## Abstract

A highly sensitive optical fiber twist sensor has been proposed by employing a Sagnac interferometer based on polarization-maintaining elliptical core fibers (PM-ECFs). The twist effects have been theoretically analyzed and experimentally demonstrated. Based on the photoelastic effect, the resonance wavelength linearly shifts with the increment of twist and the wavelength shift is also dependent on the torsion direction. The maximum torsion sensitivities reach 18.60nm/(rad/m) for clockwise (CW) torsion direction and 15.83nm/(rad/m) for anticlockwise (ACW) torsion direction, respectively. To eliminate the temperature cross-sensitivity effect, a sensor matrix for simultaneous measurement of twist and temperature has also been obtained. Moreover, theoretical and experimental investigations indicate that by optimizing the refractive index difference between the core and cladding, core ellipticity and cladding diameter, the twist sensitivity could be further improved.

© 2015 Optical Society of America

## 1. Introduction

Optical fiber twist sensors play an important role in the applications of spaceflight and constructional engineering owing to their compact structure, excellent flexibility, strong applicability and resistance to environmental interferences. Applying internal or external perturbation introduces asymmetric distribution of refractive index, and numerous optical fiber twist sensors have been constructed by employing long period fiber gratings (LPFGs) [1–4 ], fiber Bragg gratings (FBGs) [5,6 ], titled FBGs (TFBGs) [7,8 ], photonic crystal fiber (PCF) [9–13 ], and interferometers [14–19 ], etc. In particular, the interferometer-based twist sensors have attracted increasing research interests due to their exquisite interference fringes, fast response and ease of being implemented, which could be fulfilled by multi-modes interference [14] and Sagnac interference [15–19 ].

Among the various interferometer-based twist sensors, the Sagnac interferometer (SI) is particularly attractive due to the input light polarization independence, and moreover the free spectral range (FSR) of the spectral filter only related to the length of the birefringence fiber and is independent on the total length of the fiber loop [20]. With the development of PM-PCF or birefringence PCF, the performances of PCFSI-based twist sensors, including flexibility, sensitivity and thermal dependence, have been intensively investigated. In many related studies, the SIs are constructed with different kinds of asymmetric PCFs, including PM side-hole fiber [15], suspended twin-core fiber [16], side-Leakage PCF [17], highly birefringent (HB)-PCF with anisotropic microstructure [18] and low-birefringence (LB)-PCF [19]. The PCF-based SIs is desirable for their birefringence introduced by the irregular air holes across the fiber cross section and the phase difference produced by the two oppositely propagating waves inside the fiber loop. While certain twsit is applied onto the birefringence PCF, the photoelastic effect would give rise to fiber distortions along fast and slow axes to different degrees, causing the variation of fiber birefringence with the change of twist vector. However, high-order modes are easily excited at the splicing joints between the SMF and PCF, and thus the transmission loss will increase accordingly. In addition, the splicing joints make the twist sensor fragile. Moreover, complex fabrication process and high cost are also required. Therefore, in consideration of practical applications, twist sensors need to possess such features as fast response, low transmission loss, compactness, robustness, low cost and ease of being implemented. PM-elliptical core fibers (PM-ECFs) with all-solid fiber cross section provide a good solution to construct more robust SI-based twist sensors with lower transmission loss. They have such advantages as high birefringence, all-solid structure, good compatibility with single-mode fibers (SMFs), low cost, and particularly the fiber birefringence is proportional to the ellipticity and area of the fiber core [21]. This makes it possible to improve the fiber birefringence by fabricating the PM-ECF with designed core ellipticity and core area through fiber tapering and twisting.

In this paper, an optical fiber twist sensor based on a PM-ECFSI with high sensitivity has been proposed. To effectively achieve twist rate measurement with resolved temperature cross sensitivity, we have experimentally studied the influences of fiber twist and temperature on the transmission spectral characteristics of this device. Moreover, the factors affecting the sensor performances have also been investigated from both of experimental as well as theoretical perspectives.

