1. Introduction

Much research has been conducted in recent years on a new class of optical fibers called the photonic crystal fibers (PCFs) that can be used either as transmission media or in optical functional devices [1–4]. PCFs have many unique characteristics [5–8] that are superior to conventional fibers when applied to sensing applications such as temperature independent strain sensors [9,10] and we shall show in this paper that one can raise the temperature sensitivity of PCFs by adding a liquid with a high thermo-optic coefficient into its air holes. As the propagation modes of PCFs are known to be highly temperature-dependent [11–15], the prime candidate for this liquid to be used is liquid crystal (LC) whose refractive index can be readily tuned by either temperature or electric field [13]. Furthermore, one can modulate the propagation spectra of LC simultaneously until the original band-gap-guiding fiber structure is transformed into a total-internal-reflection-guiding PCF. In fact, one liquid core PCF sensor was constructed recently by Zhang et al by using surface enhanced Raman scattering [16] with good sensitivity in the detection of rhodamine 6G, human insulin, and tryptophan. Another micro-fluidic refractive index sensor was also reported to have been constructed [17] by using some solid core photonic crystal fibers that are arranged in a directional coupler architecture. In this paper, wavelengths are used as the input signal for the liquid-filled PCF sensors even though wavelength demodulation is complicated and costly in commercial practice.

This paper presents for the first time a PCF temperature sensor that is based on intensity modulation and liquid ethanol filled air holes in the index-guiding PCF. Light is still guided by total internal reflection (TIR) because liquid ethanol has a smaller refractive index than the material in the fiber core and the transmission power of the ethanol-filled PCF is used as the sensor signal to investigate its temperature properties. The temperature dependence of the transmission power of this device is investigated thoroughly using different transverse structures and excited wavelengths with a view of highlighting the various advantages of this intensity-based sensor over its wavelength-based counterpart.

2. Numerical method

The full-vector finite element method (FEM) divides the cross-section of a waveguide into a patchwork of triangular elements with different sizes, shapes, refractive indexes and anisotropies [10]. The perfectly matched layer (PML) is therefore used as the boundary condition for the problem after the PCF cross-section, incident wavelength and material parameters have all been initialized and the cross-section of the PCF with liquid ethanol filled air holes is then divided into many sub-domains that are either triangular or quadrilateral in shape. The eigenvalue equation of propagation in PCFs can then be solved in the Perpendicular Hybrid-Mode and the field distribution and propagation constant β_eff determined from the equation n_eff = β_eff /k ₀ = β_effλ/(2π), where k ₀ is the free-space wave number and λ is the propagation wavelength. The material dispersion, in particular, is taken to be the refractive index of the pure silica Sellmeier equation [11] during the simulations and the thermo-optic coefficient α of liquid ethanol is defined to be n = n ₀-α(T-T ₀), where n and n ₀ are the refractive indices at temperature T and T ₀ respectively. Because the coefficient α of liquid ethanol is 3.94 × 10⁻⁴ /K, which is two orders of magnitude higher than that of pure silica (α = 8.6 × 10⁻⁶ /K), the refractive index of the silica fibers is set as a constant at all temperatures during the simulations. Finally, n ₀ is initialized to be 1.36048 at the input wavelength of 589.3 nm and T ₀ = 20°C.

Now, loss of the PCFs is evitable in practice for a number of reasons such as intrinsic material absorption, confinement loss as well as losses arising in the fabrication process (e.g. water contamination, absorption due to impurities, scattering, etc.). In single-material PCFs, the core has the same refractive index as the material beyond the cladding region and so all propagating modes are intrinsically leaky with confinement loss. More precisely, the relative confinement loss P_L of the fiber core is given by where L is the length of the fiber.

To investigate the dependence of the propagation characteristics of the PCFs on their structure parameters, a series of PCFs with identical cladding air holes and hole-to-hole spacing (Λ = 2.3 μm) have been used with different air-filling ratios d/Λ = 0.3, 0.4, 0.5, 0.6, 0.7. The results are shown in Fig. 1 where the mode effective indices and confinement losses are plotted against the wavelengths applied and the results can be interpreted as an increasing functional relationship between the index contrast between the core and cladding and the air filling ratio. A greater value of the air-filling ratio is hence congenial to the confinement of light and the reduction of confinement loss.

 

Fig. 1 After introducing liquid ethanol into the holes, The mode effective index (a) and the confinement loss (b) versus wavelength by varying the air-filling ratios.

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The mode index obviously decreases with the wavelength and so the confinement loss increases with it because the index contrast between the core and cladding is reduced. The confinement loss is sensitively dependent on the wavelength after the holes have been filled with liquid ethanol, especially for PCFs with air-filling ratios greater than d/Λ = 0.7. Figure 2 shows the confinement loss as functions of temperature at 800 nm and 1550 nm for PCFs with d/Λ = 0.7 and it is clear that there is a stronger relationship between confinement loss and temperature at 1550 nm than at 800 nm. As a result of the high temperature sensitivity of the mode fields of PCFs with holes filled with liquid ethanol of high thermo-optic coefficients, a highly increasing functional relationship exists between the d/Λ ratio and the input wavelength. The propagation properties of PCFs can therefore be used as a temperature-sensing tool.

 

Fig. 2 The confinement loss as functions of temperature at 800 nm and 1550 nm.

