Abstract

A compact temperature-insensitive optical fiber twist sensor based on multi-phase-shifted helical long period fiber grating has been proposed and experimentally demonstrated in this paper. A multi-phase-shifted helical long period fiber grating is fabricated with a multi-period rotation technology. A π/2 and a 3π/2 phase shift is introduced in the helical long period fiber grating by changing the period. The helical pitch can be effectively changed with a different twist rate, which is measured by calculating the wavelength difference between two phase shift peaks. Although the wavelength of the phase shift peak also shifts with a change of the temperature, the wavelength difference between two phase shift peaks is constant due to two fixed phase shifts in the helical long period fiber grating, which is extremely insensitive to temperature change for the multi-phase-shifted helical long period fiber grating. The experimental results show that a sensitivity of up to 1.959 nm/(rad/m) is achieved.

© 2014 Optical Society of America

1. Introduction

Measurements of twist angle are increasingly essential in many practical applications, such as the automotive industry, nacelle rotation, anthropomorphic robots, and so on. In smart structure monitoring, twist angle is one of the most critical mechanical parameters for infrastructure deterioration. In principle, twist can be detected by electrical methods, which are associated essentially with variations in strain-based electrical resistance [1]. However, a shortcoming of these sensors is their high sensitivity to electrical noise and temperature. Another conventional method for the measurement of twist is based on electromagnetic phenomena, such as Faraday’s law, magnetostriction, and the magnetoelastic effect [2]. The electromagnetic-phenomena-based twist sensor possesses remarkable resolution, good accuracy, and easier installation. The associated drawbacks are complicated manufacturing, bulky heavy structure, and need for a robust magnetic shield.

Optical fiber twist sensors have attracted a great deal of attention over the past decade because of their particular characteristics, such as light weight, small size, high sensitivity, and immunity to electromagnetic fields [3]. The most common approach to the fabrication of fiber twist sensors is the natural characteristics of the polarization in the fiber. The orthogonal polarization modes or single polarization mode can be excited through various types of fiber components, such as UV-inscription tilted fiber gratings (TFGs) [4], polarization-maintaining fiber Bragg gratings (PM-FBGs) [5], or high-birefringence fibers [6]. The direction of the polarization mode is changed by rotating the fiber, and the twist angle is measured by interrogating the visibility or intensity of the optical light. Besides, high-birefringence-based fiber twist sensors have attracted much attention by researchers because the birefringence in the fiber is changed by twisting. Thus the Sagnac loop structure or distributed Bragg reflector (DBR) fiber grating laser has been investigated in detail for the measurement of the twist [79]. On the other hand, long period fiber gratings (LPFGs) can be fabricated by using CO2 radiation [10], corrugated structures [11], UV radiation [12], or mechanical deformation [13]. Both the elliptical birefringence and the unsymmetrical distribution of the refractive index induced by the twist angle cause a wavelength shift for the transmission dip. However, the temperature always results in cross-sensitivity for the LPFG, which is unsuitable for real applications. In addition, a fiber twist sensor based on the interference between multi-mode or two linear polarization (LP) modes is presented [14, 15]. The interferometric twist sensors not only show a high sensitivity of twist angle, but also possess low temperature cross-sensitivity. Moreover, a novel helical photonic crystal fiber (PCF) has been presented recently. The “space-filling” mode (SM) in the cladding forms an orbital angular momentum, which results in the tunable refractive index vector of the SM mode along the helical path [16].

The helical structure of the long-period fiber grating (HLPFG) has attracted much attention by researchers since its first demonstration. The periodic effective indices perturbation in the fiber is generated by the helical structure [17]. The transmission spectrum of an HLPFG displays several dips that correspond to coupling of light from the core mode to the cladding modes. An HLPFG pair was inserted into a null core hollow optical fiber or a single mode fiber (SMF) [18, 19]. As a torsional stress is applied to the HLPFG pair, the helical pitch can be effectively reduced or enlarged, and the resonances of the HLPFG pair moves to a shorter or a longer wavelength, respectively. Although the HLPFG possesses high sensitivity, it suffers from serious temperature cross-sensitivity, similarly to conventional LPFGs.

In this paper, we report a temperature-insensitive optical fiber twist sensor with a multi-phase-shifted HLPFG (MPS-HLPFG). The MPS-HLPFG is fabricated with a multi-period rotation technology that involves heating the fiber with a CO2 laser. A π/2 phase-shift and a 3π/2 phase-shift are introduced in an HLPFG by changing the period in the HLPFG. The resonance wavelength dip of the transmission spectrum would shift as a torsional stress is applied to the sensor since the helical pitch can be effectively changed. Compared with the conventional LPFG-based sensor, the locations of the phase shift peaks in the enveloped MPS-HLPFG are hardly changed by the temperature due to the identical thermal expansion effects between the original period and the changed period. Therefore, the temperature cross-sensitivity can be eliminated by calculating the wavelength difference between two phase shift peaks.

2. Operation principle

Fiber twisting rotates the principal axis of the conventional HLPFG. For each period, the end of the period is rotated and the helical pitch can be enlarged, as shown in Figs. 1(a) and 1(b). The changed angle for the end of the period between pre- and post-twisting is θ, as shown in Fig. 1(c). The associated helical pitch of the HLPFG is changed to

Λa=2π2πθΛb
where Λb and Λa are the pitch of HLPFG before and after twisting.

 

Fig. 1 The changed pitch of each period induced by twisting: (a) before twisting; (b) after twisting. (c) The changed angle for each period before and after twisting.

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According to the phase-matching condition, the wavelength dip of the HLPFG would shift as the pitch of the HLPFG changes. Although the twist angle can be measured by interrogating the wavelength shift of the HLPFG, the variance of temperature also causes the same change in the pitch of the HLPFG, which suffers a serious temperature cross-sensitivity. In order to eliminate the temperature cross-sensitivity, the wavelength distance between two phase-shift peaks in the MPS-HLPFG is used to measure the twist angle in our experiment.

