We have experimentally investigated the birefringent properties of photonic crystal fiber (PCF) coils in cooperation with a Sagnac loop interferometer. By reducing the bending radius of the PCF coils, very clear interference patterns can be observed for the bending-induced stress effect. Increasing the fiber turns can result in more obvious interference patterns with smaller fringe spacing but has no contribution to the increment of the birefringence value. The fabricated PCF coil is employed in the transverse displacement sensing. Very high sensing sensitivity of 90.4 nm/mm can be achieved due to the large displacement-induced bending radius variations.
© 2011 OSA
Conventional birefringent fibers, such as elliptical-core fibers  with elliptical fiber cores or PANDA fibers  with mechanical stress through the elasto-optic effects, can provide high birefringence to reduce the coupling between two orthogonally polarized modes in optical fibers. Recently, photonic crystal fibers (PCFs)  with air holes in the fiber cladding have also been designed to provide high birefringence by means of air holes with different sizes or an asymmetrical distribution [4–6]. These birefringent fibers have been widely employed in optical devices and communication systems to control the polarization state of the propagating light and eliminate the polarization mode dispersion (PMD). In addition, birefringent fibers can also be adopted to form interferometers to function as sensitive sensors for temperature , pressure [6,8], strain , and torsion .
In spite of using asymmetrical fiber structures or elasto-optic effects, birefringence in optical fibers can also be induced by bending [11–13]. Figure 1 illustrates a section of a bent fiber with the fiber radius r. The bending-induced birefringence Bb can be expressed as [11,13]:Eq. (1), one can see that, with fixed material parameters, the bending-induced birefringence Bb can be easily enlarged by reducing the bending radius R.
However, the bending-induced birefringence is undesirable in many fiber coil devices formed by bent fibers, such as fiber optic gyroscopes , optical microfiber coil delay lines , fiber coil resonators , and refractive index, pressure, and current sensors [16–20]. The bending-induced birefringence may change the polarization state of the light and result in the degradation in the device performance. To suppress the bending-induced birefringence, one can use annealing procedures  or introduce lateral compressive stress  to form birefringence-free fiber coils. Nevertheless, the undesired bending-induced birefringence in fiber coils can also be utilized in sensing applications. In this paper, we will experimentally investigate the birefringence properties of fiber coils formed by winding optical fibers on straws. Instead of using conventional single-mode fibers (SMFs), PCFs are adopted to form PCF coils due to their low thermal sensitivity . The effect of the bending radius and fiber turns on the induced birefringence will be analyzed. In addition, the fabricated PCF coils will be employed in the transverse displacement sensing. The displacement sensing sensitivity will be measured and discussed.
2. PCF coils and measurement setup
The PCF coil in our experiment was fabricated by winding a PCF on a cylinder. The PCF we employed was the LMA-10 PCF form NKT photonics A/S. The LMA-10 PCF contains four air-hole rings surrounding the central solid core as shown in Fig. 2(a) . The lattice constant and diameter of the air holes are Λ = 6.72 μm and d = 3.1 μm, respectively. To prevent the fiber break during the coil fabrication, the outer coating of the PCF was kept and the diameter of the PCF was about 240 μm. In addition, due to the effective index profile of the PCF is approximately circularly symmetric, the effect of different fiber bending orientations can be ignored. Figure 2 (b) demonstrates a fabricated PCF coil formed by winding the PCF on a straw with 24 fiber turns. The diameter D of the straw is 1.2 cm and the length of the PCF coil with 24 fiber turns is 6 mm.
To find out the birefringent properties of the PCF coils, the Sagnac loop interferometer (SLI) containing a 3-dB coupler and a fiber loop was adopted in the measurement setup as shown in Fig. 2(c). The fabricated PCF coil was placed into the fiber loop and connected to the 3-dB coupler through two SMFs. Incident light from a broadband light source was lunched to the 3-dB coupler and split into two light beams propagating along the fiber loop in clockwise and counterclockwise directions, respectively. As the two beams propagated through the birefringent PCF coil, two orthogonally polarized fundamental modes were excited with different propagation velocities. After passing through the PCF coil, the two beams were recombined by the same 3-dB coupler, and the transmission spectrum was collected by an optical spectrum analyzer (OSA) to obtain the birefringence patterns resulted from the accumulated phase difference of the two beams.
3. Birefringent properties of PCF coils
We first consider the effect of the bending radius R on the birefringent properties of the PCF coils. The total length of PCF is 90 cm. By winding the length-fixed PCF on straws of different sizes, we can obtain PCF coils with variant values of R. Figure 3(a) is the measured output spectrum of the SLI with our fabricated PCF coils. The pink dashed line represents the result of the straight PCF without winding in the SLI. Due to no bending along the PCF, no interference fringes can be observed. As we wound the PCF on straws with R being 0.76 cm, 0.61 cm, 0.49 cm, and 0.39 cm, very clear interference patterns can be obtained as shown in Fig. 3(a). The averaged spacing of the interference fringes became smaller as we reduced the value of R. In addition, unlike the endless single-mode property of the solid-core PCF, there exist short-wavelength band edges for the PCF coils. At shorter wavelengths, the index difference between the core and cladding regions of the PCF is decreased, resulting in a weaker confinement and large bending losses with the applied bending [21,22]. We can also observe that the short-wavelength band edges moved toward longer wavelengths with the decreased R due to the increasing bending losses.