## 2. Principle and experiment

Figure 1 shows the schematic experiment setup of the SI-based twist sensing system. The twist sensor is fabricated by splicing a segment of PM-ECF (PME 1300-10) of 8.5cm in length with the two output ports of a 3-dB coupler (Corning SMF28-e). The output light of a supercontinuum broadband source (SBS) is launched into the SI loop and the spectral interference fringes are monitored by an optical spectrum analyzer (OSA, Yokogawa AQ6370C, operation wavelength ranges from 600nm to 1700nm) with a resolution of 0.5nm. A polarization controller (PC) is employed to optimize the interference spectral pattern. One end of the sensor head is clamped by a fiber holder, and the other end is mounted at the center of a rotator with an engraved dial embedded to apply twist onto the PM-ECF. The distance between two stages is 48cm. A 5g weight is attached after the rotator to keep the device straight. The inset on the right shows the microscopic cross sectional image of the PM-ECF. The initial fiber birefringence is introduced by an elliptical Ge-doped core with a mode field area of about 6.5μm × 3μm, and the silica cladding diameter is 125μm. To enhance the twist sensitivity, the PM-ECF is etched with hydrofluoric acid to reduce the cladding to about 62.5μm.

The 3-dB optical coupler splits the input light into two
counter-propagating waves, and they will re-enter the 3-dB coupler after
passing through the PM-ECF along opposite directions. When theses waves
propagate though the PM-ECF, they experience different phase retardations,
and thus the transmission spectrum at the output port of the 3-dB coupler
turns out a wavelength-dependent interference pattern. The reflection
spectrum of the SI is shown in Fig.
2
, which is approximately a periodic wavelength-dependent function.
The FSR $\Delta \lambda $ of the transmission spectrum could be
roughly evaluated by $\Delta \lambda ={\lambda}^{2}/(B{L}_{0})$. By neglecting the insertion loss of 3-dB
coupler, the spectral transmission $t$ can be described as $t=\left[1-\mathrm{cos}(\phi )\right]/2$ [22],
where, $\phi =2\pi B{L}_{0}/\lambda $is the phase difference introduced by the two
orthogonal guided modes propagating through the PM-ECF, $B={n}_{s}-{n}_{f}$is the birefringence between the fast- and
slow-axis polarization modes and λ is the operation wavelength. Without
the birefringence induced by the PM-ECF, $\phi =0$ and thus *t* = 0. This means
that all of the input light would be completely reflected by an ideal 3-dB
coupler and no transmission light could be acquired at the output port
[19]. While certain twist is
applied onto the PM-ECF, a torsion stress field is introduced in the
PM-ECF. Based on the photoelastic effect, the variations in the effective
refractive indices variation of the elliptical core can be respectively
described by the photoelastic coefficient along the fast and slow axes
[22]:

*g*and

_{s}*g*are the photo-elastic constants along the slow and fast axes, respectively; τ is twist rate defined by the torsion change rate per unit length. Therefore, the birefringence variation of the PM-ECF is$\Delta B=\Delta {n}_{s}-\Delta {n}_{f}$. Assume the torsion has no effect on the length of PM-ECF, and thus the change of phase difference is only related to the birefringence variation $\Delta \phi =2\pi {L}_{0}\Delta B/\lambda $. The wavelength shift can be described as $\delta \lambda =\Delta \lambda \Delta \phi /\left(2\pi \right)$ [22].

_{f}According to the above analysis and considering the birefringence dispersion of the PM-ECF, the wavelength shift in terms of the twist rate:

For the HB-PCF, the twist caused circular birefringence is smaller than the
inherent linear birefringence, and the factor $({g}_{s}{n}_{s}-{g}_{f}{n}_{f})/\left(B-\lambda \frac{\partial B}{\partial \lambda}\right)$is a wavelength-independent constant. and
consequently, the wavelength shift is linearly proportional to the twist
rate *τ*.

