Long-Period Grating with Asymmetrical Modulation for Curvature Sensing

Abstract

We propose and demonstrate a curvature sensor based on long-period fiber grating (LPFG) with asymmetric index modulation. The LPFG is fabricated in single-mode fiber with femtosecond laser micromachining. The grating structure is not introduced in the central fiber core, but is located off-axis with a distance of a few micrometers. Experimental results indicate that the offset distance has direct influence on the grating spectra. By utilizing such an asymmetric structure, two-dimensional vector curvature sensing can be realized. For an LPFG with an offset distance of 6 μm, the curvature sensitivity is around 29 nm/m⁻¹ in the 0° and 180° direction and about 20 nm/m⁻¹ in the 90° and 270° direction. The difference in curvature sensitivity in different bending directions makes the sensor capable of distinguishing the curvature orientation. The temperature response of the sensor is also experimentally investigated, and results indicate that the sensor has a very low temperature cross-sensitivity of 0.003 m⁻¹/°C. The characteristics of high curvature sensitivity, two-dimensional bending direction identification, and compact structure make the device an ideal candidate to be applied in the field of power grid health monitoring and intelligent robotics.

1. Introduction

In recent years, the monitoring of the health conditions of magnificent structures such as bridges and power grid towers has attracted great attention. The measurement of curvature is of special importance in structural health monitoring for civil engineering and aerospace industries. Curvature monitoring based on the optical method could make entire sensors compact, simple, accurate, and reliable [1]. Compared with traditional electrical sensors, optic fiber sensors offer a number of advantages such as fast response, remote monitoring, resistance to harsh environments, and immunity to electromagnetic interference. Furthermore, their compact size, lightweight, and flexibility make it easy for sensors to be embedded into structures in order to monitor certain parameters like strain, temperature, and curvature, making the use of optical fiber sensors an ideal solution in several industrial applications like civil engineering or robot arms. Based on the difference in device configurations, fiber curvature sensors could be roughly divided into categories based on interferometers and fiber gratings [2]. Curvature sensors based on interferometers usually adopt a splicing single-mode fiber (SMF) with a special optical fiber, such as photonic crystal fiber (PCF), and multicore fiber [3,4]. And to improve the sensing characteristics, some of them usually use the method of lateral-offset splicing. For example, Xu et al. proposed a curvature sensor consisting of a lateral-offset spliced single-mode four-core single-mode fiber Mach-Zehnder interferometer and achieved a curvature sensitivity of −18.75 nm/m⁻¹ [4]. The lateral splicing could effectively improve the sensitivity, but the sensor structures are usually fragile [5]. The other types of curvature sensors are those based on fiber gratings, including the fiber Bragg grating (FBG) [6,7,8] and long-period fiber grating (LPFG) [9,10]. These types of sensors usually just use single-mode fibers to fabricate the curvature sensor. Compared with FBGs, LPFGs are usually more sensitive to fiber bending since cladding modes are excited in the fiber sensor. LPFG usually has periodic refractive index (RI) change or a periodic geometry structure along the fiber length, which can couple light from the guided core mode to the cladding mode at phase-matched wavelengths. The periodic change in RI or geometry along the fiber length can be realized by various means such as UV light illumination, CO2 laser irradiation, electric-arc discharge, and femtosecond (fs) laser pulse irradiation [9,10]. Several methods were utilized to fabricate LPFGs, such as laser-introduced refractive index modulation, or periodical splicing of different types of optical fibers. Jin et al. proposed a bending sensor formed by periodical splicing of SMF and a multimode fiber (MMF) [11]. In other cases, a CO2 laser or femtosecond laser are used to induce LPFGs [12] in optical fibers. Other methods of mechanically introducing LPFGs have also been proposed, e.g., using laminated plates [13] or 3D-printed periodic grooved plates [14].