When the pitch of one period in the HLPFG is different with other period, a phase-shift would be inserted into the HLPFG, which forms a MPS-HLPFG. The phase shift in the MPS-HLPFG can be approximately expressed as [20]

ϕ=2πL(1Λo1Λc)
where ϕ is the inserted phase shift, Λo and Λc are the pitch of the original period and the changed period in MPS-HLPFG, and L is the length of the changed period.

The MPS-HLPFG can be described by the conventional coupled-mode theory between the core and the cladding modes [21]. Therefore, the transmission matrix method can be applied to analyze the MPS-HLPFG [22]. Assuming that a π/2 phase-shift and a 3π/2 phase-shift is introduced into the HLPFG, respectively. The whole MPS-HLPFG is divided into three segments by using the transmission matrix method, which can be expressed as

(aco(L)acl(L))=(ei(Δβ2)L100ei(Δβ2)L1)(t1r1r1t1*)×(eiϕ1/200eiϕ1/2)×(ei(Δβ2)L200ei(Δβ2)L2)(t2r2r2t2*)×(eiϕ2/200eiϕ2/2)×(ei(Δβ2)L300ei(Δβ2)L3)(t3r3r3t3*)×(aco(0)acl(0)).
where aco and acl represent the modal amplitudes of the core and the cladding modes, respectively, Li is the length of the HLPFG separated by the phase shifts, ϕ1 and ϕ2are phase shifts, which are π/2 and 3π/2, respectively, and ri and tidescribe the cladding mode coupling ratio and the core mode transmission ratio of each HLPFG, which are given by
ti=cos(SmLi)+jδmSmsin(SmLi)ri=jκmSmsin(SmLi)
where κm is the coupling constant, and Δβis the phase-matching condition.Δβ=βcoβcl22πΛ, Λ is the grating period, βco and βcl are the propagation constants of the core and the cladding modes, respectively, andSm=κm2+δm2.

The transmission matrix of the MPS-HLPFG is similar to that of a conventional phase-shifted LPFG, whereas the phase-matching condition is Δβ=βcoβcl22πΛ, while the phase-matching condition for a conventional LPFG isΔβ=βcoβcl2πΛ [17].

The simulation of the MPS-HLPFG is shown in Fig. 2(a) by calculating Eq. (3). Given that the coupling coefficient is κm=2.15×105, the length of the grating is L1=L2=L2=5mm, and the period is Λ=450um.

 

Fig. 2 The simulation of the MPS-HLPFG with different twist angles: (a) 0°, (b) 20°, (c) 40°, (d) 60°.

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Due to the inserted phase-shifts, the original loss band of the HLPFG is split into three loss-dips, as shown in Fig. 2(a). When the inserted phase-shift is π/2, a phase-shift peak appears on the left side. On the contrary, when the phase-shift is 3π/2, the other phase-shift peak appears on the right side. Those two phase-shift peaks are located in the enveloped loss band symmetrically.

As a torsional stress is applied to the MPS-HLPFG, both the pitch of the original helical period and that of the changed period are changed simultaneously, which can be expressed as

Λo'=2π2πθΛoΛc1'=2π2πθΛc1Λc2'=2π2πθΛc2
where Λo and Λo' are the pitch of the original period before and after twisting, Λc1and Λc1'are the pitch of the changed period for π/2 phase shift before and after twisting, and Λc2 and Λc2' are the pitch of the changed period for3π/2 phase shift before and after twisting.

Because of the changed pitch induced by the fiber twisting, the phase shift is changed to

ϕ1'=2πλL(1Λo'1Λc1')=2πλL(1(2π2πθ)Λo1(2π2πθ)Λc1)=(2πθ2π)2πλL(1Λo1Λc1)=(2πθ2π)ϕ1=(2πθ2π)π2ϕ2'=2πλL(1Λo'1Λc2')=2πλL(1(2π2πθ)Λo1(2π2πθ)Λc2)=(2πθ2π)2πλL(1Λo1Λc2)=(2πθ2π)ϕ2=(2πθ2π)3π2
whereϕ1' and ϕ2' are the phase shifts for π/2 and 3π/2 after twisting.

It is obvious that the change for the π/2 and 3π/2 phase shifts are different. Therefore, the location of two phase shift peaks is not symmetrical in the enveloped loss band. The transmission of the MPS-HLPFG under different rotation angles is numerically investigated by combining Eqs. (3) and (6), as shown in Figs. 2(b)2(d). With the increase of the rotation angle, the enveloped loss band shifts to a longer wavelength. Furthermore, the locations of these two phase shift peaks in the enveloped loss band are also changed simultaneously. The wavelength distance between two phase shift peaks is 23, 19, and 15 nm when the rotation angle is 20, 40, and 60°, respectively, which indicates that the twist rate can be measured by interrogating the wavelength distance between two phase shift peaks.

For the temperature cross-sensitivity, the thermal expansion effects between the original period and the changed period are identical. Therefore, the original period, the changed period, and the length of the changed period would change with the same thermal expansion coefficient, and the phase-shift inserted in the MPS-HLPFG can be approximately expressed as

ϕ1''=2πλ(T+1)L(1(T+1)Λo1(T+1)Λc1)=2πλL(1Λo1Λc1)=ϕ1=π2ϕ2''=2πλ(T+1)L(1(T+1)Λo1(T+1)Λc2)=2πλL(1Λo1Λc2)=ϕ2=3π2
where ϕ1'' and ϕ2'' are the π/2 and 3π/2 phase shifts with the change in temperature, is the thermal expansion coefficient, and Tis the temperature change.

According to Eq. (7), the phase-shift inserted in the MPS-HLPFG is kept constant at different temperatures. We also calculate the transmission spectrum of the MPS-HLPFG at different temperatures, as shown in Figs. 3(a)3(c). The simulation results show that although the phase shift peaks shift to a longer wavelength with the increase of the temperature, the wavelength distance between two phase shift peaks is fixed because of the fixed phase shifts. Therefore, the MPS-HLPFG can measure the twist angle without the temperature cross-sensitivity.

 

Fig. 3 The simulation of the MPS-HLPFG with different temperatures: (a) 0 °C; (b) 100 °C; (c) 200 °C.

