Twist effect and sensing of few mode polymer fibre Bragg gratings

Optics Communications 359 (2016) 411–418

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Optics Communications journal homepage: www.elsevier.com/locate/optcom

Twist effect and sensing of few mode polymer fibre Bragg gratings Binbin Yan a, Yanhua Luo b,c,n, Kishore Bhowmik c, Ginu Rajan c, Minning Ji d, Jianxiang Wen d, Gang-Ding Peng c a

State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China State Key Laboratory for Modification of Chemical Fibers and Polymer Materials, Donghua University, Shanghai 200051, China c Photonics & Optical Communications, School of Electrical Engineering, University of New South Wales, Sydney 2052, NSW, Australia d Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai University, Shanghai 200072, China b

art ic l e i nf o

a b s t r a c t

Article history: Received 12 June 2015 Received in revised form 23 September 2015 Accepted 24 September 2015

For the development of the twist sensor based on few mode polymer optical fibre (POF) gratings, we investigated the twist effect of few mode (FM) POF Bragg gratings with large twist, and found the twist effect on reflection is highly mode dependent-insignificant on the fundamental mode and considerable on higher order modes, which seems closely related to the symmetry of modal field. In addition, Bragg wavelengths of both the fundamental mode and higher modes red-shift with the twisting and blue-shift with the twist releasing, and they almost display the similar response trend without any mode dependence. Further analysis found that the red-shift of the Bragg wavelength should be attributed to the redistribution of the pre-strain applied upon the POF, activated by twist. Finally, based on the reflection response to the twist, one kind of twist sensing scheme with few mode POF gratings has been demonstrated, showing great potential as a twist sensor. & 2015 Elsevier B.V. All rights reserved.

Keywords: Polymer optical fibre (POF) POF gratings Few mode POF Twist effect Twist sensing Torsion

1. Introduction Twist/torsion is an important sensing parameter that needs to be monitored for scientific research, industry and civil engineering applications, such as bridges, buildings, and many other civil structures [1,2]. In optical fibre sensing, twist sensors based on fibre Bragg gratings (FBGs), long period gratings (LPGs), Sagnac Interferometer, etc have already been proposed [1,2]. In general, fundamental mode (LP01) was relative insensitive to the twist compared to LP11 and LP21. The LP11 mode was sensitive to twist [3], while the LP21 mode had a perfect linear dependence upon the rotation angle [4]. Based on these, it is feasible try to use three modes few mode fibres (FMFs) as the twist sensor, especially the FMF Bragg gratings, which might give different response for different modes to the twist. FMF Bragg gratings have some merits, such as easy coupling with low cost light sources for distributed sensing networks [5,6] and efficient relation between information energy and input energy [7]. So they have already been used in strain and temperature sensors [5,8–11], refractive index sensor [12], bend [13], etc [14,15]. Especially, twist sensor based silica n Corresponding author at: Photonics & Optical Communications, School of Electrical Engineering, University of New South Wales, Sydney 2052, NSW, Australia. Fax: þ61 2 93854036. E-mail address: [email protected] (Y. Luo).

http://dx.doi.org/10.1016/j.optcom.2015.09.087 0030-4018/& 2015 Elsevier B.V. All rights reserved.

fibre Bragg gratings (FBGs) with two modes’ acousto-optic filters [16] has been reported as well as other twist sensors based on silica fibre gratings, such as polarization dependent loss (PDL) analysis [17], distributed feedback (DFB) laser [18] and titled gratings structure [19]. FMF and FMF Bragg gratings mentioned above are mostly made by silica materials. POF is another material, especially the shear modulus of POF is 1.1 GPa, only about 1/38 of that of silica fibre (42.7 GPa) [20,21], which makes POF more sensitive to the shear force compared with silica fibre. Zubia has found that the torsion make the multimode (MM) POF biaxial and inhomogeneous. The new indices of refraction referred to them depend on the torsion strength, the fibre transverse coordinates, and the difference between the two components of the stress-optical tensor [22]. Especially, the output polarization state of the light varies linearly with moderate torsion angles and also depends upon the wavelength [23]. Gratings inscribed in POF have been used in a series sensing fields such as stress, strain, bend and pressure since 1999 with the development of POF [24–27]. Numerous few mode POF gratings have been fabricated [28–30] and few mode (FM) FBGs in POF has shown high stress, strain and temperature response [31–33]. Compared with single mode (SM) FBGs, the multiple reflection peaks of the Bragg grating in a FMF can provide more information than that in a SMF [31]. For example, the different strain and