For curvature measurement, the determination of the bending direction is of importance in many practical applications, and sensors that can measure both curvature magnitude and direction are preferred. Introducing an asymmetric structure to a cylindrical fiber is one of the feasible methods to recognize bending directions [15]. For example, extra asymmetric grooves could be carved to fabricate an LPFG curvature sensor that is direction-dependent. Asymmetric microhole-structured LPFGs in SMF and PCF are possible through the use of femtosecond laser drilling. The fiber core is not penetrated by the bottom but by the side wall of the microholes. These asymmetric microhole-structured LPFGs can be readily fabricated in SMF and PCF [16]. Jin et al. reported a highly sensitive vector bending sensor that uses a CO₂ laser to fabricate a D-shaped LPFG and achieves high sensitivity in four directions [9]. Using a laser to fabricate two different periods in two directions also could achieve direction discrimination. Wang et al. proposed a type of bending sensor that used CO₂ irradiation to fabricate LPFGs in an isosceles triangle arrangement in a three-core fiber, while Geng et al. reported a spatial cascaded orthogonal LPFG, and both achieved three-dimensional orthogonal sensing [17,18]. Zhang et al. proposed an LPFG bending sensor based on arc grids in SMF, and sensors based on a V shape; these two grid shapes showed good sensitivity in two different directions [19,20].

In this work, we proposed a novel bending sensor based on LPFG asymmetric index modulation, and it is capable of distinguishing different bending directions due to the asymmetric structure. The LPFG is inscribed in single-mode fiber by femtosecond laser with a point-by-point method using an oil objective. Compared with traditional LPFG, we inscribe the grating with an offset to the fiber axis. The grating spectrum is affected by the offset distance, and a larger offset leads to lower coupling efficiency, but a higher curvature sensitivity can be achieved. The LPFG exhibits different curvature sensitivities in different bending directions. The curvature responses in two orthogonal planes are experimentally investigated. The curvature sensitivity of an LPFG with an index modulation offset of 6 μm is 29 nm/m⁻¹ in the 0° and 180° plane, and 20 nm/m⁻¹ in the 90° and 270° plane. The difference in curvature sensitivity in different bending directions makes the sensor capable of distinguishing the curvature orientation. The temperature response of the sensor is also experimentally investigated, and the temperature sensitivity of the sensor is measured to be 0.087 nm/°C. The temperature cross-sensitivity is calculated to be 0.003 m⁻¹/°C, which indicates that the influence of temperature on the measurement accuracy of curvature is negligible. The LPFG curvature sensor is compact and robust, and has high sensitivity, which can be widely applied in areas such as robot arms and power grids monitoring.

2. Sensor Fabrication and Principle

To construct the proposed sensor, a standard single-mode fiber is used. The fibers we used in the experiment are SMF-28 (Yangtze Optical Fibre and Cable Joint Stock Limited Company, YOFC, Wuhan, China) with the core diameter of 8.2 μm and the nominal effective index of 1.4682 (@ 1550 nm). The fiber is stripped before being fixed on a 3D translation stage for the laser micromachining. A femtosecond laser (Spectra Physics, Solstice, Andover, MA, USA) with repetition rate of 1 kHz and wavelength of 800 nm is focused into the fiber with a 100 X oil objective, as shown in Figure 1a. The position of the focusing spot is monitored with a CCD camera. The pulse energy for the inscribing of the LPFG is 200 nJ, and the exposure time for each point is 1 s. To make a comparison, we first focus the laser into the center of the fiber core to inscribe a normal LPFG. The microscope image of the fabricated LPFG is shown in Figure 1b. Figure 2a shows the micrograph of the laser-ablated spot in the fiber core. The period of LPFG is 500 μm, and the transmission spectrum of the grating is monitored during the fabrication process. The period of 500 μm is selected so that the resonant wavelength of the LPFG can be expected to be located within the C band. The transmission spectrum is collected by a broadband source (BBS) and an optical spectrum analyzer (OSA) (Yokogawa AQ6370C). The evolution of the grating spectrum is shown in Figure 3a, where the spectra of the LPFG at different numbers of periods are plotted. From Figure 3a, we can see that three resonant dips appear as the number of periods increases. The dips are deepest when the number of periods is 20. After that number, those resonant dips start to degenerate, which corresponds to the case of overcoupling.

Then, LPFG samples with different offsets are fabricated. Figure 2b,c show the micrographics of grating modulations with offsets of 3 μm and 6 μm, respectively. The laser pulse energy used in the fabrication is the same as that used for the normal LPFG fabrication. The size of the laser-ablated spots are the same, while the locations of the modulation are different. Figure 3b shows the grating spectrum of the sample with an offset of 3 μm at different numbers of grating periods during the fabrication. The wavelength of the resonant dips are a little different from that of the normal LPFG. Such difference in the resonant wavelength is due to the change of cladding modes that are involved in the grating resonance. For the sample with an offset of 6 μm, the effective index modulation is much weaker compared with the former two cases, and the grating spectrum grows relatively slower during the fabrication process, as seen from Figure 3c. Thirty periods are introduced to fabricate the grating, and the resonant dip is not as deep as the former two. The amounts of index change introduced to the silica material in different samples are close to each other, since the laser energy deposited is the same. However, since the majority of light is propagating in the central part of the fiber, a smaller offset will have a larger influence on the mode effective index. That is why the sample with an offset of 6 μm has the weakest effective index modulation.