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3. Fabrication method of the MPS-HLPFG

The fabrication setup of the MPS-HLPFG is composed of one motorized precision rotating holder (S67-83-MO, Parker), one fiber holder (Newport), one translation stage (NRT150, Thorlabs), and a CO2 laser (series 48, Synrad) with a ZnSe cylindrical lens. Both holders were mounted on the translation stage, as shown in Fig. 4.

 

Fig. 4 The fabrication setup of the MPS-HLPFG.

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According to Eq. (2), a phase shift can be inserted into the HLPFG by changing the period of the HLPFG. Therefore, a π/2 and 3π/2 phase-shift can be fabricated by changing the rotation speed in the HLPFG. At the beginning, one end of a SMF was fixed, while the other end was rotated by using a motorized precision rotating holder along its axis at a speed of 8.7 °/s. During the rotation, the translation stage was shifted at a speed of 10 um/s, and the CO2 laser beam was scanned on the fiber with a 140 mm focal length lens. The spot beam diameter was 200 μm. The laser power was about 10 W in order to heat the fiber to the glass-softening temperature. In this way, the helical structure of the HLPFG was fabricated, as shown in Fig. 5(a). Then when the translation stage was shifted to 4.0 mm, the speed of the rotation was changed to 6.9 °/s. After a shift of 1.1 mm, the speed of the rotation was returned to 8.7 °/s. As a result, a section of the changed period was inserted into the HLPFG. According to Eq. (2), a π/2 phase-shift is formed in the HLPFG, as shown in Fig. 5(b). Then, after the translation stage continued to move to 4.0 mm, the speed of the rotation was changed to 4.8 °/s, and a 3π/2 phase-shift was also formed in the HLPFG, as shown in Fig. 5(c). Finally, the translation stage continued to move to 4.0 mm again at a speed of 8.7 °/s.

 

Fig. 5 Closed view of the MPS-HLPFG: (a) the original period; (b) the changed period of π/2 phase-shift; (c) the changed period of 3π/2 phase-shift; (d) schematic of the MPS-HLPFG.

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In the fabrication, the original helical period was about 413 um, and the changed periods were 520 and 720 µm, corresponding to the π/2 and 3π/2 phase-shifts, respectively. A total of 29 pitches were constructed along the MPS-HLPFG. The total length of the MPS-HLPFG including of phase shift areas was about 14.5 mm. The π/2 and 3π/2 phase-shift were inserted into the ninth and twentieth period in the MPS-HLPFG, respectively. The entire MPS-HLPFG is shown in Fig. 5(d).

4. Experiment and discussion

The experimental setup of the proposed twist sensor is shown in Fig. 6. The light source is a super-wideband light source (ASLD-CWDM-5-B-FA, Amonics) with wavelength covering 1250-1650 nm, and the output power is 20 mW. An optical spectrum analyzer (OSA) (AQ6317B, Agilent Technologies) with a resolution of 0.005 nm is used to measure the transmission spectrum of the MPS-HLPFG. During the experiment, one end of the MPS-HLPFG is fixed to a stationary holder, and the other end is fixed to the center of a rotatable disc that can be turned to apply twist to the MPS-HLPFG. The distance between the fiber holder and the rotator is 37 cm. The pitch of the original period for the MPS-HLPFG is 413 um, and the pitches of the changed periods corresponding to the π/2 and 3π/2 phase shifts are 520 and 720 um, respectively.

 

Fig. 6 Schematic diagram of experimental setup.

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The transmission spectrum of the MPS-HLPFG without twisting was measured, as shown in Fig. 7. As expected, two symmetrical peaks at wavelengths of 1537.54 and 1566.98 nm are shown in the enveloped loss band, which proves that a π/2 phase-shift and a 3π/2 phase-shift are created in the MPS-HLPFG. The full wave at half maximum (FWHM) of the MPS-HLPFG is 55 nm. A HLPFG without phase shift is also fabricated with the same pitch, and a comparison of the transmission spectra between the HLPFG and the MPS-HLPFG is also shown in Fig. 7. There isn’t phase shift peak in the transmission spectrum of the HLPFG because of the fixed period. The insertion loss between the MPS-HLPFG and the HLPFG was about 6 dB, which was mainly attributed to the intrinsic loss in the changed period. However, the entire FWHM of the MPS-HLPFG is wider than that of the HLPFG.

 

Fig. 7 Comparison of the transmission spectra between a MPS-HLPFG and a HLPFG with the same pitch.

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The effect of fiber twisting on the spectrum of the MPS-HLPFG was investigated experimentally. In order to obtain the twist sensitivity of the sensor, the transmission spectra were recorded by increasing the twist angle from –360 to 360 ° with an interval of 90°. In this experiment, we define an increase in the twist angle as the clockwise direction and a decrease in the twist angle as the counterclockwise direction. As the MPS-HLPFG was twisted in the clockwise direction, the pitch of the period was enlarged, and the enveloped loss band exhibited a red shift as shown in Fig. 8(a). On the contrary, the transmission spectrum of the MPS-HLPFG shifted to the shorter wavelength when the MPS-HLPFG was twisted in a counterclockwise direction, which was induced by the reduction of the pitch, as shown in Fig. 8(b).

 

Fig. 8 (a) The transmission spectrum of the MPS-HLPFG with (a) clockwise and (b) counterclockwise twisting.

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Then we analyze the optical characteristics of the individual phase shift peak separately, as shown in Fig. 9. For the π/2 phase shift peak, the increased rotation angle resulted in a shift to a longer wavelength. However, the wavelength of the 3π/2 phase shift peak exhibits a blue shift with the increase of the rotation angle. The twist rate is defined as R=θ/L, and the linear fitting curves of two phase shift peaks are calculated. The sensitivity of the π/2 phase shift peak is 1.025 nm/(rad/m), which is larger than that of the 3π/2 phase shift peak (0.937 nm/(rad/m)). After analyzing the spectral characteristics of individual phase shift peak, we also calculate the wavelength difference between the π/2 and 3π/2 phase shift peaks. The wavelength difference decreased with the increase of the rotation angle. The twist sensitivity of the MPS-HLPFG is achieved as 1.959 nm/(rad/m). Because the resolution of the OSA was 0.005 nm, the resolution of the MPS-HLPFG was 0.002 rad/m.

