Highly sensitive twist sensor employing Sagnac interferometer based on PM-elliptical core fibers

Binbin Song; Hao Zhang; Yinping Miao; Wei Lin; Jixuan Wu; Haifeng Liu; Donglin Yan; Bo Liu

doi:10.1364/OE.23.015372

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.

Fig. 1 Schematic experiment setup of the SI-based twist sensing system. Inset: Enlarged view of sensor head (left) and microscopic cross sectional image of the PM-ECF (right).

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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 $Δ λ$ of the transmission spectrum could be roughly evaluated by $Δ λ = λ^{2} / (B L_{0})$ . By neglecting the insertion loss of 3-dB coupler, the spectral transmission $t$ can be described as $t = [1 - \cos (φ)] / 2$ [22], where, $φ = 2 π B L_{0} / λ$ 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, $φ = 0$ 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]:

Δ n_{s} = g_{s} τ n_{s}, Δ n_{f} = g_{f} τ n_{f}

where, g_s and g_f 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

Δ B = Δ n_{s} - Δ 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

Δ φ = 2 π L_{0} Δ B / λ

. The wavelength shift can be described as

δ λ = Δ λ Δ φ / (2 π)

[22].

Fig. 2 (a). Reflection spectrum of the SI-based PM-ECF with no twist applied. (b) Reflection spectral evolution of the SI-based PM-ECF when the twist angle ranges from −120 degrees to 120 degrees.

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

δ λ = λ τ (g_{s} n_{s} - g_{f} n_{f}) / (B - λ \frac{\partial B}{\partial λ})

For the HB-PCF, the twist caused circular birefringence is smaller than the inherent linear birefringence, and the factor $(g_{s} n_{s} - g_{f} n_{f}) / (B - λ \frac{\partial B}{\partial λ})$ 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 $Δ λ = λ^{2} / (B L_{0})$ .

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.

Fig. 3 Wavelength shift as functions of the twist rate for (a) Dip a, (b) Dip b, (c) Dip c, and (d) Dip d, respectively.

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Table 1. A comparison of the twist sensitivity between our work with other related reports

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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]:

δ λ_{i} = k_{T i} Δ T + k_{τ i} Δ τ, (i = a, d)

where,

k_{T i}

and

k_{τ i}

represent the temperature and twist rate sensitivity, respectively.

k_{T} = \frac{λ}{B - λ \frac{\partial B}{\partial λ}} (\frac{\partial B}{\partial T} + \frac{B}{L} \frac{\partial L}{\partial T}), K_{τ} = \frac{λ}{B - λ \frac{\partial B}{\partial λ}} (g_{s} n_{s} - g_{f} n_{f})

The change of temperature and twist rate could be acquired from the wavelength shift of dip a and dip d by using the following sensor matrix:

(\begin{matrix} Δ T \\ Δ τ \end{matrix}) = \frac{1}{D} (\begin{matrix} k_{τ d} & - k_{τ a} \\ - k_{T d} & k_{T a} \end{matrix}) (\begin{matrix} Δ λ_{a} \\ Δ λ_{d} \end{matrix})

where,

D = k_{T a} k_{τ d} - k_{τ a} k_{T d}

. According to our experimental results, the above sensing matrix could be written as:

Fig. 4 Temperature dependences of the wavelength shift for the four interference spectral dips.

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\begin{array}{l} CW case : (\begin{matrix} Δ T \\ Δ τ \end{matrix}) = \frac{1}{- 4.9008} (\begin{matrix} 18.6 & - 10.68 \\ 0.29 & - 0.43 \end{matrix}) (\begin{matrix} Δ λ_{a} \\ Δ λ_{d} \end{matrix}) \\ ACW case : (\begin{matrix} Δ T \\ Δ τ \end{matrix}) = \frac{1}{- 1.7432} (\begin{matrix} 14.73 & - 15.83 \\ 0.29 & - 0.43 \end{matrix}) (\begin{matrix} Δ λ_{a} \\ Δ λ_{d} \end{matrix}) \end{array}

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:

\frac{d δ λ}{d τ} = λ (g_{s} n_{s} - g_{f} n_{f}) / B_{0}

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, B₀, 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.

Table 2. A comparison of the twist sensitivities at 1310nm for different settings of core/cladding refractive index and core ellipticity.

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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.

Fig. 5 (a). Interference spectra of the PM-ECF before and after HF acid etching; (b) Operation wavelength shift of Dip c as a functions of twist angle for the PM-ECF before and after HF acid etching.

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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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Literatures	Twist sensitivity	Order of magnitude
Our work	18.60nm/(rad/m) or (0.68nm/degree)	——
C.Y. Lin et al. [1]	1.06nm/(rad/m)	10¹
J Ruan et al. [2]	0.072nm/(rad/m)	10³
D. E. Ceballos-Herrera et al. [3]	12.4nm(rad/cm)	10²
R. Gao et al. [4]	1.959nm/(rad/m)	10¹
S.M. Nalawade et al. [9]	79.83pm/degree	10¹
H.F. Xuan et al. [13]	70pm/(rad/m)	10³
Our previous work [14]	1.28615nm/(rad/m)	10¹
O. Frazão et al. [15]	0.08 nm/ degree	10¹
H.M. Kim et al. [18]	0.06 nm/ degree	10¹
Y.P. Wang et al. [23]	0.0645nm/(rad/m)	10³

Effect factor	Parameters		Twist sensitivities (nm/(rad/m))
Refractive index	Core	Cladding	Twist sensitivities (nm/(rad/m))
	1.474	1.444	11.84
	1.473(our PM-ECF)		12.40
	1.472		15.48
Core ellipticity	a/b = 4/1.5		17.72
	a/b = 3.25/1.5(our PM-ECF)		12.40
	a/b = 3/1.5		10.63

Literatures	Twist sensitivity	Order of magnitude
Our work	18.60nm/(rad/m) or (0.68nm/degree)	——
C.Y. Lin et al. [1]	1.06nm/(rad/m)	10¹
J Ruan et al. [2]	0.072nm/(rad/m)	10³
D. E. Ceballos-Herrera et al. [3]	12.4nm(rad/cm)	10²
R. Gao et al. [4]	1.959nm/(rad/m)	10¹
S.M. Nalawade et al. [9]	79.83pm/degree	10¹
H.F. Xuan et al. [13]	70pm/(rad/m)	10³
Our previous work [14]	1.28615nm/(rad/m)	10¹
O. Frazão et al. [15]	0.08 nm/ degree	10¹
H.M. Kim et al. [18]	0.06 nm/ degree	10¹
Y.P. Wang et al. [23]	0.0645nm/(rad/m)	10³

Effect factor	Parameters		Twist sensitivities (nm/(rad/m))
Refractive index	Core	Cladding	Twist sensitivities (nm/(rad/m))
	1.474	1.444	11.84
	1.473(our PM-ECF)		12.40
	1.472		15.48
Core ellipticity	a/b = 4/1.5		17.72
	a/b = 3.25/1.5(our PM-ECF)		12.40
	a/b = 3/1.5		10.63

Highly sensitive twist sensor employing Sagnac interferometer based on PM-elliptical core fibers

Abstract

1. Introduction

2. Principle and experiment

3. Experimental results and discussion

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Tables (2)

Equations (7)

Optics Express