Considering that nonuniformities are introduced to fabricated the LPFG, conventional coupled mode theory is not applicable here. On the other hand, the coupled local mode theory can be adopted to deal with such a case. Based on this theory, electric or magnetic fields in the fiber can be expressed by a superposition of local modes and radiation field, and the core mode is partially coupled into the individual cladding modes and the radiation modes when light propagates through the nonuniform waveguide section. The coupling behavior between the core mode and the cladding mode can be expressed by the following equations [21]:

$$\begin{array}{l}\frac{\mathrm{d}{b}_{\mathrm{co}}}{\mathrm{d}z}-i{\beta }_{\mathrm{co}}{b}_{\mathrm{co}}=C(z)\cdot b_{\mathrm{cl}}\\ \frac{\mathrm{d}{b}_{\mathrm{cl}}}{\mathrm{d}z}-i{\beta }_{\mathrm{cl}}{b}_{\mathrm{cl}}=C^{*}(z)\cdot b_{\mathrm{co}}\\ \end{array}$$

(1)

where b represents the magnetic or electric field of a mode, and β is the propagation constant. The resonant wavelength λ can be described as follows:

$$\lambda =(n_{co}^{eff}-n_{cl}^{eff})\Lambda$$

(2)

where n_co^eff and n_cl^eff are the effective indices of the core and cladding modes, respectively. The transmitted core mode is characterized by cos(κL), where L is the grating length and κ is the coupling coefficient, defined by [22]:

$$\kappa =k_0{\iint }_{-\infty }^{+\infty }\delta n\left|F_{co}\left(x,y\right)\right|\left|F_{cl}\left(x,y\right)\right|dxdy$$

(3)

where δn is RI perturbation, F_co(x,y) and F_cl(x,y) are the transverse mode profiles of the core mode, and k₀ is the wave number. The coupling coefficient is influenced by the overlap of the mode profiles of the core and the cladding mode. For the LPFG fabricated in this work, the RI modulation is asymmetrically distributed, predominately in cladding; as a result, circularly asymmetric mode coupling is induced. In the sample with smaller offset, the overlap between core mode and the asymmetric cladding mode is larger; thus, the coupling efficiency is higher, and the grating grows faster in the fabrication process. Otherwise, the coupling coefficient is lower, and grating grows slower.

3. Experiments and Results

In the fabrication process, three LPFGs are written in SMF with different offsets, which will exhibit different bending sensing characteristics. Figure 4a depicts the experimental setup for the bending sensing experiment. A pair of displacement platforms are used to fix the sample during the curvature sensing, the separation of which is tuned to introduce different curvature values. A broadband light source (BBS) and an optical spectrometer analyzer are used to monitor the transmission spectrum during the experiment. The curvature sensing experiments are performed with three samples separately. To introduce curvature to the LPFG, the grating is fixed between the two platforms, one of which is kept still while the other is pushed towards the former one with a certain increment. The curvature could be approximately expressed by the following [23]:

$$c=\frac{1}{R}\cong \sqrt{\frac{24x}{L^3}}$$

(4)

where x is the feed displacement and L is the distance between the two stages. In the curvature measurement, the curvature response is tested in four bending directions. Each time after the curvature measurement, the displacement platform is initialized, the sample is rotated 90°, and four directions are tested, as depicted in Figure 4b. The curvature response of the LPFG sample without index modulation offset is firstly investigated. The curvature applied to the grating is increased from 0 to 4.83 m⁻¹, and transmission spectra of the grating are recorded. Figure 5a shows the transmission spectra at different curvature values, from which we can see that with the curvature increasing, the transmission spectra exhibit an obvious blueshift response. The change of the resonant wavelength is due to the curvature-introduced index variation in the fiber material, which in turn influences the effective indices of the modes involved in the grating resonance.