## 3. Experimental results and discussion

The input light is split into two counter-propagating portions by the 3-dB coupler. Owing to the intrinsic birefringence induced by the elliptical core, each wave would experience a corresponding phase delay after passing through the PM-ECF. And the interference spectrum could be acquired at the port connected with the OSA, as shown in Fig. 2(a). The interference spectrum is approximately a periodic wavelength-dependent function. Four interference Dips specified as a ~d have been analyzed for a wavelength range of 1150nm to 1625nm. The FSRs between adjacent two dips are 91.6nm, 102.4nm, 111.6nm, respectively. Experimental results show that the spectral interval between adjacent transmission dips increases as the operation wavelength shifts toward longer wavelength region, which is in agreement with the FSR expression $\Delta \lambda ={\lambda}^{2}/(B{L}_{0})$.

When the PM-ECF is twisted, the torsion-induced distortion and shearing
stress in the elliptical core would result in elliptical birefringence
[23]. Based on the photoelastic
effect, the effective refractive indices of the elliptical core along slow
and fast axis would change accordingly. According to Eq. (2), the change of
n_{s} and n_{f} results in the interference spectral
wavelength shift, as shown in Fig.
2(b). From this figure, it could be seen that the interference
fringes show opposite wavelength shifts as twist is respectively applied
along CW or ACW directions. Figure
3
shows the wavelength shift as functions of the twist rate for the
four interference notches a~d in Fig.
2(a). Within a twist rate range of −4.36rad/m to 4.36rad/m, the dip
wavelength shifts towards longer wavelength region as CW twist is applied
onto the PM-ECF, whereas it shifts toward shorter wavelength region as the
ACW twist is applied. This is due to the fact that the torsion-induced
circular birefringence and the intrinsic birefringence of PM-ECF would
produce an elliptical birefringence. The elliptical birefringence is
proportional to the torsion angle, and its rotary direction is determined
by the torsional direction. And the elliptical birefringence is
right-rotary when the PM-ECF is twisted along CW direction while it is
left-rotary as ACW twist is applied [23]. Different rotary directions results in the opposite change of
phase difference, which causes the operation wavelength to shift toward
longer wavelength or shorter wavelength region. The wavelength shift
sensitivities to the twist rate are 10.68nm/(rad/m), 12.40nm/(rad/m),
14.88nm/(rad/m) and 18.60nm/(rad/m) for Dip a ~d in the CW case,
respectively. And their respective wavelength shift sensitivities are
15.83nm/(rad/m), 15.56nm/(rad/m), 15.37nm/(rad/m) and 14.73nm/(rad/m) in
the ACW case. A comparison between our experimental results and other
related works is given in Table
1
. It is obvious that our proposed twist sensor shows a high
sensitivity of one to three orders of magnitude higher.

Considering the thermo-optic effect of the germanium-doped elliptical core, the temperature dependence of the interference fringes has been also investigated. The PM-ECF is placed inside a temperature-controlled oven with a temperature precision 0.1°C. When the environmental temperature increases from 27.3°C to 90°C, the interference spectral notch shifts toward shorter wavelength region, as shown in Fig. 4 . The temperature sensitivities are −0.43nm/°C, −0.39nm/°C, −0.33nm/°C, and −0.29nm/°C for dip a, b, c and d, respectively. To eliminate the temperature cross sensitivity effect, a sensor matrix for simultaneous measurement of twist rate and temperature has been set up. Dip a and d are selected to construct the sensor matrix. Considering the resultant effect of the twist and temperature, the wavelength shift can be expressed as [15]:

where, ${k}_{Ti}$ and ${k}_{\tau i}$ represent the temperature and twist rate sensitivity, respectively.In order to further improve the sensing performances of our proposed PM-ECF-based interferometer, we have theoretically as well as experimentally investigated the factors affecting its twist sensitivity.

