tiny variations of temperature and refractive index of filled liquid analyte.

In addition to the flexible selective filling pattern, the anti-crossing points in the bandgap [10] also affect the birefringence features. By combing the selective filling pattern and different bandgaps, we predict diverse selective-filled HiBi PCFs with unique characteristics would have very large capacity for multi-parameter sensing and tunable optical devices.