To study the direction dependence of the curvature sensing, the measurement is carried out in four bending directions. The wavelength shifts against curvature in the four bending directions are plotted in Figure 5b. In Figure 5b, one can see that the curvature responses are quite similar for the four directions. The curvature sensitivities are 10.85 nm/m⁻¹, 11 nm/m⁻¹, 11.14 nm/m⁻¹, and 10.43 nm/m⁻¹ for the bending angle of 0°, 90°, 180°, and 270°, respectively. Such similarity is because the LPFG sample has a cylindrical symmetric structure, and bending the fiber to different directions has the same effect on the grating. On the other hand, for the other two samples where the gratings are introduced to the fiber with an offset to the fiber core, the results are quite different.

We then test the curvature response of the LPFG sample with offset of 3 μm. Prior to the curvature measurement, the orientation of the grating with respect to the fiber core is marked. The curvature sensing experiment starts from the bending direction that is parallel to the grating-fiber core plane, which is marked as the bending angle of 0°. Curvature is applied to the LPFG in the same way as described before. The transmission spectrum is found to shift towards shorter wavelength, as shown in Figure 6a. Then, the bending direction is changed to 90°, which is vertical to the grating-fiber core plane. The spectrum response to curvature is shown in Figure 6b. Figure 6c,d show the curvature response of the other two bending directions, 180° and 270°, respectively. It is obvious that all bending directions have wavelength shift response to increasing curvature; however, the sensitivity may not be the same. The wavelength shifts against curvature in different bending directions are plotted in Figure 7. From Figure 7, we can see that the curvature sensitivities of the bending direction of 0° and 180° are close to each other, while the sensitivities of 90° and 270° are similar. Compared with other curvature sensors based on asymmetric LPFGs, the curvature responses in directions of 0° and 180° are not opposite; this is because even through asymmetric index modulations are introduced to fabricate the LPFG, the excited cladding modes intensity distributions are not too far away from the fiber axis, and bending the fiber to different directions does not have an opposite influence on the effective index of the cladding mode. Linear fittings are applied to the data, and the sensitivities are estimated to be 16.39 nm/m⁻¹ and 16.38 nm/m⁻¹ for bending angles of 0° and 180°, respectively. For bending angles of 90° and 270°, the sensitivities are 14 nm/m⁻¹ and 12.93 nm/m⁻¹. In general, the sensitivities are higher compared to the LPFG without any offset. On the other hand, the curvature sensitivity changes in different bending directions. In the grating-fiber core plane (bending angles of 0° and 180°), the sensitivity is higher, while in the other plane (bending angles of 90° and 270°), the sensitivity is low. Since the LPFG is fabricated with an asymmetric structure, the grating resonance results from the circularly asymmetric mode coupling, and that asymmetry is in the plane of the 0° and 180° directions. That means that bending the fiber in these two directions has a larger influence on the effective index of the cladding mode than bending the fiber in the 90° and 270° directions; thus, the curvature sensitivities are higher. The difference of sensitivity in different bending directions means that the sensor is capable of distinguishing the orientation of the curvature. By referring to the sensitivities in different bending directions, the direction of the curvature can be determined.

For the sample with an offset of 6 μm, the curvature sensing characteristic is investigated in the same way as the previous sample. The curvature responses in different bending directions are plotted in Figure 8. The results indicate that the sensitivity of this sample is further improved compared to the sample with offset of 3 μm, and the sensitivities in the bending direction of 0° and 180° are also close, which are 28.6 nm/m⁻¹ and 29.4 nm/m⁻¹, respectively, while the sensitivities in the other two directions, 90° and 270°, are 20.4 nm/m⁻¹ and 20.8 nm/m⁻¹, respectively, which are much smaller. The higher sensitivity is attributed to the larger separation between the fiber core and the index modulation area. Increasing the separation not only increases the curvature sensitivity, but also leads to much larger differences in sensitivities of the orthogonal bending directions. In this way, it would be much easier to distinguish the orientation of the curvature. It is clear that to achieve higher curvature-sensing performance, the offset of the grating modulation should be large; however, as discussed above, the large offset could lead to a very weak grating resonance. A compromise should be made between the sensing performance and the grating strength, since weak grating resonance will lead to low signal–noise ratios and the line width will also be large, which causes the detection limit of the sensor to be quite poor.

Table 1. Comparisons between the LPG sensors for vector bending measurement.

Sensor Structure	Curvature Range (m−1)	Bending Sensitivity (nm/m−1)	Reference
LPFG in three-core fiber	0 to 0.588	Maximum 3.234	[16]
Spatial cascaded orthogonal LPFG	0 to 2.0	Maximum 11.568	[17]
V-shaped LPFG	0.5 to 2.2	16.315 and −23.085	[19]
Interfaced tilted LPFG	0.997 to 2.997	−5.14 and 9.16	[8]
Side-grooved LPFG	0 to 2.52	Maximum 27.76	[24]
Asymmetric LPG	0 to 4.59	29.4	This work

gives the comparison of the sensing performance of our work and other curvature sensors, from which we can see that our sensor has higher sensitivity in a larger curvature measurement range.