B. Yan et al. / Optics Communications 359 (2016) 411–418

temperature characteristics for different modes enabled FM POF gratings to measure strain and temperature simultaneously [31]. Therefore, the study of the response of few mode POF gratings to the twist would be of great interest for its potential as the novel fibre optic twist sensor, especially in practice a fibre/matrix might often experience some twist which results in a shear component to the stress [21]. The twist effect of FM POF gratings with only 3 turns’ twist has been demonstrated in our previous work [34]. Here, to bring out the complete effect and phenomena, large twist (16 turns’ twist) of FM POF gratings has been applied for the first time to our knowledge. Especially, the change of the Bragg wavelength shift and the reflection due to the twist has been further analysed and illuminated in theory and experiment. Finally, based on the reflection response, the twist sensing with FM POF gratings has been schemed.

-50

pk1 0o

pk3 pk2

-55

Reflection [dBm]

412

2880o o

5760 -60

-65

-70

-75 1526

1528

1530

1532

1534

1536

1538

Wavelength [nm] Fig. 2. Reflection spectra of POF gratings with different twist angle. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2. Experiment and results circa 1530 nm. A short length POF of  10 cm is used to inscribe the FBG and joined to a silica SM fibre pigtail using UV curable glue [24].

2.1. POF The photosensitive poly(methyl methacrylate) (PMMA) based POF used in this work is fabricated as our previous report [35], where the cladding and the core are made of the copolymer of MMA and ethyl methacrylate (EMA), and MMA, EMA and benzyl methacrylate (BzMA), respectively. The POF has a core refractive index of 1.4855, a cladding refractive index of 1.4769 and the refractive index difference between core and cladding of 0.0086. The POF (Fig. 1) has an outer diameter of 211.5 μm and 12.6 μm core diameter. The cross section of POF in Fig. 1 shows that the fibre core is off-center with 3.0 μm offset (r). 2.2. POF gratings POF gratings are fabricated by phase mask technique using a 50 mW 325 nm Kimmon He–Cd laser as reported before [24]. The phase mask is 10 mm long and has a pitch of 1030 nm, which is designed for a writing wavelength of 320 nm and to produce 10 mm long gratings (Lg ¼10 mm) with peak reflected wavelength

2.3. Twist experiment with POF gratings Fig. 1 also shows the setup to do the twist experiment of FM POF gratings at room temperature (before and after the test, the temperature was checked by thermometer to be 22 °C). One end of POF glued with silica fibre was fixed on a metal block mounted on a 3-dimentional (3D) positioner by glue, and the other end of POF was glued with a shaft, which had a hole through the centre. (The POF is  1 mm off-center of the shaft due to the movement during the consolidation of the glue.) The shaft was mounted with a fixed bearing. Then the POF was strained by moving back a bit of 3D positioner. Compared with unstrained POF gratings, Bragg wavelength of pre-strained POF gratings with a strain of  0.1% red-shifted from 1529.94 to 1531.66 nm (pk1 in Fig. 2). The length of the POF between two fixed points is 6.7 cm (L) and the FBG location is 4.5 cm to the shaft. Twist was performed by rotating the shaft. The reflection spectrum of POF gratings was characterized

Fig. 1. Twist experimental setup of FM POF gratings.

B. Yan et al. / Optics Communications 359 (2016) 411–418

pk2

1535 1534 1533 1532 1531

0

2000

4000

6000

1533 1532 1531 1530 1529

0

o

pk1

-54 4000

1530 1529 1528

0

6000

o

Twist Angle [ ]

pk3

-56 -58 2000

6000

-50

-54

0

4000 o

-52

-60

2000

Twist Angle [ ]

Reflection [dBm]

Reflection [dBm]

Reflection [dBm]

-53

2000

6000

pk2

-50

-52

0

4000

1531

Twist Angle [ ]

-51

-55

2000

1532

o

Twist Angle [ ]

-50

pk3

1534

Bragg Wavelength [nm]

1536

Bragg Wavelength [nm]

Bragg Wavelength [nm]

pk1

413

4000

6000

o

Twist Angle [ ]

-52 -54 -56 -58 -60

0

2000

4000

6000

o

Twist Angle [ ]

Fig. 3. Bragg wavelength and reflection of pk1, pk2 and pk3 vs twist angle when POF gratings is largely CW twisted (○ line) and then released (□ line).

