Twist (torsion) is an important parameter that reflects the stress state and health condition of structures such as bridges. Recently, the application of optical fiber sensors (OFSs) in twist sensing has intensified, due to their advantages of flexibility, light weight, and resistance to electromagnetic interference. Though many different schemes have been proposed, optical fiber twist sensors (OFTSs) can be mainly classified into two types: one interrogated with wavelength (e.g.,  specially designed fiber gratings^[1–8], Sagnac interferometer^[9–11], and helical fiber structure^[12–14]), and the other with intensity (e.g.,  Solc filter^[15], Lyot filter^[16], Mach–Zehnder interferometers^[17–19], and fiber gratings^[20–30]). Note that for the first type, the wavelength measurement involves the use of an expensive and bulky optical spectrum analyzer (OSA) or tunable narrow-linewidth laser, whereas, for the second type, intensity measurement only requires an optical power meter (or photodetector), which allows more compact and cost-effective interrogation than the first type. In this regard, OFTSs allowing intensity interrogation are more preferred.

The intensity-interrogated OFTSs can be further categorized into two main types: fiber interferometers and fiber gratings. The construction of fiber interferometers usually requires the use of special fiber^[1–17] or modification of the fiber physical structure^[18,19], which decreases the fiber mechanical strength, and the length of fiber interferometers can be very long (e.g.,  a 96 m long elliptical-core spun fiber is used in Ref. [15]). Fiber gratings can be directly introduced into the fiber without damaging the fiber physical structure, maintaining the mechanical strength and enabling more compact and stable twist sensing. To realize intensity-interrogated fiber grating twist sensors, one common principle is introducing a polarization dependent element (PDE)^[20–29]. In this way, when the fiber is twisted, the input polarization entering the PDE will also change, resulting in a change of the output intensity of the PDE. Currently, fiber-grating-based PDEs mainly include a tilted fiber grating^[20–26], phase shift fiber Bragg grating (FBG)^[27], angularly cascaded long period fiber grating (LPFG)^[28], and grating in special fiber, such as polarization maintaining fiber^[29].

Recently, we found that polarization dependent coupling can be achieved in LPFGs with much smaller grating periods, i.e., the so-called small period LPFG (SP-LPFG)^[31]. Thanks to the strong polarization dependence, SP-LPFGs are good candidates for the PDE in twist sensing applications. In this work, we propose and demonstrate a sensitive OFTS based on an SP-LPFG that is inscribed with a femtosecond (fs) laser in a normal single mode fiber (SMF). The adopted SP-LPFG is compact in size with a total length of only 2.8 mm and is insensitive to strain and temperature change. Apart from intensity-based interrogation, the proposed sensor also exhibits sensitive wavelength shift to twist and thus can be interrogated by wavelength.

As shown schematically in Fig. 1, LPFG is a kind of all in fiber device that consists of periodic modification along the fiber axis (usually the modification of the refractive index). In LPFGs, light of the core mode is coupled to fiber cladding modes, which attenuates quickly, leaving serial attenuation peaks in the transmission spectrum of the LPFG. The wavelengths of those attenuation peaks can be determined from the phase matching condition: λpeak=(neff-co−neff-cli)·Λ,(1)where neff-co and neff-cli are the effective indexes of the core mode and cladding mode, with i denoting the cladding mode order, and Λ is the grating period. Standard LPFGs usually have a period of several hundred micrometers, and core mode light is coupled to low-order cladding modes that satisfy the weakly guiding approximation, whereas in SP-LPFGs, with a small grating period less than 50 µm, coupling to high-order cladding modes is enabled. These high-order cladding modes are far away from weakly guiding regime and present strong vectorial behavior^[32–34], resulting in the strong polarization dependent peaks in SP-LPFGs. Such strong polarization dependence makes SP-LPFGs good candidates for the PDE in twist sensing applications.

In our experiment, a fs laser (800 nm, 1 kHz, 150 fs) was focused into the core of a stripped SMF (SM 28) by a 100× objective lens. The stripped SMF was mounted on a high resolution three-dimensional stage to gain translational motion relative to the laser focus. To keep the fiber straight, constant axial stress is applied to the fiber. The fiber positon was monitored by a CCD camera, guaranteeing that the fiber is at the right position. The whole fabrication process was controlled by a computer. To fabricate the LPFG, a pulse energy of 200 nJ was used, and the fiber was translated along the fiber axis with a constant speed of 20 µm/s; at the same time, the laser was turned on and off periodically by a mechanical shutter to introduce the periodic refractive index modulations (RIMs) into the fiber core, which construct the grating. During the fabrication, the transmission spectrum of the LPFG was monitored by an OSA in real time.

Figure 2 depicts the experimentally measured transmission spectrum of the fabricated grating, which has a period of 40 µm and a duty cycle of 50%, and 70 periods are introduced, corresponding to a total length of 2.8 mm (see inset of Fig. 2). This length is much more compact than that of normal LPFGs (usually tens of millimeters), since the induced RIM is highly localized in the core, i.e., occupying part of the fiber core in the cross section. Compared with the RIM that occupies the whole core transversely in normal LPFGs (Fig. 1), such highly localized RIM suppresses the cancellation of negative and positive coupling to high-order cladding modes, thus allowing much stronger coupling. The spectrum in Fig. 2 is measured with un-polarized light, where the deepest dip shows strength of ∼15dB. The insertion loss is ∼4dB (indicated by the red dash line in Fig. 2), which mainly results from Mie scattering of the localized RIM^[35]. The insertion loss can be reduced by using decreased laser energy, at a cost of lower coupling efficiency, which should be balanced according to the requirements of practical applications. Note that though a relatively higher pulse energy is used, the grating survives at >3000µε strain, which is comparable to LPFGs inscribed with a CO2 laser^[36], indicating that the mechanical strength of the grating is well maintained.