Temperature is another important parameter that should be monitored during certain engineering processes. To investigate the temperature response of the LPFG, a heating treatment with a tube furnace (LCO 102 SINGLE, ECOM Co., Ltd., Ishikari, Japan) is applied to the grating. Temperature is increased from room temperature to 60 °C with a step of 5 °C. Each temperature is kept for 10 min before the spectrum is recorded. Figure 9a gives the grating spectrum under different temperature values. From Figure 9a, we can see that temperature does not cause much change in the resonant wavelength. The spectrum shifts slightly towards longer wavelength as temperature rises.

The wavelength shift is caused by the thermo-optic effect and the thermal-expansion effect of the fiber material. When temperature changes, the refractive index of the silica material, as well as the length of the fiber, will change, which will lead to the variation of the modes’ effective indices and the grating periods. Thus, the resonant wavelength of the grating will experience a shift. By differentiating the phase matching condition with respect to temperature, the temperature sensitivity can be given as

$$\frac{d\lambda }{dT}=\frac{d(n_{co}^{eff}-n_{cl}^{eff})}{dT}\Lambda +(n_{co}^{eff}-n_{cl}^{eff})\frac{d\Lambda }{dT}$$

(5)

The first component of Equation (5) is the thermo-optic effect of temperature sensing, in which the effective index of the core mode and cladding mode are both affected by temperature changing. Such thermal-optic effect can be shown as,

$$\begin{array}{l}\frac{d{n}_{co}^{eff}}{dT}={\alpha }_{co}{n}_{co}^{eff}\\ \frac{d{n}_{cl}^{eff}}{dT}={\alpha }_{cl}{n}_{cl}^{eff}\end{array}$$

(6)

where α_co and α_cl are the thermo-optic coefficient of the core and cladding mode, respectively. The second component of Equation (5) is the thermal-expansion effect in the temperature sensing, which causes the period of the grating to change. However, the thermal-expansion coefficient of the fiber is much lower compared to the thermo-optic coefficient; thus, this effect is negligible. The temperature sensitivity is mainly dependent on the difference between α_co and α_cl. If such a difference is large, the temperature sensitivity would be very high; otherwise, it will be quite low.

Figure 9b shows the wavelength response against temperature, from which we can see that the resonant wavelength exhibits a linear response to rising temperature. The temperature sensitivity is estimated to be 0.087 nm/°C.

Since both curvature and temperature cause the resonant wavelength to shift, the influence of temperature response to the curvature measurement should be estimated. The temperature cross-sensitivity can be calculated by S_temp/S_curv, where S_temp and S_curv are the temperature and curvature sensitivities, respectively. The cross-sensitivity is calculated to be 0.003 m⁻¹/°C, which is quite low. That indicates that the influence of temperature during the curvature measurement can be ignored.

4. Conclusions

In this article, a curvature sensor based on LPFG with asymmetric index modulation in a single-mode fiber is proposed and experimentally demonstrated. Femtosecond laser micromachining is used to inscribe the grating structure into the single-mode fiber. The grating structure is not introduced in the central fiber core, but is located off-axis with a distance of a few micrometers. Experimental results indicate that the offset distance affects the grating spectra. By utilizing such an asymmetric structure, two-dimensional vector curvature sensing can be realized. The curvature sensitivity increases with the amount of offset, and for an LPFG with offset distance of 6 μm, the curvature sensitivity is around 29 nm/m⁻¹ in the 0° and 180° direction and about 20 nm/m⁻¹ in the 90° and 270° direction. Larger offset also leads to larger sensitivity difference in different curvature orientations. The difference in curvature sensitivity in different bending planes makes the sensor capable of distinguishing the curvature orientations. The temperature response of the sensor is experimentally investigated, and the temperature sensitivity of the sensor is measured to be 0.087 nm/°C. The temperature cross-sensitivity is calculated to be 0.003 m⁻¹/°C, which indicates that the influence of temperature on the measurement accuracy of curvature is negligible. The sensor structure is compact and the sensitivity is high, making it an ideal candidate to be applied in the fields of structure health monitoring or intelligent robotics.