For simplicity, when fiber dispersion is neglected Eq. (2) could be modified as:

For the HB-PCF the twist-induced circular birefringence is much weaker than the intrinsic linear birefringence, and therefore, the factor $C=({g}_{s}{n}_{s}-{g}_{f}{n}_{f})/B$is approximately a constant. It is obvious that the twist sensitivity is approximately a linear function of the operation wavelength.Considering the perfect boundary constraint, the photo-elastic constants
for circular core should comply with ${g}_{s}={g}_{f}$. For the elliptical core, the photo-elastic
constants along the slow and fast axes is a function of ellipticity, which
could be characterized by $\frac{{g}_{s}}{{g}_{f}}\approx \frac{a}{b}$ (a = 3.25μm and b = 1.5μm for semi-major and
semi-minor axes, respectively). Based on finite element method, the
elliptical fiber employed in our experiment, we could acquire the values
of n_{s}, n_{f}, B_{0}, g_{s} and
g_{f} at 1310nm. (Dip b in Fig.
2(a)).

The sensitivities of the PM-ECF-based twist sensor could be improved by optimizing the refractive index of core and cladding, core ellipticity, and etching size. Table 2 gives a comparison of the twist sensitivities at 1310nm for different settings of the refractive index of core and cladding and core ellipticity. It is clearly that smaller difference between the core and cladding refractive index and higher ellipcity would help to the improvement of fiber twist sensitivity.

In order to investigate the effect of etching PM-ECF on the twist sensitivity, the twist sensitivities of the PM-ECF before and after HF acid etching processing have been experimentally measured. The PM-ECF is etched with hydrofluoric acid to reduce the cladding diameter to about 62.5μm. Figure 5 shows the operation wavelength shift as a function of twist rate for Dip c. Due to the measurement error caused for higher torsion angles, the torsional angle is limited from −90 to 90 degrees. Figure 5(a) shows the interference spectra of the PM-ECF before and after HF acid etching processing. It could be seen that the PM-ECF before etching possesses the twist sensitivities of 0.21nm/degree and 0.23nm/degree for CW and ACW cases, respectively, as shown in Fig. 1(b). These sensitivities are much lower than the ones of the etched PM-ECF (0.44nm/degree and 0.54nm/degree for CW and ACW cases, respectively). This phenomenon could be attributed to is the fact that the etched PM-ECF would experience stronger physical deformation than the unetched fiber for the same twist angle.

From the above comparisons, we could draw a conclusion that by reducing the refractive index difference between the core and cladding, increasing the core ellipticity and decreasing the cladding diameter, the twist sensitivity could be improved.

## 4. Conclusion

A highly sensitive PM-ECFSI-based twist sensor has been proposed and experimentally demonstrated. Based on the photoelastic effect, the birefringence variation is proportional to the change of the torsional angle. And the rotary direction of the resultant elliptical birefringence is dependent on the torsion direction. The interference dip wavelength shifts toward longer wavelength region with the maximum sensitivity of 18.60nm/(rad/m) as CW twist is applied onto the PM-ECF, while the dip wavelength shifts toward shorter wavelength region with the maximum sensitivity of 15.83nm/(rad/m) as ACW twist is applied. In addition, to eliminate the temperature cross sensitivity effect, a sensor matrix for simultaneous measurement of twist and temperature has been obtained. Moreover, by optimizing the refractive index difference between the core and cladding, core ellipticity and cladding diameter, the twist sensitivity could be further improved. The proposed twist sensor has great potential in the applications of spaceflight and constructional engineering due to its prominent advantages such as compactness, good sensitivity, robustness, and immunity to the temperature cross sensitivity effect.

## Acknowledgments

This work was jointly supported by the National Natural Science Foundation of China under Grant Nos.61377095, 11274182 and 11204212, the 863 National High Technology Program of China under Grant No.2013AA014201, Key Natural Science Foundation Project of Tianjin under Grant No.13JCZDJC26100, China Postdoctoral Science Foundation Funded Project under Grant No.2012M520024, the National Key Basic Research and Development Program of China under Grant No.2010CB327605, and the Fundamental Research funds for the Central Universities.

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