using a setup which consisted of a circulator, an amplified spontaneous emission (ASE) source (BW TEK BWC-ASE) and an optical spectrum analyser (Agilent 86140B OSA, RBW¼ 0.2 nm). 2.4. Evolution of few mode POF gratings with large twist The normalized frequency V is  4.1 and mode number transmitted @1530 nm is calculated to be 9 (calculated from theory and parameters measured, which might still have some errors due to the deviation of the ideal model.) [33], so this POF will be a nominally FMF at the operating wavelength, with the different Bragg peaks as shown in Fig. 2. Seen from Fig. 2, there are mainly three mode reflected, which are marked as pk1 @  1531.66 nm, pk2 @  1529.89 nm and pk3 @  1528.12 nm, respectively. The reflection peaks pk1, pk2 and pk3 might be corresponded to LP01, LP11 and LP21 modes respectively, according to the wavelength of each modes [31]. Large twist experiment with 16 turns has been performed and the results are shown in Figs. 2 and 3. Change in the reflection spectra was recorded with clockwise (CW) twisting of the shaft (Fig. 2). The thick black solid line, red dash dot line and dot blue in Fig. 2 present the reflection spectra with twist angle (θ) of 0°, 2880° (8 turns) and 5760° (16 turns), respectively. It can be seen from Fig. 2 that the Bragg wavelengths of pk1, pk2 and pk3 all redshift and the reflection of pk1, pk2 and pk3 vary a lot as well. Besides the variation of the reflection for each mode, there are almost no extra losses induced by twist even when twist is very large. The experimental results of the Bragg wavelength and reflection for pk1, pk2 and pk3 in 16 turns’ CW twist and release have further been plotted in Fig. 3(a) and (b), respectively. Seen from Fig. 3, in CW twist, Bragg wavelengths of pk1, pk2 and pk3 almost display the similar changing trend and red-shift with the increment of the twist angle overall, with an maximum shift of 3.3 nm, 3.5 nm and  3.5 nm. In addition, it is also found that the red-shift displays a periodicity of 360° to some extent, which is similar to the observation with small twist [34]. In release process, they also display the blue-shifting, with similar trend to the CW twist process. Especially, the wavelength shift with the twist angle of lower than 1080° is very small, consistent with the result of small twist [34].

It can also be seen from Fig. 2 that in large CW twist and release, the reflection varies with the twist angle. In CW twist process, the reflection of mode pk1 decreases first, then increases, and decreases and increases again, and finally reaches a steady value of ∼ 53.0 dBm with the increment of twist angle, while in the release process, it also keeps still ∼  53.0 dBm till 4000°, and then increases to a steady value of ∼  51.0 dBm at 2000° with the twist release. In CW twist process, the reflection of mode pk2 increases from ∼ 55.0 dBm to a maximum reflection of   52.0 dBm at 810° first, then decreases to  59.3 dBm at 2000°, increases to  53.0 dBm and decreases again, while the reflection of mode pk3 decreases from  54 dBm to  59.5 dBm first, then increases to  53.0 dBm and then decreases again to  57.5 dBm, then increases to 52.0 dBm and decreases, and finally increases again to  52.0 dBm. When releasing, the changing trend of mode pk2 and pk3 are not quite clear, which fluctuates a lot. The trend between the CW twist process and the release process in large twist is much different from that in 3 turns' twist [34], where the latter can repeat well, although in both cases, the wavelength shift can almost totally repeat. It hints the complicated principles exist in the twist and release processes, especially for the reflection of different modes.

3. Discussion 3.1. Periodical wavelength shift The periodical small shifts of Bragg wavelength in Fig. 3 are all 360°, which is the same as the twisting process. It means that this periodical shift in the twist experiment should come from the twisting setup. The setup can’t twist the POF gratings in the rotating centre perfectly, resulting in the periodical existence of the far and near positions. To further confirm this point, purposely increasing the offset of the POF from the rotating centre (by moving the 3D positioner 2 mm perpendicularly towards paper.) will increase the variation of Bragg wavelength in CW twist evidently from 0.22 nm to 0.32 nm as reported before [34].