 

Fig. 9 Wavelength shift of the phase shift peaks and the wavelength difference.

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For optical fiber twist sensors, especially LPFG-based fiber twist sensors, temperature is always a serious cross-sensitivity. Although some methods are presented to overcome the temperature cross-sensitivity, such as the PCF-based Sagnac interferometer or multi-mode interferometer, such sensors consist of many optical devices, whose integration should be improved for practical applications. In our experiment, the temperature dependence of the sensor is investigated by fixing the MPS-HLPFG in a chamber, whose temperature is adjusted within the range from 20 to 120 °C. The variation of the wavelength shift with the temperature change for the π/2 and 3π/2 phase shift peaks and the wavelength difference between the two phase shift peaks are shown in Fig. 10(a). Although the π/2 and 3π/2 phase shift peaks were shifted to the longer wavelength simultaneously, it can be observed that the locations of the two phase shift peaks changed slightly with the rise in temperature in the enveloped loss band, which resulted in the fixed wavelength difference, as shown in Fig. 10(b). This result is in agreement on the calculation of Eq. (7). The standard variation of the wavelength difference is only 0.04 nm in the temperature range from 20 to 120 °C. This value is smaller than that of the twist sensor based on axial distributed Bragg reflector fiber laser [9] and the multi-mode interferometer-based twist sensor [14]. Therefore, the proposed sensor is extremely insensitive to temperature change, which overcomes the temperature cross-sensitivity of the LPFG-based fiber twist sensor.

 

Fig. 10 (a) Transmission spectra of the MPS-HLPFG at different temperatures. (b) Wavelength shifts and wavelength difference of two phase shift peaks at different temperatures.

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For the analysis of polarization characteristics, we measured the polarization-dependent loss (PDL) of the fabricated MPS-HLPFG. The PDL is defined as the maximum change in the transmitted power for polarizations. A tunable laser diode (81980A, Agilent Technologies) with wavelength covering 1450 nm-1750 nm was used as the light source, and the output power was 20 mW. A polarization controller (PC030, Thorlabs) was used to control the polarization of the light source. A powermeter (PM20, Thorlabs) with a resolution of 0.01 dB was used to measure the intensity of the transmission spectrum. We measured the PDL of the MPS-HLPFG with the wavelength range from 1520 nm to 1570 nm, as shown in Fig. 11. The MPS-HLPFG shows a dramatically low PDL value (1.73 dB), which indicates that the MPS-HLPFG is insensitive to the change of the polarization.

 

Fig. 11 The PDL of the MPS-HLPFG at different wavelength.

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The relationship between the pitch of the MPS-HLPFG and the sensitivity has also been investigated. Three MPS-HLPFGs with the same original period of 413 um were fabricated. The pitch of π/2 phase-shift for all MPS-HLPFGs is 520 µm. However, the pitch for the other phase-shift in each MPS-HLPFG was different, which was 630 µm, 720 µm, and 780 µm, respectively. The transmission spectra of the MPS-HLPFG with different pitch are shown in Fig. 12(a). With the increase of the pitch, the wavelength difference between two phase shift peaks is increased simultaneously, which indicates that different phase – shifts were inserted into the MPS-HLPFGs. The wavelength difference between two phase shift peaks for fiber twisting are shown in Fig. 12(b). The sensitivity of the MPS-HLPFG rise as the pitch of the MPS-HLPFG increases, and the maximum sensitivity of the sensor with the pitch of 780μm is 2.075 rad/m.

 

Fig. 12 (a) Transmission spectra of the MPS-HLPFG with different pitch. (b) Wavelength difference of two phase shift peaks.

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The repeatability of the sensor was also experimentally tested. A section of the MPS-HLPFG was measured by applying torsional stress in clockwise and counterclockwise twisting directions, respectively. The pitch of the original period for the MPS-HLPFG is 413 um, and the pitches of the changed periods corresponding to the π/2 and 3π/2 phase shifts are 520 and 720 um, respectively. The corresponding wavelength difference between two phase shift peaks is shown in Fig. 13. Results in clockwise and counterclockwise twisting directions are in good agreement with each other, and the maximum variation is only 0.03 nm with the twist rate of 4.7 rad/m. The experimental data indicates that the MPS-HLPFG possesses high reproducibility.

 

Fig. 13 Wavelength difference in clockwise and counterclockwise twisting directions.

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In order to investigate the axial strain cross-sensitivity of the sensor, one end of the MPS-HLPFG was fixed, whereas the other end was stretched by using a manual translation stage. Strain was calculated from the elongation of the stretched fiber divided by the original length. Transmission spectra with the strain change are shown in Fig. 14(a). Both phase shift peaks for the π/2 and 3π/2 phase-shift shift to the longer wavelength with the increase of the axial strain, and the strain sensitivity of the MPS-HLPFG is 7 pm/ με. However, the locations of two phase shift peaks in the enveloped attenuation band were changed slightly with the rise of axial strain. Figure 14(b) represents the wavelength difference between the two phase shift peaks response to axial strain in the range of 0 to 1000με. It can be seen that the wavelength difference almost keeps constant. The standard variation of the wavelength difference is only 0.02 nm, indicating that the wavelength difference is nearly independent with the axial strain. This can be explained by the fixed phase shifts in the MPS-HLPFG. The original period, the changed period, and the length of the changed period would change with the same elongation, and the phase-shift inserted in the MPS-HLPFG can be approximately expressed as [23]

ϕ1'''=2πλ(FAE+1)L(1(FAE+1)Λo1(FAE+1)Λc1)=2πλL(1Λo1Λc1)=ϕ1=π2ϕ2'''=2πλ(FAE+1)L(1(FAE+1)Λo1(FAE+1)Λc2)=2πλL(1Λo1Λc2)=ϕ2=3π2
where ϕ1''' and ϕ2''' are the π/2 and 3π/2 phase shifts with the change of axial strain, F, A, and E are strain, cross-sectional areas of the MPS-HLPFG, and Young`s Modulus, which are same in one MPS-HLPFG. Therefore, the origin of the spectra changes of the MPS-HLPFG comes from the tortional stress, rather than the longitudinal stress in axial direction. This characteristic could be very useful for practical applications since the axial strain effect can be also eliminated.