To realize polarization-related twist sensing, more of our concern is the polarization dependence. During the measurement, the polarization of light entering the grating is controlled by a polarizer followed by a polarization controller (PC), and the measured spectra of the peak around 1528 nm for two orthogonal polarizations are shown in Fig. 3. It can be seen from Fig. 3 that two peaks are fully distinguishable with polarized input light, and a strength over 25 dB is achieved for one of the polarizations (blue line in Fig. 3). Such strong polarization dependence mainly results from the vectorial nature of the high-order cladding modes, since the grating period is very small^[31]. Sensitive twist sensing will be achieved by the strong polarization dependence, as will be discussed in the next section.

The schematic of the setup for twist sensing is depicted in Fig. 4, broadband light from a super-continuum (SC) source passes through a polarizer, providing the initial polarized light whose polarization is controlled by the following PC, and the evolution of the output spectrum is monitored with an OSA. The grating is fixed between a fiber holder and a fiber rotator with an engraved dial. During the measurement, the grating is slightly strained to keep it straight, thus eliminating the unwanted perturbation such as bending.

Before rotating the fiber, we adjusted the initial polarization state using the PC to fully excite the peak on the shorter wavelength side (represented by P1 in Fig. 3). To characterize the twist sensing properties of the grating, the fiber rotator was rotated by 180 deg clockwise with 10 deg steps, and the transmission spectrum was recorded every 10 deg. Figure 5(a) shows the spectral evolution of the grating under twist. It can be clearly seen that, with the increase of twist angle, the strength of the peak on the short wavelength side decreases [see black circles in Fig. 5(a)], and beyond certain angles, this peak fully disappears, whereas the other peak appears and starts to grow. The dependence of the peak intensity on twist angle is depicted in Fig. 5(b), which shows a sine-like function that agrees with previous reports^[24]. The slopes of two linear fitting regions from 0 to 40 deg and from 130 to 170 deg are 0.257 dB/deg and −0.131dB/deg, respectively. In view of the practical application, the grating can be pre-twisted to this region in order to achieve a high sensitivity and linear response. The twist direction can also be detected with the pre-twist, depending on whether the peak intensity increases or decreases. It should be noted that the peak intensity is not a monotonic function of twist angle, i.e., different twist angles can result in the same peak intensity. Therefore, to guarantee reliable twist sensing, the detectable angle range using peak intensity should be limited to 90°, or supplementary judgment by wavelength [Fig. 5(c)] is required.

It can be seen from Fig. 5(a) that the peak wavelength [denoted by black circle in Fig. 5(a)] also evolves with twist angle, suggesting that the grating can also work as a wavelength-interrogated twist sensor. Figure 5(c) depicts the peak wavelength as a function of the twist angle, where the wavelength evolution of the deepest peaks is fitted with quadratic functions separately [see blue and red lines in Fig. 5(c)]. Figure 5(d) shows the sensitivity calculated from the fitted function in Fig. 5(c) at each measurement point, with a maximum sensitivity of ∼0.115nm/deg.

A comparison between our work and several typical previously reported OFTSs based on the fiber grating is listed in Table 1, including tilted FBG (TFBG) both in SMF and multimode fiber (MMF), and helical LPFG (HLPFG), where the unit of the twist sensitivity is unified for convenient comparison. It can be seen from Table 1 that our SP-LPFG sensor offers high sensitivity as well as compactness and vector sensing ability, while requiring no additional coating or use of a special fiber. Moreover, the measured wavelength sensitivity in Fig. 5 is higher than many of the reported schemes (see wavelength-interrogated schemes in Table 1), indicating the potential of the SP-LPFG in wavelength-interrogated twist sensing application.

The cross sensitivity of the proposed twist sensor to strain is also characterized, utilizing the setup depicted in Fig. 4. To investigate the influence of strain on twist sensing, the spectral response of the grating to strain is measured with pre-twist angles of 10, 30, and 50 deg, respectively. Figure 6 depicts the measured evolution of peak intensity and wavelength with increasing strain, where the linear fitting for each measurement is also shown (see the red lines in Fig. 6). We can see that the slope of each fitting is very small, with a maximal slope of 0.000033 dB/µε for peak intensity and −0.000157nm/µε for peak wavelength, suggesting that the proposed twist sensor is insensitive to strain, which is one of the important perturbations in twist measurement.

We also characterized the cross sensitivity of the proposed grating to temperature, which is another important perturbation in twist measurement. During the characterization, the grating was heated from 30°C to 60°C with 5°C steps, under pre-twist angles of 10, 30, and 50 deg, respectively. The measured results are depicted in Fig. 7, with the maximal coefficient of 0.0095 dB/°C for intensity interrogation [Fig. 7(a)] and 0.0037 nm/°C for wavelength interrogation [Fig. 7(b)], respectively, indicating a low temperature cross sensitivity.

To conclude, a sensitive vector twist sensor based on SP-LPFG is proposed and demonstrated. The SP-LPFG is much more compact compared with normal LPFGs, with a total length of only 2.8 mm. The proposed twist sensor can be interrogated by both intensity and wavelength, and high twist sensitivity of 0.257 dB/deg and 0.115 nm/deg is achieved for the two interrogation schemes. Such high sensitivity is achieved without modifying the physical structure of the fiber, such as post-coating or partially removing the fiber cladding, enabling more stable grating structures. Moreover, the proposed sensor is insensitive to strain and temperature, which are two of the most important perturbations in twist measurement. With the above advantages, the proposed sensor is a good candidate for structure monitoring applications.