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3.2. Bragg wavelength vs twist angle 3.2.1. Longitudinal strain induced by twist According to Bragg condition, the central reflected wavelength (λB) has the following relationship with the grating period (Λ) and the effective refractive index of the guide mode (neff) [32]:

λB = 2nef fΛ

(1)

when the optical fibre takes strain or the temperature changes, the Bragg wavelength λB will change due to that elastic-optic effects and thermal-optic effects cause the change of neff, and the thermal expansion effects and stress deformation cause the change of the grating period Λ. It can be seen from Fig. 3 that with twist angle increasing, λB red-shifts, giving positive ΔλB. So the red-shift can be induced by tensile strain or temperature change. Due to the stabilized temperature during the experiment, we can regard Bragg wavelength λB shift as the function of length of POF core (Lg) only as [36]:

⎡ ⎛ ⎛ ∂Λ ⎞ ⎤ ∂neff ⎞ ⎟ + 2nneff ⎜ ⎟ ⎥ ΔL g ΔλB = ⎢ 2Λ ⎜ ⎢⎣ ⎝ ∂L g ⎠ ⎝ ∂L g ⎠T ⎥⎦ T0 0

(2)

If there exist the longitudinal strain induced by the twist, the POF core will elongate ΔLg. The path-integrated longitudinal strain is given by [36]:

εg =

view of single POF twist deformation is shown in Fig. 4, where the red line is assumed as the twisting trace of the fibre core. When POF was twisted to obtain a mean value of the twist angle, θ, which was converted to N, the number of twist turns, for the sake of convenience in comparison. Obviously, N ¼ θ/360. Therefore, the tensile strain of POF core under torsion shear stress can be calculated from the following equation:

ε=

(3)

In addition, the longitudinal strain sensitivity can be determined and is expressed in terms of an effective photoelastic constant pei , so that [36]:

ΔλB = (1 − pei ) εg λB

(4)

where pei is the photoelastic constant in the radial direction. To confirm the feasibility of the explanation above, the quickest and easiest way is to compare the values of ΔλB and εg. λB

In fact, as the fibre core is off-center with an offset r ¼3.0 μm, so the tensile strain will be induced by the twist. The twist in the fibre will lead to some tensile strain in the fibre core. A schematic

(5)

Here, if it is assumed that the longitude strain induced by twist is evenly distributed along POF, then there will be:

εg = ε =

L −L ΔL = ε L L

(6)

According to Ref. [37], the length of the POF core will become Lε after the elongation by N turns' twist, which can be given by the following equation:

Lε =

(2πr⋅N )2 + L2

(7)

By combining Eqs. (6) and (7), the tensile strain will become:

εg =

ΔL g Lg

ΔL L −L = ε L L

⎛ 2πr⋅N ⎞2 ⎟ −1 1+⎜ ⎝ L ⎠

(8)

where the elongation will result in the red-shift of Bragg wavelength in the POF gratings. Take pk1 mode for example, after 16 turns’ twisting, the red shift ΔλB is about 3.3 nm, so ΔλB/λB ¼0.22%, while the twist induced strain εg ¼ 0.001% calculated from Eq. (8). By comparison of ΔλB/λB and εg, their values have much difference and it is hardly to stratify Eq. (4).Therefore, strain induced by the twisting POF core with off-center cannot be the main reason for the red-shift of Bragg wavelength in Fig. 3. 3.2.2. Shear strain induced by twist The shear stress can also lead to the red shift of the Bragg wavelength [38]. It is very known that when the shear stress applied to the FBGs, the shear strain will be induced. In case of the shear strain, the reflection of the x-polarization and y-polarization will be split. However, no evident splitting of the Bragg reflection peaks can be observed in Fig. 2. Therefore, the shear strain possibly induced by twist will not be the main reason to result in the observed red-shift of the Bragg wavelength either. 3.2.3. Index change induced by twist Through Eq. (1), another possibility may be attributed to the change of the effective refractive index along fibre induced by the twist. For an undisturbed POF is an isotropic, transparent, and homogeneous medium, the photoelastic or stress-optical effect can be described by the following relation [22]

ΔBi = qij σj

Fig. 4. Geometry to calculate twist-induced strain.