 

Fig. 14 (a) Transmission spectra of the MPS-HLPFG with different axial strain. (b) Wavelength difference of two phase shift peaks with different axial strain.

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5. Conclusion

In conclusion, a compact temperature-insensitive optical fiber twist sensor based on the MPS-HLPFG has been proposed and experimentally demonstrated in this paper. The MPS-HLPFG is fabricated with a multi-period rotation technology. A π/2 and a 3π/2 phase shift are introduced in an HLPFG by changing the period in the HLPFG. The twist rate can be measured by calculating the wavelength difference between phase shift peaks. Although the wavelength of the phase shift peak would shift with the change in temperature, the fixed phase shift induces a constant wavelength difference, which is extremely insensitive to temperature change for the MPS-HLPFG. The experimental results show that a sensitivity of up to 1.959 nm/(rad/m) is achieved. Therefore, the simple scheme for an optical fiber twist sensor with a low temperature cross-sensitivity is expected to be used in the fields of structural health monitoring, the automotive industry, nacelle rotation, and so on.

Acknowledgments

This work was supported by the Natural Scientific Foundation of China (51075037), the Defense Equipments Foundation of China (9140A0206041213Q1028), the Aeronautics Key Foundation of China (20110343004), and the Doctoral Foundation of the Education Ministry of China (20101101110014).

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14. B. B. Song, Y. P. Miao, W. Lin, H. Zhang, J. X. Wu, and B. Liu, “Multi-mode interferometer-based twist sensor with low temperature sensitivity employing square coreless fibers,” Opt. Express 21(22), 26806–26811 (2013). [CrossRef]   [PubMed]  

15. H. Xuan, W. Jin, M. Zhang, J. Ju, and Y. B. Liao, “In-fiber polarimeters based on hollow-core photonic bandgap fibers,” Opt. Express 17(15), 13246–13254 (2009). [CrossRef]   [PubMed]  

16. X. M. Xi, G. K. L. Wong, T. Weiss, and P. St. J. Russell, “Measuring mechanical strain and twist using helical photonic crystal fiber,” Opt. Lett. 38(24), 5401–5404 (2013). [CrossRef]   [PubMed]  

17. S. Oh, K. R. Lee, U. C. Paek, and Y. J. Chung, “Fabrication of helical long-period fiber gratings by use of a CO2 laser,” Opt. Lett. 29(13), 1464–1466 (2004). [CrossRef]   [PubMed]  

18. W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).

19. W. J. Shin, B. A. Yu, Y. C. Noh, J. M. Lee, D. K. Ko, and K. Oh, “Bandwidth-tunable band-rejection filter based on helicoidal fiber grating pair of opposite helicities,” Opt. Lett. 32(10), 1214–1216 (2007). [CrossRef]   [PubMed]  

20. H. Ke, K. S. Chiang, and J. H. Peng, “Analysis of Phase-Shifted Long-Period Fiber Gratings,” IEEE Photon. Technol. Lett. 10(11), 1596–1598 (1998). [CrossRef]  

21. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]  

22. T. Erdogan, “Cladding-mode resonances in short- and long-period fiber gratings filters,” J. Opt. Soc. Am. A 14(8), 1760–1773 (1997). [CrossRef]  

23. M. Rosenberger, S. Hessler, S. Belle, B. Schmauss, and R. Hellmann, “Compressive and tensile strain sensing using a polymer planar Bragg grating,” Opt. Express 22(5), 5483–5490 (2014). [CrossRef]   [PubMed]  

