Experimental and theoretical study of the in- fiber twist sensor based on quasi-fan Solc structure filter

Chunran Sun; Muguang Wang; Shuisheng Jian

doi:10.1364/OE.25.019955

1. Introduction

Twist is the very frequently measured physical parameter, and has become one of the most important mechanical parameters for security monitoring of civil engineering, industrial application and arm of humanoid robot [1, 2]. For the conventional twist sensors based on electromagnetic phenomena [3, 4] and electrical methods [5], the large size and complicated manufacture limit the practical application due to the incompatible with monitored structures. Another shortcoming of these sensors is their sensitivity to electrical noise and temperature.

Recently, the measurement of mechanical parameters through application of optical fibers is gaining significant commercial interest in various industry sectors. Twist sensors have become a topic of intense fiber-optic sensor research. Compared with traditional twist sensors, optical fiber twist sensors have drawn a lot of attention due to their unique features such as high sensitivity, insensitivity to electromagnetic interference, compact size, fast response, and so on. Consequently, a variety of optical fiber twist sensors have been reported in recent years [6–22]. In general, fiber-optic twist sensors can be classed into four main principal categories [23]: sensors based on birefringence modulation, sensors based on share stress refractive index modulation, sensors based on E-field displacement detection and other approaches. Each of these groups has a distinctive set of properties, and many of these approaches are based on the interrogation of the sensor’s spectral response. In terms of the fiber optic devices, the fiber twist sensors can be divided into two types. One is the fiber grating-based twist sensor, which has been constructed by employing fiber Bragg gratings (FBGs) [6, 7], long period fiber gratings (LPFGs) [8–10], titled FBGs (TFBGs) [11, 12] or polarization-maintaining chirped FBG (PM-CFBG) [13]. However, most fiber grating sensors suffer from the cross sensitivity of the temperature and axial strain, and they also need expensive interrogation equipment for wavelength demodulation. The other common type of twist sensor is based on fiber interferometers, which include Sagnac interferometers (SIs) [14–18], multi-modes interferometers (MMIs) [19] and Mach-Zehnder interferometers (MZIs) [20–22]. Although this kind of twist sensor is particularly attractive due to the fast response, easy fabrication and great interference fringes, the splicing joints between the single-mode fiber (SMF) and special fiber (e.g. photonic crystal fiber, polarization-maintaining fiber and no-core fiber) which are usually in the torsion structures, make the sensor fragile and a short service life. Moreover, high cost and complex manufacture also cannot be ignored.

Birefringent filters are well known for their spectral flexibility and narrow bandwidth, which include two common types: Lyot filter [24] and Solc filter [25]. Compared to the Lyot filter, the Solc filter has attracted more attention and widespread applications due to its simple configuration and low loss. However, both Lyot and Solc filters built only in the bulk form (by using birefringent crystals) are incompatible in all-optical networks. In order to solve this problem, fiber-optic Solc filters [26–28] and Solc-Sagnac filters [29–31] based on SMFs or high-birefringence fibers (HBFs) have been widely studied and applied in the Raman amplification [27], gain flattening filters [29], fiber sensing for strain and temperature [30] and single sideband modulation [31]. Nevertheless, all of these fiber-optic Solc and Solc-sagnac filters usually need many sections of HBF or SMF as well as certain spliced angles between two adjacent fibers in order to obtain narrow bandwidth and high extinction ratio (ER), which will lead to high loss and complex manufacturing procedure.

In this work, a novel twist sensor based on a quasi-fan Solc birefringent fiber filter (QFSBFF) by employing elliptical-core spun fiber (ECSF) is proposed and demonstrated. We also present a more general model for the quasi-fan Solc filter and numerically analyze the transmission characteristics of the proposed twist sensor. Compared to the regular (linear) birefringent fiber, the ECSF has its slow and fast axes rotating along the fiber like a helix structure. It is produced by spinning the glass preform of a linearly birefringent fiber in the drawing process and therefore the fiber has a very short spin period without introducing large stress to it. As a result, the overall birefringence of the fiber is reduced, while locally the fiber exhibits high birefringence making it more tolerant to random birefringence induced by bending or environmental disturbances. In the experiment, a section of SMF with the length of 0.15 m is used as a sensor head whose response is insensitive to the temperature and axial strain. By detecting the amplitude response of the resonance dip, the maximum twist sensitivity of 0.02219 dB/(°/m) in the range from −180° to 180° is achieved.