(9)

where ΔBi is a symmetric second-rank tensor of the change of coefficient in the index ellipsoid under the twist, si(i¼ 1, …, 6) is six independent components of stress (a symmetric second-rank tensor) and the stress-optical tensor, qij, is a fourth rank tensor with 36 components (i,j¼1,…,6). For the isotropic medium such as a POF, the number of independent elements in the tensor qi j is finally reduced to two different q11 and q12, described as [22]

B. Yan et al. / Optics Communications 359 (2016) 411–418

sphere. If it goes far away from the POF axis, the index ellipsoid becomes more and more asymmetric and the POF itself more birefringent. At the core-cladding interface, the difference between the refractive indices with stress will reach the maximum. The fact can only lead to the change of a polarization state of light transmitted along the twisted POF. In a word, twisting POF will make POF biaxial and inhomogeneous, but the effective index along the POF axis will have no change. So the photoelastic effect by twist is not the main reason to result in the red-shift of the Bragg wavelength either.

nco z

y x

Fig. 5. Geometry of the POF under torsion by applying pure shear forces at both ends of the fibre.

⎤ ⎡q q q 0 0 0 ⎥ ⎢ 11 12 12 q q q 0 0 0 ⎥ ⎢ 12 11 12 ⎥ ⎢ q12 q12 q11 0 0 0 ⎥ ⎢ [q] = ⎥ ⎢ 0 0 0 q11 − q12 0 0 ⎥ ⎢ q11 − q12 0 0 ⎥ ⎢ 0 0 0 ⎥ ⎢ 0 0 0 q q 0 0 − ⎣ 11 12 ⎦

(10)

The light travels along POF by means of the total refraction at the core-cladding interface. When one end of POF is fixed and the other end is twisted, shear forces will be applied at both ends of the fibre section to produce torsion on it (Fig. 5). In this situation, the components of the stress tensor will become [22]:

σ1 = σ 2 = σ 3 = σ6 = 0; σ4 = μτx; σ 5 = μτy ,

(11)

where τ is the torsion angle, defined as τ = dθ /dz , and μ is the shear modulus. Substituting these components into Eq. (9), two nonzero components of tensor ΔBi will be given by:

ΔB4 = (q11 − q12 ) μτx; ΔB5 = − (q11 − q12 ) μτy .

(12)

The initially isotropic POF will have a spherical indicatrix as [22]: 2 x2 + y2 + z 2 = nco

(13)

nco is the uniform index of the refraction of the fibre core without any stress. After twisting, the optical indicatrix in principal coordinate system becomes [22]:

⎡⎣ 1 − μτr (q − q ) n 2 /2⎤⎦ co 11 12 2 nco

+

x2 +

415

⎡⎣ 1 + μτr (q − q ) n 2 /2⎤⎦ co 11 12 2 nco

1 2 z =1 2 nco

y2

3.2.4. Error by twist experiment Thermal effect can also lead to the red-shift of the Bragg wavelength, although the environment temperature was measured and controlled the same before and after the experiment. It is known that only when temperature decreases, the Bragg wavelength of POF gratings can increase [39]. Especially, the temperature sensitivity of the POF is  149 pm/°C [39]. So if the red-shift were attributed to the temperature decrease, the temperature must decrease  22 °C, which evidently contradicts with the fact of the fixed environment temperature. Meanwhile, the temperature shift is always random and would not achieve almost reversible experiment results in twist and release process. Hence, the thermal effect will not be the main reason for the red-shift in Fig. 3 either. In addition, the repeatability of Bragg wavelength shift during the twisting and releasing process in Fig. 3 is not too bad. So it also excludes the possibility of the operating error during the twist. 3.2.5. Redistribution of pre-strain activated by twist Possible reasons described above are all excluded. So what could be the reason to lead to such large and recoverable red-shift of the Bragg wavelength? Thereinto, for the longitudinal strain consideration, there is an assumption for Eq. (6) that the POF itself is isotropic and uniform. But the fact is that the materials are actually non-uniform. Especially grating writing with UV light will result in the damage for the POF [40], which will become the point of the stress concentration, and finally reduce the strength of POF gratings region. That is why the fracture damage can be observed at the grating region after 16 turns’ twisting experiment shown in Fig. 6. Although the existence of the non-uniformity in POF gratings has been confirmed, it still can’t explain why the Bragg wavelength of the POF gratings red-shifts with twist and blue-shifts with twist release. In fact, before the twisting experiment, the POF gratings have been pre-strained for about 0.1%, which means that the POF has been stretched for  67 μm overall. Before twisting, the tensile pre-strain is evenly distributed along the POF. It can maintain such metastable state for a long time without change (more than 30 mins without evident shifting, which belongs to a quasi-static response [41]) when this pre-strain is far lower than the yield strain (6.1%) [42]. However, if there is any non-uniform disturbance, such as twisting POF, metastable state will be broken. The pre-strain will be redistributed along the POF. The stress at the weaker region (the grating region) will further concentrate, be stretched more, increase the longitude strain of the POF gratings, and finally result in the red-shift of the Bragg wavelength. In

(14) 2

2 1/2

where r is the usual polar coordinate, r¼(x þy ) . So the eigenvalues of the index ellipsoid at the stressed direction will differ 2 from the nonstress index of the refraction nco by μτr (q11 − q12 ) nco /2, much smaller than the unity and dependent only on the radial coordinate. Along the POF axis r¼ 0, the index ellipsoid becomes a

Fig. 6. Fracture damage in POF grating after twisting.