References

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  1. P. L. Fulmek, F. Wandling, W. Zdiarsky, G. Brasseur, and S. P. Cermak, “Capacitive sensor for relative angle measurement,” IEEE Trans. Instrum. Meas. 51(6), 1145–1149 (2002).
    [Crossref]
  2. D. Vischer and O. Khatib, “Design and development of high-performance torque controlled joints,” IEEE Trans. Robot. Autom. 11(4), 537–544 (1995).
    [Crossref]
  3. W. Yiping, M. Wang, and X. Q. Huang, “In fiber Bragg grating twist sensor based on analysis of polarization dependent loss,” Opt. Express 21(10), 11913–11920 (2013).
    [Crossref] [PubMed]
  4. Z. J. Yan, C. B. Mou, K. M. Zhou, X. F. Chen, and L. Zhang, “UV-inscription, polarization-dependant loss characteristics and applications of 45° tilted fiber gratings,” J. Lightwave Technol. 29(18), 2715–2724 (2011).
    [Crossref]
  5. F. Yang, Z. J. Fang, Z. Q. Pan, Q. Ye, H. W. Cai, and R. H. Qu, “Orthogonal polarization mode coupling for pure twisted polarization maintaining fiber Bragg gratings,” Opt. Express 20(27), 28839–28845 (2012).
    [Crossref] [PubMed]
  6. D. Lesnik and D. Donlagic, “In-line, fiber-optic polarimetric twist/torsion sensor,” Opt. Lett. 38(9), 1494–1496 (2013).
    [Crossref] [PubMed]
  7. H. M. Kim, T. H. Kim, B. Kim, and Y. J. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
    [Crossref]
  8. P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011).
    [Crossref]
  9. J. Wo, M. Jiang, M. Malnou, Q. Sun, J. Zhang, P. P. Shum, and D. Liu, “Twist sensor based on axial strain insensitive distributed Bragg reflector fiber laser,” Opt. Express 20(3), 2844–2850 (2012).
    [Crossref] [PubMed]
  10. D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Meter, and A. M. Vengsarker, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34(3), 302–303 (1998).
    [Crossref]
  11. C. Y. Lin, L. A. Wang, and G. W. Chern, “Corrugated long-period fiber gratings as strain, torsion, and bending sensors,” J. Lightwave Technol. 19(8), 1159–1168 (2001).
    [Crossref]
  12. D. A. Gonzalez, C. Jauregui, A. Quintela, F. J. Madruga, P. Marquez, and J. M. Lopez-Higuera, “Torsion induced effects on UV long-period fiber gratings,” In Second European Workshop on Optical Fibre Sensors. International Society for Optics and Photonics. (192–195) (2004).
  13. Y. N. Zhu, P. Shum, X. Y. Chen, C. H. Tan, and C. Lu, “Resonance-temperature-insensitive phase-shifted long-period fiber gratings induced by surface deformation with anomalous strain characteristics,” Opt. Lett. 30(14), 1788–1790 (2005).
    [Crossref] [PubMed]
  14. B. B. Song, Y. P. Miao, W. Lin, H. Zhang, J. X. Wu, and B. Liu, “Multi-mode interferometer-based twist sensor with low temperature sensitivity employing square coreless fibers,” Opt. Express 21(22), 26806–26811 (2013).
    [Crossref] [PubMed]
  15. H. Xuan, W. Jin, M. Zhang, J. Ju, and Y. B. Liao, “In-fiber polarimeters based on hollow-core photonic bandgap fibers,” Opt. Express 17(15), 13246–13254 (2009).
    [Crossref] [PubMed]
  16. X. M. Xi, G. K. L. Wong, T. Weiss, and P. St. J. Russell, “Measuring mechanical strain and twist using helical photonic crystal fiber,” Opt. Lett. 38(24), 5401–5404 (2013).
    [Crossref] [PubMed]
  17. S. Oh, K. R. Lee, U. C. Paek, and Y. J. Chung, “Fabrication of helical long-period fiber gratings by use of a CO2 laser,” Opt. Lett. 29(13), 1464–1466 (2004).
    [Crossref] [PubMed]
  18. W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).
  19. W. J. Shin, B. A. Yu, Y. C. Noh, J. M. Lee, D. K. Ko, and K. Oh, “Bandwidth-tunable band-rejection filter based on helicoidal fiber grating pair of opposite helicities,” Opt. Lett. 32(10), 1214–1216 (2007).
    [Crossref] [PubMed]
  20. H. Ke, K. S. Chiang, and J. H. Peng, “Analysis of Phase-Shifted Long-Period Fiber Gratings,” IEEE Photon. Technol. Lett. 10(11), 1596–1598 (1998).
    [Crossref]
  21. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
    [Crossref]
  22. T. Erdogan, “Cladding-mode resonances in short- and long-period fiber gratings filters,” J. Opt. Soc. Am. A 14(8), 1760–1773 (1997).
    [Crossref]
  23. M. Rosenberger, S. Hessler, S. Belle, B. Schmauss, and R. Hellmann, “Compressive and tensile strain sensing using a polymer planar Bragg grating,” Opt. Express 22(5), 5483–5490 (2014).
    [Crossref] [PubMed]

2014 (1)

2013 (4)

2012 (2)

2011 (2)

P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011).
[Crossref]

Z. J. Yan, C. B. Mou, K. M. Zhou, X. F. Chen, and L. Zhang, “UV-inscription, polarization-dependant loss characteristics and applications of 45° tilted fiber gratings,” J. Lightwave Technol. 29(18), 2715–2724 (2011).
[Crossref]

2010 (1)

H. M. Kim, T. H. Kim, B. Kim, and Y. J. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

2009 (1)

2008 (1)

W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).

2007 (1)

2005 (1)

2004 (1)

2002 (1)

P. L. Fulmek, F. Wandling, W. Zdiarsky, G. Brasseur, and S. P. Cermak, “Capacitive sensor for relative angle measurement,” IEEE Trans. Instrum. Meas. 51(6), 1145–1149 (2002).
[Crossref]

2001 (1)

1998 (2)

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Meter, and A. M. Vengsarker, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34(3), 302–303 (1998).
[Crossref]

H. Ke, K. S. Chiang, and J. H. Peng, “Analysis of Phase-Shifted Long-Period Fiber Gratings,” IEEE Photon. Technol. Lett. 10(11), 1596–1598 (1998).
[Crossref]

1997 (2)

1995 (1)

D. Vischer and O. Khatib, “Design and development of high-performance torque controlled joints,” IEEE Trans. Robot. Autom. 11(4), 537–544 (1995).
[Crossref]

Belle, S.

Brasseur, G.

P. L. Fulmek, F. Wandling, W. Zdiarsky, G. Brasseur, and S. P. Cermak, “Capacitive sensor for relative angle measurement,” IEEE Trans. Instrum. Meas. 51(6), 1145–1149 (2002).
[Crossref]

Cai, H. W.

Cermak, S. P.

P. L. Fulmek, F. Wandling, W. Zdiarsky, G. Brasseur, and S. P. Cermak, “Capacitive sensor for relative angle measurement,” IEEE Trans. Instrum. Meas. 51(6), 1145–1149 (2002).
[Crossref]

Chan, C. C.

P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011).
[Crossref]

Chen, L. H.

P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011).
[Crossref]

Chen, X. F.

Chen, X. Y.

Chern, G. W.

Chiang, K. S.

H. Ke, K. S. Chiang, and J. H. Peng, “Analysis of Phase-Shifted Long-Period Fiber Gratings,” IEEE Photon. Technol. Lett. 10(11), 1596–1598 (1998).
[Crossref]

Chung, Y. J.

H. M. Kim, T. H. Kim, B. Kim, and Y. J. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

S. Oh, K. R. Lee, U. C. Paek, and Y. J. Chung, “Fabrication of helical long-period fiber gratings by use of a CO2 laser,” Opt. Lett. 29(13), 1464–1466 (2004).
[Crossref] [PubMed]

Davis, D. D.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Meter, and A. M. Vengsarker, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34(3), 302–303 (1998).
[Crossref]

Dong, X. Y.

P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011).
[Crossref]

Donlagic, D.

Eom, T. J.

W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).

Erdogan, T.

Fang, Z. J.

Fulmek, P. L.