2. Experimental setup and results

The experiment setup for measuring twist angle based on the QFSBFF is constructed as shown in Fig. 1. The filter consists of two linear polarizers (LPs), a polarization controller (PC), a section of SMF (SMF-28) and a 96 m length of ECSF (produced by manufacturer, IVG). The amplified spontaneous emission (ASE, AFC BBS 1550A-TS) is used as the light source, and the transmission spectra are detected by an optical spectrum analyzer (OSA, AQ6317B) with a resolution of 0.02 nm. The spin period of ECSF is 3 mm, while the beat length of ECSF is 9.47 mm at 1550 nm which corresponds to a birefringence of 1.6375 × 10⁻⁴. The two LPs (LP1 and LP2) and a PC are used to maintain linearly polarized light and perform polarization interference as well as modulating the polarization state of incident light before ECSF. One end of the SMF is fixed by a fiber clamp, and the other end is fixed on a fiber rotator. The distance between the fiber clamp and rotator is 0.15 m.

Fig. 1 Experimental setup of proposed filter for twist sensing.

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The measured interference spectrum (black solid line) of proposed filter without rotation on the SMF can be seen in Fig. 2. Also, the spectrum of the broadband light source is measured at 20 °C in the range from 1548 nm to 1553 nm (red line). The free-spectral range (FSR) and ER of measured transmission spectrum of the filter are about 0.98 nm and 25 dB, respectively. Taking the connection of LPs and SMF-ECSF splices into account, the intrinsic insertion loss is about 6.5 dB. Here we chose the dip nearby wavelength of 1549.5 nm as a reference dip (Dip R) which is used to monitor the intensity change when twist is applied on the sensor.

Fig. 2 Measured optical spectra of the quasi-Solc filter without twist and the light source at 20 °C.

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For twist sensing measurement (at fixed room temperature 20 °C), the pre-strain is applied to the fiber to keep it straight in order to reduce the influence of any bending effect. We rotate the rotator to twist the SMF from −180° to 180° with a 10° interval in the clockwise direction. Figure 3(a) shows the transmission spectra of the sensor with different twist angles ranging from 20° to 120°. When twist is applied, the polarization state of incident light before LP2 varies, resulting in the variation of intensity for each resonance dip. On the other hand, the birefringence change of the SMF induced by the torsion is too little to shift the wavelength of the fringe dip evidently. Based on intensity modulation, the intensity difference (V_P-P) between the dip and peak wavelengths corresponding to 1549.5 nm and 1549 nm is used to calculate the ER when twist applied on the sensor. It is obvious that the intensity of peak isalmost unchanged as shown in Fig. 3(a), so we can just detect the variation of intensity of Dip R for the twist sensing. As the twist angle is different at different positions along the fiber axial direction between fiber clamp and rotator, it is necessary to use γ = τ/L to quantify the twist rate [32], where the length of SMF L between the dial and the twist angle fiber holder is about 0.15 m and the twist angle τ is varied from −180° to 180°. According to the definition of twist rate, the calculated value of twist rate should be about −1200 (°/m) to 1200 (°/m). The intensity of the Dip R changes periodically with the twist rate as a sine-like function as shown in Fig. 3(b). The twist sensitivity of proposed sensor are −0.02169 dB/(°/m) and 0.02219 dB/(°/m) by linear fitting the particular regions, which are from 40° to 90° and −10° to −60° with a correlation coefficient (R²) of 0.99713 and 0.97204, respectively. Compared to the previous fiber twist sensor by using intensity modulation (0.995 × 10⁻² dB/(rad/m) with the calculation range from 0° to 180° [6], 0.1466 dB/(rad/m) with the calculation range from 0° to 100° [13], 0.1788 dB/(rad/m) with the calculation range from 30° to 90° [18] and 0.33904 dB/(rad/m) with the calculation range from −120° to −30° [22]), the proposed sensor based on QFSBFF has a higher maximum twist sensitivity of 1.2714 dB/(rad/m) in the range from 40° to 90°.

Fig. 3 (a) Transmission spectra evolution of proposed twist sensor in clockwise direction from 20° to 120° with step of 20°. (b) The measured intensity of the selected dip (Dip R) under the corresponding torsion rate from −1200 (° /m) to 1200 (° /m)

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The responses of the sensor to axial strain and temperature are also measured separately. When temperature is fixed at 20°C, the increasing axial strain (0∼600 με) is applied on the sensor with adjustable translation stage. The relationship between the axial strain and intensity of Dip R is shown in Fig. 4(a) without additional applied twist, and the strain coefficient of the proposed sensor is only −0.86 × 10⁻³ dB/με by fitting experimental data based on the linear regression. For the temperature measurement, the sensing fiber is put on a heating block and heated from 20 °C to 80 °C with a step of 10 °C. Figure 4(b) shows the functional relationship between the ambient temperature and intensity of Dip R. Linear fitting is also done to the temperature measurement, and a temperature sensitivity of 2.46 × 10⁻³ dB /°C is experimentally obtained. The corresponding strain cross-sensitivity of −0.0388 (°/m)/με and temperature cross-sensitivity of 0.1109 (°/m)/°C can be calculated. Therefore, the proposed sensor can be considered insensitive to the temperature and strain, and the cross-sensitivity problem existing in most other twist sensors is avoided.