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B. Yan et al. / Optics Communications 359 (2016) 411–418

0.0010

Bragg Wavelength [nm]

0.0008

0.0006 1534 0.0004

Released 1533

0.0002 1532

Relative reflection [dB]

CW Twisted 1535

22

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1531 0

1000

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20 18

pk3

16

pk2

14 12 10 8

0

100

200

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300

400

500

600

700

800

900

Equivalent Twist Angle [o]

-0.0002 6000

Fig. 8. Relative reflection of modes pk1, pk2 and pk3 vs equivalent twist angle.

Fig. 7. Bragg wavelength of pk1 vs twist angle when POF gratings is largely CW twisted and then released, and Bragg wavelength shifting rate of pk1 vs twist angle when POF gratings is released.

addition, Fig. 7 shows the shifting rate vs twist angle for pk1 (take pk1 for example). As it can be seen from Fig. 7, the shifting rate will increase with the increment of twist angle at the beginning and reach the maximum at  2000°. With further increment of twist angle, the shifting rate will decrease. The reason is that at the beginning the pre-strain is the maximum, the stress will quickly concentrate at the grating region under the disturbance (twist angle increasing), and the grating region will be strained fast, resulting in the faster shifting rate of the Bragg wavelength, while later on, after the grating region is strained, the pre-strain will reduce overall and the stress concentration become slowly, leading to the slower shifting rate of the Bragg wavelength. Furthermore, the 0.1% pre-strain required the POF to be stretched  67 μm. If the pre-strain are all concentrated to the gratings region with both end of POF fixed, the maximum strain of gratings region can reach 0.67%. In our previous work [43], we have reported that the photoelastic constant of POF Bragg gratings is 0.05, giving out the ΔλB/λB ¼0.95εg. In our case, λB ¼1531.7 nm, so the maximum red-shift of the Bragg wavelength is up to 9.7 nm. This value is much larger than the observed value (3.3 nm) in Fig. 3. It is reasonable as it is hardly to relax all the prestrain to the POF gratings region. Therefore, the redistribution of the pre-strain activated by the twist is the main reason, which can explain well the large red-shift of Bragg wavelength due to the twist. In addition, in the tensile strain process, the tensile strain yield of POF gratings can reach up to 3.5% [43]. However, in the twist situation, no more than 0.67% longitude strain will result in the evident fracture failure in Fig. 6, which hints that twist (torsion) is relative easier damaged the POF gratings than tensile strain. 3.3. Reflection vs twist angle Though the whole POF (L) is twisted, the twist for the grating depends on the grating length (Lg) and the location of the grating region. Therefore, we can define the equivalent twist angle (θe) (assuming the torsion is uniform) as:

θe =

Lg ×θ L

belonging to the small twist [34]. In this work, the maximum twist angle is  5760° and it will lead to the equivalent twist of 860° (Fig. 8), which is  2.5 half turns, belonging to the large twist. For comparison, the reflection of each modes should be corrected the variation of the spectra of the source itself resulted from the large red-shift of Bragg wavelength. After the compensation of the source influence, Fig. 8 shows the plot of the relative reflection of pk1, pk2 and pk3 vs equivalent twist angle. The principle of pk1 is not quite evident and the reflection of pk1 increases a bit overall. It is clearly shown that the changing trend of the reflection of pk2 and pk3 are almost the opposite. Furthermore, the whole period of the reflection of pk2 and pk3 are displayed from 20° to 400°. The reflection for further twist varies a little and has no evident principle there. The variation period for pk2 and pk3 are  349° (half period is from 134 to 309°) close to 360° and  186° (half period is 108–201°) close to 180°, respectively. The former is close to twice of the latter, which is similar to that of the small twist [34]. In addition, the maximum intensity of pk2 and pk3 has a typical difference of 67° (maximum position of pk2 at 134° and that of pk3 at 201°.), which is close to 45°. As mentioned above, the transmission in POF has LP01, LP11 and LP21 modes. The typical intensity profile of LP01 (pk1), LP11 (pk2) and LP21 (pk3) modes is shown in Fig. 9 [44]. The profile of LP01 (pk1) is centro-symmetric. So the reflection of pk1 will be almost independent upon the twist, which is consistent with the experimental results shown in Fig. 8. Meanwhile, the profiles of LP11 (pk2) and LP21 (pk3) modes are axisymmetric. The specklegram of these two modes will rotate following the twist of the POF [3, 4], with the rotating period of 180° and 90°. However, POF itself has geometry asymmetry (core off-center) and the fibre grating is written by the side illumination, so the POF used here has an intrinsic birefringence, which will result in the deformation of the lobes distributed symmetrically of LP11 and LP21. Profiles of LP11 (pk2) and LP21 (pk3) modes can still keep axisymmetric but the rotating period will be doubled and become 360° and 180°, respectively. Therefore, the period of reflected signal of LP11 (pk2)

y

(15)

According to Eq. (15), 3 turns’ twist of the POF end can only generate the equivalent twist of  160° in the gratings region. It means that after 3 turns’ twist, the principle axis of grating start section to that of grating end section twists less than half turn,

x

LP01

LP11

LP21

Fig. 9. Schematic intensity profile of LP01, LP11 and LP21 modes [45].

B. Yan et al. / Optics Communications 359 (2016) 411–418

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which can give out the linear twist response coefficient of 0.012 dBm/° between 180 and 540°. Given the smaller shear modulus of the POF fibre compared with silica optical fibre and the bio-compatible nature, this work has demonstrated the great potential of few mode POF gratings used for twist sensing in civil and bio-medical field.

Acknowledgement

Fig. 10. Linear fitting (180–540°) for the reflection of pk2 vs twist angle with small twist.

and LP21 (pk3) modes will become 360° and 180°, respectively, in consistent with the results in the paragraph above. Furthermore, the difference between the maximum center of pk2 and the minimum center of pk3 has 45°, which is consistent with the difference for the maximum intensity lobes of LP11 and LP21. In addition, too large twist will induce the totally deformation of the profile and destroy the symmetry, especially in the case of the non-uniformity embedded in POF gratings mentioned above. That is why when the equivalent twist angle is larger than 360° and there is no evident principle. Especially, it will also result in the unrepeated reflection changing trend in CW twist and release process in Fig. 3, although it can be repeated in case of twisting 3 turns [34]. 3.4. Scheme of twist sensing With small twist (3 turns) [34], the reflection of pk2 vs the twist angle in twist and release processes are almost the same, which is repeatable in 3 times’ experiment. For simple case, the good linear region of the reflection of pk2 vs twist angle between 180° and 540° in twist process is select out as shown in Fig. 10. The linear fitting can give out the twist response coefficient of 0.012 dBm/° (180–540°). It should be noted that through the proper calibration, it can totally be used for the twist sensing. Although the twist effect of few mode POF gratings is complicated, our aim in this paper is to demonstrate the proof of concept that the few mode POF gratings can be used for the twist sensing. More research is currently ongoing for the application design of this twist sensor. Given the smaller shear modulus of the POF fibre compared with silica optical fibre and the bio-compatible nature, it has great potential for twist sensing in civil and bio-medical field, such as the robotic needle steering.

4. Conclusions Twist effect in few mode POF gratings has been demonstrated with large twist for the first time. The result shows that the Bragg wavelength is insensitive with small twist (o1080°), while the reflection for higher modes is sensitive to twisting. But the Bragg wavelength shows the red-shift in large twist, due to the redistribution of the pre-strain activated by the twist. In addition, the twist effect on reflection seems closely related to the symmetry of modal field and matches with its mode profile. The result also demonstrates that torsion easier damaged the POF gratings than tensile strain. Especially, based on the reflection response of pk2 mode, one kind of the twist sensing has been demonstrated,

Authors are thankful for the support by Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications) (IPOC2014B010), State Key Laboratory for Modification of Chemical Fibers and Polymer Materials, Donghua University (LK1502), State Key Laboratory of Advanced Optical Communication Systems Networks, China, National Natural Science Foundation of China (61405014 and 61520106014) and wish to express their thanks to the referees for critically reviewing the manuscript and making important suggestions.

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