P. L. Fulmek, F. Wandling, W. Zdiarsky, G. Brasseur, and S. P. Cermak, “Capacitive sensor for relative angle measurement,” IEEE Trans. Instrum. Meas. 51(6), 1145–1149 (2002).
[Crossref]

Gaylord, T. K.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Meter, and A. M. Vengsarker, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34(3), 302–303 (1998).
[Crossref]

Glytsis, E. N.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Meter, and A. M. Vengsarker, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34(3), 302–303 (1998).
[Crossref]

Gong, T. X.

P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011).
[Crossref]

Hellmann, R.

Hessler, S.

Huang, X. Q.

Jiang, M.

Jin, W.

Jin, Y. X.

P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011).
[Crossref]

Ju, J.

Ke, H.

H. Ke, K. S. Chiang, and J. H. Peng, “Analysis of Phase-Shifted Long-Period Fiber Gratings,” IEEE Photon. Technol. Lett. 10(11), 1596–1598 (1998).
[Crossref]

Khatib, O.

D. Vischer and O. Khatib, “Design and development of high-performance torque controlled joints,” IEEE Trans. Robot. Autom. 11(4), 537–544 (1995).
[Crossref]

Kim, B.

H. M. Kim, T. H. Kim, B. Kim, and Y. J. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

Kim, H. M.

H. M. Kim, T. H. Kim, B. Kim, and Y. J. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

Kim, T. H.

H. M. Kim, T. H. Kim, B. Kim, and Y. J. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

Ko, D. K.

W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).

W. J. Shin, B. A. Yu, Y. C. Noh, J. M. Lee, D. K. Ko, and K. Oh, “Bandwidth-tunable band-rejection filter based on helicoidal fiber grating pair of opposite helicities,” Opt. Lett. 32(10), 1214–1216 (2007).
[Crossref] [PubMed]

Kosinski, S. G.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Meter, and A. M. Vengsarker, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34(3), 302–303 (1998).
[Crossref]

Lee, J.

W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).

Lee, J. M.

Lee, K. R.

Lee, Y. L.

W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).

Lesnik, D.

Liao, Y. B.

Lin, C. Y.

Lin, W.

Liu, B.

Liu, D.

Lu, C.

Malnou, M.

Meter, S. C.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Meter, and A. M. Vengsarker, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34(3), 302–303 (1998).
[Crossref]

Miao, Y. P.

Mou, C. B.

Noh, Y. C.

W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).

W. J. Shin, B. A. Yu, Y. C. Noh, J. M. Lee, D. K. Ko, and K. Oh, “Bandwidth-tunable band-rejection filter based on helicoidal fiber grating pair of opposite helicities,” Opt. Lett. 32(10), 1214–1216 (2007).
[Crossref] [PubMed]

Oh, K.

W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).

W. J. Shin, B. A. Yu, Y. C. Noh, J. M. Lee, D. K. Ko, and K. Oh, “Bandwidth-tunable band-rejection filter based on helicoidal fiber grating pair of opposite helicities,” Opt. Lett. 32(10), 1214–1216 (2007).
[Crossref] [PubMed]

Oh, S.

Paek, U. C.

Pan, Z. Q.

Peng, J. H.

H. Ke, K. S. Chiang, and J. H. Peng, “Analysis of Phase-Shifted Long-Period Fiber Gratings,” IEEE Photon. Technol. Lett. 10(11), 1596–1598 (1998).
[Crossref]

Qu, R. H.

Rosenberger, M.

Russell, P. St. J.

Schmauss, B.

Shin, W.

W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).

Shin, W. J.

Shum, P.

Shum, P. P.

Song, B. B.

Sun, Q.

Tan, C. H.

Vengsarker, A. M.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Meter, and A. M. Vengsarker, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34(3), 302–303 (1998).
[Crossref]

Vischer, D.

D. Vischer and O. Khatib, “Design and development of high-performance torque controlled joints,” IEEE Trans. Robot. Autom. 11(4), 537–544 (1995).
[Crossref]

Wandling, F.

P. L. Fulmek, F. Wandling, W. Zdiarsky, G. Brasseur, and S. P. Cermak, “Capacitive sensor for relative angle measurement,” IEEE Trans. Instrum. Meas. 51(6), 1145–1149 (2002).
[Crossref]

Wang, L. A.

Wang, M.

Weiss, T.

Wo, J.

Wong, G. K. L.

Wu, J. X.

Xi, X. M.

Xuan, H.

Yan, Z. J.

Yang, F.

Ye, Q.

Yiping, W.

Yu, B. A.

W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).

W. J. Shin, B. A. Yu, Y. C. Noh, J. M. Lee, D. K. Ko, and K. Oh, “Bandwidth-tunable band-rejection filter based on helicoidal fiber grating pair of opposite helicities,” Opt. Lett. 32(10), 1214–1216 (2007).
[Crossref] [PubMed]

Zdiarsky, W.

P. L. Fulmek, F. Wandling, W. Zdiarsky, G. Brasseur, and S. P. Cermak, “Capacitive sensor for relative angle measurement,” IEEE Trans. Instrum. Meas. 51(6), 1145–1149 (2002).
[Crossref]

Zhang, H.

Zhang, J.

Zhang, L.

Zhang, M.

Zhang, Y. F.

P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011).
[Crossref]

Zhou, K. M.

Zhu, Y. N.

Zu, P.

P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011).
[Crossref]

Electron. Lett. (1)

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Meter, and A. M. Vengsarker, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34(3), 302–303 (1998).
[Crossref]

IEEE Photon. Technol. Lett. (3)

H. M. Kim, T. H. Kim, B. Kim, and Y. J. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011).
[Crossref]

H. Ke, K. S. Chiang, and J. H. Peng, “Analysis of Phase-Shifted Long-Period Fiber Gratings,” IEEE Photon. Technol. Lett. 10(11), 1596–1598 (1998).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

P. L. Fulmek, F. Wandling, W. Zdiarsky, G. Brasseur, and S. P. Cermak, “Capacitive sensor for relative angle measurement,” IEEE Trans. Instrum. Meas. 51(6), 1145–1149 (2002).
[Crossref]

IEEE Trans. Robot. Autom. (1)

D. Vischer and O. Khatib, “Design and development of high-performance torque controlled joints,” IEEE Trans. Robot. Autom. 11(4), 537–544 (1995).
[Crossref]

J. Lightwave Technol. (4)

Z. J. Yan, C. B. Mou, K. M. Zhou, X. F. Chen, and L. Zhang, “UV-inscription, polarization-dependant loss characteristics and applications of 45° tilted fiber gratings,” J. Lightwave Technol. 29(18), 2715–2724 (2011).
[Crossref]

C. Y. Lin, L. A. Wang, and G. W. Chern, “Corrugated long-period fiber gratings as strain, torsion, and bending sensors,” J. Lightwave Technol. 19(8), 1159–1168 (2001).
[Crossref]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

W. Shin, K. Oh, B. A. Yu, Y. L. Lee, T. J. Eom, Y. C. Noh, D. K. Ko, and J. Lee, “All-fiber bandpass filter based on helicoidal long-period grating pair and null core hollow optical fiber with flexible transmission control,” J. Lightwave Technol. 20(2), 153–155 (2008).