From the measured fringe spacing, the corresponding birefringence can be deduced according to:Fig. 3(b). It can be seen that the value of birefringence was dramatically increased as we reduced the bending radius. Thus, to obtain highly birefringent PCF coils, one can use a control system and a CO2 laser  to fabricate miniature PCF coils with a very small value of R. In addition, the measured birefringence of the PCF coils with fixed bending radius R is almost wavelength independent, which agrees well with Eq. (1) and is quite useful in the sensing applications.
Figure 4(a) shows the transmission spectra of PCF coils with variant fiber turns N for the bending radius R = 0.61 cm. With the increasing fiber turns, the bending PCF was lengthened. As a result, the accumulated phase difference is enlarged with the increasing fiber turns, and we can observe smaller fringe spacing Δλ as shown in Fig. 4(a). However, a larger value of fiber turns with smaller fringe spacing does not correspond to larger birefringence. Figure 4(b) plots the calculated birefringence for the PCF coils with variant bending radius R and fiber turns N. According to Eq. (3), the calculated birefringence is inversely proportional to the product of the fringe spacing Δλ and fiber length L. Although larger fiber turns results in smaller fringe spacing, it also increases the fiber length. Thus, we can observe that the birefringence values for PCF coils with variant fiber turns and fixed bending radius are almost the same. Increasing the fiber turns can only result in more obvious interference fringes due to the increased fiber length and accumulated phase difference.
4. Transverse displacement sensing
Since the birefringent characteristics of the PCF coils mainly rely on the bending radius, the measured spectrum corresponds obviously to the variation of the bending radius. Making use of this property, the PCF coil was utilized in the application of transverse displacement sensing. The fabricated PCF coil with R = 0.61 cm was placed between two planes as demonstrated in Fig. 5(a) . The distance of the two planes was controlled by a 5-axis translation stage. As we fixed one plane and moved the other plane for a displacement Δ, the bending radius along the PCF coil was changed as shown in Fig. 5(a). Figure 5(b) displays the measured transmission spectra of the PCF coil with variant values of Δ. Very obvious wavelength shift of the transmission dip can be observed even as the displacement Δ is only 0.02 mm.
Figure 5(c) plots the wavelength shift of the dip versus the displacement Δ. The black squares are the measured results and the black solid line represents a linear fitting. One can see that as the displacement was increased from 0 mm to 0.25 mm, the wavelength shift of the transmission dip was linearly proportional to the displacement. The displacement sensing sensitivity of the PCF coil is 90.4 nm/mm. We also measured the sensing sensibility of a SMF coil with the same bending radius and fiber turns for comparison. The red circles and solid line in Fig. 5(c) are the measured wavelength shifts and the linear fitting for a SMF coil. Similar to the PCF coil, a linear relationship can be obtained with the sensing sensitivity is 30.8 nm/mm. The measured displacement sensitivity of the PCF coil is almost three times than that of the SMF coil and much larger than other PCF-based displacement sensors . Please note that as the cylinder is laterally compressed, both the bending radius and the longitudinal stress will not be uniform along the coiled fiber as demonstrated in Fig. 5(a). If we further increase the value of Δ, the wavelength shift of the transmission dip may not be linearly proportional to the displacement due to the nonuniform distribution of the bending radius and the longitudinal stress. In our measurement, linear transverse displacement sensitivity can still be observed as Δ is 1.8 mm.
We have also measured the temperature sensitivities of the fabricated PCF and SMF coils as demonstrated in Fig. 6 . The squares and circles denote the measured wavelength shifts of the transmission dip at variant temperature for the PCF coil and SMF coil, respectively. The solid lines represent the linear fitting curves. One can see that the PCF coil possesses smaller temperature sensitivity than that of the SMF coil. However, compared with other PCF-based interferometers, our fabricated PCF coil shows more sensitive to temperature [9,23]. In addition, the measured temperature sensitivity of the birefringence is in the order of 10−8, which can be attributed to the thermal expansion of the polymer coating along the PCF and the straw used to fabricate the PCF coil. Although the temperature sensitivity of the birefringence is very small, the total length of the bending PCF is very large, resulting in the high temperature sensitivity of the transmission dip. To reduce the temperature sensitivity of our PCF coils, one can employ winding cylinder made from more temperature-insensitive materials or using uncoated PCFs to form the PCF coils . By applying these techniques to reduce the temperature effects, our PCF coil with very high displacement sensitivity is potential in the transverse displacement sensing.
We have fabricated birefringent PCF coils by simply winding PCFs on straws. The fabricated PCF coils were put into a Sagnac loop interferometer to obtain the birefringent properties. As we reduced the bending radius of the PCF coils, the fringe spacing was decreased and the birefringence in the order of 10−5 can be obtained. We have also measured the birefringence value with variant fiber turns. It is found that increasing fiber turns can only result in smaller fringe spacing while the bending-induced birefringence remains unchanged. Due to the bending-sensitive birefringence, the PCF coil was adopted in the transverse displacement sensing. Very high displacement sensitivity of 90.4 nm/mm can be obtained, making the PCF coils potential in the transverse displacement sensing.
This work was supported by the National Science Council of the Republic of China under Grants No. NSC98-2221-E-110-011-MY3 and by the Ministry of Education of the Republic of China under an “Aim for the Top University Plan” grant.
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