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3. Fiber properties and experimental setup

The modal characteristics of an index-guiding air-silica PCF with a hexagonal lattice of holes are primarily determined by the air-hole diameter d and the pitch Λ (the spacing between the holes). For comparison purposes, three different PCFs with the same cladding diameter of 125 μm were used and tested with the PCFs for these experiments all supplied by Yangtze Optical Fiber and Cable Company Ltd. (YOFC, China) and fabricated by using a modified conventional optical fiber drawing process. The cross-sections of three PCFs are shown in Figs. 3(a) PCF1, 3(b) PCF2 and 3(c) PCF3. These PCFs are with the following structure parameters. For PCF1, pitch Λ = 4.2 µm, hole diameter d = 3.8 µm, and core diameter of 2.7 µm. For PCF2, Λ ₁ = 5.3 µm (outer), Λ ₂ = 6.1 µm (inner) and hole diameter d ₁ = 2.8 µm (outer), d ₂ = 5.8 µm (inner), and core diameter of 3.3 µm. For PCF3, pitch Λ = 5.6 µm, hole diameter d = 3.6 µm, and core diameter of 7.6 µm.

 

Fig. 3 Optical microscopic images of cross-sections of three PCFs, (a): PCF1, (b): PCF2 and (c): PCF3. The dark circles are air holes while the bright regions are silica. PCF1 with air-filling fraction d/Λ = 0.9, PCF2 with air-filling fraction d/Λ = 0.95 for inner air holes, PCF3 with air-filling fraction d/Λ = 0.64.

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Even after liquid ethanol (Analytical reagent, AR) has been inserted into the holes by capillary force and air pressure, the PCF is still made up of a high index solid silica core surrounded by a lower index cladding. (because the index of ethanol is lower than that of silica). Light is therefore guided through this fiber by total internal reflection in the higher index core and the index of the ethanol within the holes is continuously adjusted by varying the temperature (which changes the propagation modes of the PCF such as the mode index and confinement loss).

To measure the temperature dependence, a PCF with a fixed length is filled with liquid ethanol and then positioned into the splicer (FSM-60S, fusion current 11mA and fusion time 3s). The two ends of the PCF are then spliced with single mode fibers (SMF) and placed into a digital oven (from −5°C to 100°C, ± 0.05°C). The PCF is then placed in the V-groove of an aluminous slab to avoid bending effects and laser diodes at different wavelengths (850 nm, 980 nm, 1310 nm, 1550 nm) are then used as light sources. Each light source is coupled via a 10 dB SMF coupler into one end of the PCF and the opposite end is fed directly into an optical power meter (AI9402A, with measured range from −90~3 dBm). The power output of the light source is also measured through the 10% end of the coupler to provide a control reference. Transmission power is recorded from 20°C to 70°C and then back down to 20°C at 5° intervals. Figure 4 shows a scheme of the experimental setup for the temperature-dependence measurements and the transmission power of ethanol-filled PCF is used as a sensor signal for investigating the temperature properties.

 

Fig. 4 The scheme of the experimental setup for temperature sensor.

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4. Results and discussion

Figure 5(a) shows the transmission power at 1550 nm for PCF3 as a function of temperature from 20°C to 70°C where the temperature dependence is obvious. The experimental and simulation results are also remarkably consistent with all the slight discrepancies being accounted for by the losses arising in the fabrication process (water contamination, absorption due to impurities, scattering, etc.).

 

Fig. 5 (a) Temperature dependence of transmission power for PCF3 at 1550 nm, (squares: Theoretical data; triangle: Experimental data); (b) Temperature dependence of transmission power change for PCF3 at different wavelengths (Experimental data).

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Figure 5(b) plots the transmission power as a function of temperature at different input wavelengths of the experiments with the highest temperature sensitivity occurring at 1550 nm. The dependence on temperature at 1310 nm, 980 nm, 850 nm is much weaker than that at 1550 nm. It is also observed at 1550 nm that the power received is in direct proportion to the temperature and this is a fact that is consistent with theory because a lowered refractive index of the liquid ethanol is equivalent to an increased contrast between the core and cladding indices. The light leakage to the cladding, and hence also the confinement loss, is reduced with temperature. Finally, owing to the broadening of the propagation modes of the fibers with increasing wavelengths, the temperature dependence is more sensitive for longer wavelength inputs.

To investigate the relationship between the structure parameters and the transmission power, three different types of PCFs with identical lengths were used at the same input wavelength of 1550 nm. The experimental results are shown in Fig. 6 . The temperature sensitivities (∆P/∆T) are estimated by using linear regression fits, which are 0.315 dB/°C for PCF1, 0.194 dB/°C for PCF2 and 0.017 dB/°C for PCF3. The temperature sensitivity is higher for greater values of d/Λ and longer input wavelengths. Figure 7(a) plots the transmission power of two PCFs with different lengths as a function of temperature and it is observed that they are in a direct proportion relationship. Using linear regression fits, the temperature sensitivities are estimated to be 0.358 dB/°C for a 19-cm-long PCF and 0.315 dB/°C for a 10-cm-long PCF. The linear relationship is strong with the R-squared values all lying within 0.996 of the temperature range from 25°C to 70°C. Longer PCFs are therefore more congenial to temperature sensitivity.

 

Fig. 6 Temperature dependence of transmission power for three PCFs at 1550 nm;

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Fig. 7 (a) Transmission power vs temperature for PCF1 at different lengths, squares: 19 cm; circles: 10 cm; (b) Temperature dependence of transmission power at the wavelength of 1550 nm during increasing and decreasing temperatures.

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Figure 7(b) plots the transmission power as a function of temperature for both the temperature-increasing and temperature-decreasing processes with consistent results. The experimental measurements are also easily reproducible.

5. Conclusion

We presented a novel PCF temperature sensor that is based on intensity modulation and liquid ethanol filling. The temperature sensitivity of this sensor was estimated to be 0.315 dB/°C for a 10-cm-long PCF by using linear regression fits and the linearity of the temperature dependence is quite high. The experimental measurements are easily reproducible and the sensor is simple and convenient to use compared to its conventional wavelength-based counterpart, the new sensor can also be produced at a low cost and so provides a new avenue for ultrasensitive temperature sensing devices.