J. Opt. Soc. Am. A (1)

Opt. Express (6)

Opt. Lett. (5)

Other (1)

D. A. Gonzalez, C. Jauregui, A. Quintela, F. J. Madruga, P. Marquez, and J. M. Lopez-Higuera, “Torsion induced effects on UV long-period fiber gratings,” In Second European Workshop on Optical Fibre Sensors. International Society for Optics and Photonics. (192–195) (2004).

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Figures (14)

Fig. 1
Fig. 1 The changed pitch of each period induced by twisting: (a) before twisting; (b) after twisting. (c) The changed angle for each period before and after twisting.
Fig. 2
Fig. 2 The simulation of the MPS-HLPFG with different twist angles: (a) 0°, (b) 20°, (c) 40°, (d) 60°.
Fig. 3
Fig. 3 The simulation of the MPS-HLPFG with different temperatures: (a) 0 °C; (b) 100 °C; (c) 200 °C.
Fig. 4
Fig. 4 The fabrication setup of the MPS-HLPFG.
Fig. 5
Fig. 5 Closed view of the MPS-HLPFG: (a) the original period; (b) the changed period of π/2 phase-shift; (c) the changed period of 3π/2 phase-shift; (d) schematic of the MPS-HLPFG.
Fig. 6
Fig. 6 Schematic diagram of experimental setup.
Fig. 7
Fig. 7 Comparison of the transmission spectra between a MPS-HLPFG and a HLPFG with the same pitch.
Fig. 8
Fig. 8 (a) The transmission spectrum of the MPS-HLPFG with (a) clockwise and (b) counterclockwise twisting.
Fig. 9
Fig. 9 Wavelength shift of the phase shift peaks and the wavelength difference.
Fig. 10
Fig. 10 (a) Transmission spectra of the MPS-HLPFG at different temperatures. (b) Wavelength shifts and wavelength difference of two phase shift peaks at different temperatures.
Fig. 11
Fig. 11 The PDL of the MPS-HLPFG at different wavelength.
Fig. 12
Fig. 12 (a) Transmission spectra of the MPS-HLPFG with different pitch. (b) Wavelength difference of two phase shift peaks.
Fig. 13
Fig. 13 Wavelength difference in clockwise and counterclockwise twisting directions.
Fig. 14
Fig. 14 (a) Transmission spectra of the MPS-HLPFG with different axial strain. (b) Wavelength difference of two phase shift peaks with different axial strain.

Equations (8)

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Λ a = 2π 2πθ Λ b
ϕ=2πL( 1 Λ o 1 Λ c )
( a co (L) a cl (L) )=( e i( Δβ 2 ) L 1 0 0 e i( Δβ 2 ) L 1 )( t 1 r 1 r 1 t 1 * )×( e i ϕ 1 /2 0 0 e i ϕ 1 /2 ) ×( e i( Δβ 2 ) L 2 0 0 e i( Δβ 2 ) L 2 )( t 2 r 2 r 2 t 2 * )×( e i ϕ 2 /2 0 0 e i ϕ 2 /2 ) ×( e i( Δβ 2 ) L 3 0 0 e i( Δβ 2 ) L 3 )( t 3 r 3 r 3 t 3 * )×( a co (0) a cl (0) ).
t i =cos( S m L i )+j δ m S m sin( S m L i ) r i =j κ m S m sin( S m L i )
Λ o ' = 2π 2πθ Λ o Λ c1 ' = 2π 2πθ Λ c1 Λ c2 ' = 2π 2πθ Λ c2
ϕ 1 ' = 2π λ L( 1 Λ o ' 1 Λ c1 ' )= 2π λ L( 1 ( 2π 2πθ ) Λ o 1 ( 2π 2πθ ) Λ c1 ) =( 2πθ 2π ) 2π λ L( 1 Λ o 1 Λ c1 )=( 2πθ 2π ) ϕ 1 =( 2πθ 2π ) π 2 ϕ 2 ' = 2π λ L( 1 Λ o ' 1 Λ c2 ' )= 2π λ L( 1 ( 2π 2πθ ) Λ o 1 ( 2π 2πθ ) Λ c2 ) =( 2πθ 2π ) 2π λ L( 1 Λ o 1 Λ c2 )=( 2πθ 2π ) ϕ 2 =( 2πθ 2π ) 3π 2
ϕ 1 '' = 2π λ (T+1)L( 1 (T+1) Λ o 1 (T+1) Λ c1 )= 2π λ L( 1 Λ o 1 Λ c1 )= ϕ 1 = π 2 ϕ 2 '' = 2π λ (T+1)L( 1 (T+1) Λ o 1 (T+1) Λ c2 )= 2π λ L( 1 Λ o 1 Λ c2 )= ϕ 2 = 3π 2
ϕ 1 ''' = 2π λ ( F AE +1)L( 1 ( F AE +1) Λ o 1 ( F AE +1) Λ c1 )= 2π λ L( 1 Λ o 1 Λ c1 )= ϕ 1 = π 2 ϕ 2 ''' = 2π λ ( F AE +1)L( 1 ( F AE +1) Λ o 1 ( F AE +1) Λ c2 )= 2π λ L( 1 Λ o 1 Λ c2 )= ϕ 2 = 3π 2

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