Fig. 4 (a) The relationship between intensity of Dip R and the axial strain from 0 to 600 με with step of 66.7 με. (b) The relationship between intensity of Dip R and the temperature from 20 to 80 °C with step of 10 °C.

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3. Theoretical model of quasi-fan Solc birefringent fiber filter

The configuration of an in-line quasi-fan Solc structure filter is illustrated in the Fig. 5. It consists of a section of spun fiber with elliptical-core which is inserted between two LPs, and a PC using to control polarization state into the ECSF. The spun fiber can be regarded as a long birefringent crystal with continuously rotational optical axes, and can be seen as composed of a lot small sections of the fiber. Each of them is equivalent to a retarder. The discrete model of the spun fiber has been built in our previous work [33]. We supposed that the whole ECSF is divided into N sections forming N retarders, the Jones matrix of each retarder (a small section of spun fiber) with its slow axis in x-axis direction is assumed to be

W (Γ) = [\begin{array}{l} \exp (i Γ / 2) \\ 0 \end{array} \begin{array}{l} 0 \\ \exp (- i Γ / 2) \end{array}]

where Γ is the phase retardation, which is expressed as

Γ = \frac{2 π L_{E C S F} B}{λ N}

where L_ECSF and B is the length and the birefringence of the ECSF, λ represents the wavelength of the input light. Due to the uniform rotation of fiber core, each retarder is rotated around the previous retarders by a certain azimuth angle (Ψ_n) which is shown in Fig. 5. The constant azimuth angle between the slow-axis of adjacent retarder can be written by

ψ = ψ_{n} = \frac{2 π L_{E C S F}}{p N}, n = 1, 2, 3... N

where p is the spin period of ECSF. The rotation matrix can be described as

Fig. 5 Schematic configuration and the model of quasi-fan Solc structure filter with ECSF.

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R (ψ_{n}) = [\begin{array}{l} \cos ψ_{n} \\ - \sin ψ_{n} \end{array} \begin{array}{l} \sin ψ_{n} \\ \cos ψ_{n} \end{array}], n = 1, 2, 3...... N

For the PC, we can use a generic unitary matrix, U_PC, to represent it [33]:

U_{P C} = [\begin{array}{l} e^{i ξ} \cos β \\ - e^{- i σ} \sin β \end{array} \begin{array}{l} e^{i σ} \sin β \\ e^{- i ξ} \cos β \end{array}]

The matrix can be characterized by ξ, σ and β, which are three real continuous parameters. Then, the whole Jones matrix of QFSBFF can be given by

\begin{array}{l} J_{f i l t e r} = M_{2} \cdot J_{E C S F} \cdot U_{P C} \cdot M_{1} \\ = M_{2} \cdot W (Γ) R (ψ_{n - 1}) W (Γ) ... R (ψ_{2}) W (Γ) R (ψ_{1}) W (Γ) \cdot U_{P C} \cdot M_{1} \\ = M_{2} \cdot R (- ψ) \cdot [^{R (ψ) W (Γ)] N} \cdot U_{P C} \cdot M_{1} \end{array}

where M₁ and M₂ are the Jones matrices of LP1 and LP2 shown in Fig. 5, which can be expressed as

M_{1} = [\begin{array}{l} \cos^{2} α_{1} \\ \sin α_{1} \cos α_{1} \end{array} \begin{array}{l} \cos η_{1} \sin α_{1} \\ \sin^{2} α_{1} \end{array}]

M_{2} = [\begin{array}{l} \cos^{2} α_{2} \\ \sin α_{2} \cos α_{2} \end{array} \begin{array}{l} \cos α_{2} \sin α_{2} \\ \sin^{2} α_{2} \end{array}]

where α₁, α₂ are the angles for aligning the polarization directions of LP1 and LP2 relative to the slow-axis of the ECSF. The part to the power of N in the Eq. (6) can be simplified by using Chebyshev’s identity [34]:

{[R (ψ) W (Γ)]}^{N} = {[\begin{array}{l} \frac{e^{Γ i / 2} \cos ψ \sin N χ - \sin (N - 1) χ}{\sin χ} \frac{e^{- Γ i / 2} \sin ψ \sin N χ}{\sin χ} \\ - \frac{e^{Γ i / 2} \sin ψ \sin N χ}{\sin χ} \frac{e^{- Γ i / 2} \cos ψ \sin N χ - \sin (N - 1) χ}{\sin χ} \end{array}]}_{}^{}

where

χ

is determined by

\cos χ = c o s ψ c o s (Γ / 2)

. Figure 6 shows the polarization characteristics of QFSBFF and evolution of polarization states when the light propagates along the z-axis. A section of SMF between ECSF and LP2 is used as twist sensor head. The incident light (E_in) is converted to linearly polarized light after propagating the LP1. By transmitting through the ECSF, the linearly polarized light is split into two beams propagating along the fast-axis and slow-axis, and produce a relative phase difference (Δφ) induced by the birefringence of the ECSF. After passing through the SMF with no rotation (twist angle τ = 0), a polarization interference will occurs at the output of LP2 finally. The transmitted light field vector and the transmissivity of the filter are then given by

E_{T} = M_{2} J_{E C S F} U_{P C} M_{1} E_{i n} = J_{f i l t e r} E_{i n}

T = \frac{I_{T}}{I_{i n}} = \frac{{(J_{f i l t e r}^{*} E_{i n}^{*})}^{T} J_{f i l t e r} E_{i n}}{E_{i n}^{*} E_{i n}}

where I_T represents the intensity of transmitted light, and I_in is the intensity of input light. (J^*E_in^*)^T denotes the conjugate transpose matrix of E_T.

Fig. 6 The polarization characteristics in the proposed configuration of quasi-fan Solc birefringent fiber filter.

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The simulated transmission spectrum (blue dash line) is shown in Fig. 7. Compared with the experimental curve (black solid line), the numerical simulation spectrum is in good agreement with the measured spectrum in shape. In the simulation, the chromatic dispersion and loss of the fiber are not taken into account, and we assume a linear input light [1, 0]^T enters into the proposed filter. The parameters of ECSF, LPs and PC used in the simulation are: L_ECSF = 96 m, p = 3 mm, B = 1.6375 × 10⁻⁴, N = 10⁹, α₁ = π/18, α₂ = 2π/5, ξ = 0, σ = 0 and β = π. The slight FSR difference between the simulation and experimental results is possibly caused by the measurement inaccuracies of L and B of the ECSF.

Fig. 7 Comparison of the simulated and measured transmission interference spectra with same ECSF parameters (L_ECSF = 96m, p = 3 mm and Β = 1.6375 × 10⁻⁴).

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4. Twist sensing analysis and discussion

When the general birefringent fiber is under linear twist without any change of other optical components, the Jones matrix of the twisted fiber can be given by [35]:

F_{L} = [\begin{array}{l} \cos η - i \frac{δ_{L}}{2} \frac{\sin η}{η} \\ - \frac{δ_{C}}{2} \frac{\sin η}{η} \end{array} \begin{array}{l} \frac{δ_{C}}{2} \frac{\sin η}{η} \\ \cos η + i \frac{δ_{L}}{2} \frac{\sin η}{η} \end{array}]

where

δ_{L} = 2 π \cdot Δ n \cdot L / λ

,

δ_{C} = 2 (1 - 2 g) \cdot τ

and

η = \sqrt{{(δ_{L} / 2)}^{2} + {(δ_{C} / 2)}^{2}}

. δ_L and δ_C are the phase terms pertaining to the inherent linear and circular birefringence of corresponding fiber, respectively. Δn is the linear birefringence, λ is the operating wavelength, τ is the twist angle, and g = 0.16 is a constant parameter for the conventional silica fiber which links the circular birefringence and the applied twist [36]. When the twist is applied onto the SMF, it can be seen as a strong twist because of the low linear birefringence of the SMF, whose circular birefringence is dominant [37]. Then, the transmission matrix of twisted SMF can be simplified as

J_{S M F} = [\begin{array}{l} \cos δ_{C} \\ - \sin δ_{C} \end{array} \begin{array}{l} \sin δ_{C} \\ \cos δ_{C} \end{array}] = [\begin{array}{l} \cos (0.92 τ) \\ - \sin (0.92 τ) \end{array} \begin{array}{l} \sin (0.92 τ) \\ \cos (0.92 τ) \end{array}]

Based on the intensity modulation, the output power of proposed twist sensor will be varied when the linear twist angle τ applying on the SMF is changing. A minimum polarization interference occurs when

Δ φ = \frac{2 π L_{E C S F} B}{λ} = (2 m + 1) π (m = 0, 1, 2...)

In this case, the phase retardation in Eq. (2) can be written by

Γ' = \frac{(2 m + 1) π}{N} (m = 0, 1, 2...)

By considering the transmission matrix of twisted SMF, the transmitted light field vector can be rewritten by

E_{T} = M_{2} J_{S M F} J_{E C S F} U_{P C} M_{1} E_{i n} = J_{f i l t e r} E_{i n}

When there is no rotation in the SMF (τ = 0), Eq. (15) can be expressed by Eq. (9). By using the new phase retardation (Γ’), the minimum transmission of the proposed filter can be expressed as

T_{\min} = \frac{I_{T}}{I_{i n}} = \frac{{(E_{T}^{*})}^{T} E_{T}}{E_{i n}^{*} E_{i n}}

When the parameters of PC and ECSF are fixed, the minimum transmission is only dependent on the direction angles (α₁, α₂) of LPs and the twist angle (τ). As SMF between the ECSF and LP2 is subjected to rotate, the polarization of the light transmitting in the SMF will be changed, resulting in the minimum transmission changes as well as the amplitude of V_P-P. It is the key characteristic for twist sensing applications by using intensity modulation.

Figures 8(a) and 8(b) show the simulation results of minimum transmittance (T_min) versus twist angle under different direction angles (α₁, α₂) of LPs. For these simulations, the parameters are assumed to be as follow: L_ECSF = 96 m, p = 3 mm, B = 1.6375 × 10⁻⁴, N = 10⁹, ξ = 0, σ = 0 and β = π. From the simulation results, we can find that due to the different direction angles of LPs, each curve is not same. But all the curves vary periodically with the torsion angle in the range from −180° to 180° as a sine-like function. As shown in the Fig. 8(a), when the direction angle of LP1 (α₁) varies, the intensity of T_min will change, whereas the corresponding twist angle forthe peak T_min remains unchanged. On the other hand, when α₁ is fixed, the direction angle of LP2 (α₂) just determines the twist angle location for a certain dip in each response curve as shown in Fig. 8(b). When α₂ enhances from 0° to 150°, the curve shifts periodically to the negative direction of twist angle axis, and the range of shift is same to the change of the α₂. Thus it is instructive to align the polarization direction of LP1 in paralleling to the principal axis of the ECSF for achieving the maximum ER and sensitivity in the measurement. In Fig. 9, the experiment data of intensity at Dip R is plotted in linear scale by black–square marks. The simulation result of the normalized minimum transmission versus twist angle is also presented by orange line when the direction angles (α₁, α₂) of LPs are assumed to be 10° and 72°. It can be seen that the simulated result agrees well with the experimental result in shape, which indicates that the established transmission model of proposed filter and analysis of twist sensing are reasonable and reliable. A slight deviation between simulation and experimental results may be resulted from the parameter misalignments of system parameter settings, such as light source, insertion loss, direction angles of LPs and others.

Fig. 8 Simulation of the intensity of minimum transmittance versus twist angle with different direction angles (α₁, α₂). (a) α₁ increases from 0° to 80° while α₂ maintains 90°. (b) α₁ keeps same value while α₂ enhances from 0° to150°.

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Fig. 9 Comparison of the simulated result and measured intensity of Dip R in linear scale when α₁ = 10°and α₂ = 72°.

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5. Conclusion

In conclusion, we have presented and experimentally demonstrated a quasi-fan Solc structure filter by using spun fiber with elliptical core for twist measurement. A discrete model of spun fiber is established and the transmissivity of the birefringent filter is derived. In the experiment, the twist angle is measured independently by a resonance dip of transmission spectrum with a maximum sensitivity of 0.02219 dB/(°/m). The spectrum response shows that the intensity of the resonance dip changes as a sine-like function with the twist angle, which is well agreed with the theoretical analysis. The strain and temperature measurements also have been demonstrated, and the sensitivities of the proposed twist sensor are respectively as low as −0.86 × 10⁻³ dB/με and 2.46 × 10⁻³ dB /°C. Therefore, it can be considered that the twist sensor has no strain and temperature cross-sensitivity problem. Moreover, the proposed twist sensor is desirable for the engineering applications with other advantages such as high sensitivity and easy fabrication.

Funding

National Natural Science Foundation of China under Grant 61475015

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Experimental and theoretical study of the in- fiber twist sensor based on quasi-fan Solc structure filter

Abstract

Corrections

1. Introduction

2. Experimental setup and results

3. Theoretical model of quasi-fan Solc birefringent fiber filter

4. Twist sensing analysis and discussion

5. Conclusion

Funding

References and links

Cited By

Figures (9)

Equations (17)

Optics Express