We demonstrate the fabrication of an angle-chirped long-period fiber grating (ACLPFG) in a single-mode fiber via CO2 laser pulses. Because of the Berry phase introduced by the ACLPFG, the interference acquires an extra phase difference determined by the torsion of the device. By using that unique characteristic of the proposed device, a high sensitivity sine function torsion response is achieved. The torsion sensitivity is significantly improved, and the temperature crosstalk is effectively avoided by using the relative measurement technology. The torsion sensitivity is ~16 folds (~0.94 nm/ (rad/m)) higher than that of the normal long-period fiber grating (LPFG) with only ~0.006 nm/°C temperature crosstalk within the range of 25-80 °C, which is ~10 folds lower than that of the normal LPFG.
© 2017 Optical Society of America
Twist is one of the most important mechanical parameters for security monitoring in civil engineering, such as bridges, buildings, dams and other structures . By monitoring the twist, the stress state and internal injury of the structure can be found. Thus, it is helpful to analyze whether the building maintains a healthy state. To measure the applied twist, fiber-optic sensors have attracted much attention because of their compact structure, accurate measurement, anti-electromagnetic interference and high sensitivity. Therefore, varieties of such sensors have been reported in recent years including special fibers and fiber gratings. Generally a twist sensor achieved in specifically designed fiber [2–4] is expensive and has a weak compatibility with the established backbone network. As the base of twist sensors, the fiber gratings are fabricated by corrugated structure , UV laser radiation [6,7], CO2 laser writing [8,9], femtosecond laser  and mechanical deformation . Moreover, the obtained sensors have the remarkable distinctions because of their different coupling mechanisms. Several reported sensors [5–7] fail to determine the twist direction and only realize the absolute measurement of torsion. For a LPFG written by a CO2-laser, because the asymmetrical distribution of refractive index change induced by the one-side exposure by the CO2 laser beam, the resonance wavelength shift has a linear response to the applied twist and strongly dependent on the twist direction . However, the twist sensitivity of the normal LPFG is relatively low. To obtain high twist sensitivity and determine torsion direction simultaneously, some complicated schemes have to be introduced into the structure, such as helical long-period fiber grating (HLPFG)  and cascaded LPFGs [13–16]. The complicated mechanisms cause difficulty to sensor fabrication and affect the sensor’s simplicity. Meanwhile, the resonance wavelength of a LPFG is highly crosstalk to the temperature and torsion, and therefore, developing a simple and inexpensive technique to reduce the crosstalk keeps going on.
To circumvent the aforementioned disadvantages, the researcher proposes a novel ACLPFG-based twist sensor via using a high-frequency-CO2-laser. Because of the non-uniform refractive index modulation and gradient characteristic of the tilt angles in the ACLPFG, the Berry phase  is introduced into guided modes when torsion is applied, which is verified by the sine function torsion response. The device’s torsion sensitivity is ~16 folds higher than that of the normal LPFG and its temperature crosstalk is only ~1/10 compared to the normal LPFG. The proposed sensor has a simpler and more compact structure, which is easier to fabricate and has a competitive advantage in price. A number of twist monitor applications, such as bridges, buildings, and dams et al., would benefit from the proposed device.
2. Fabrication and principle
The manufacturing setup is shown in Fig. 1. The sensor fabrication is described as follows: first, a normal grating was drew with a pitch of 580 μm and 41 periods, and then rotated each trench of the grating with a fixed angle around the center of the software, which can drive the CO2 laser and control the grid’s angle. The tilt angles are defined as a Heaviside step function, where φ is defined as the reference angle which are 1°, 2° and 3° in the experiments. The grid located in the geometry center is defined as i = 0, and the grids from left to right denote minus 20 to plus 20. The proposed ACLPFG has an inhomogeneous refractive index modulation contributed by the non-uniform grid angle. When the designed ACLPFG was finished in the software, one end of the selected fiber was fixed on a translation stage and the other end attached a weight with ~20 g. A high-frequency-CO2-laser (CO2-H30, Han’s laser), which delivered a maximum average output power of 15 W, was used to fabricate the grating. The schematic of the proposed sensor is shown in Fig. 2.
The angle of the ACLPFG has an adiabatic changing which serves as a loop in the parameter space. Therefore, when the torsion is applied to the sensor head, the Berry phase can be expected and the value of the Berry phase is related to the adiabatic angular changing. The larger the grid tile angle, the deeper the resonance dips in the proposed sensor, which leads to a larger signal-noise rate (SNR). Taking into account the tradeoff between the SNR in the sensor transmission spectra and the value of the Berry phase introduced by the applied torsion, the parameters of the grating grids were studied. The researcher considered the periodic refractive index modulation as a perturbation, and thus the refractive index distribution of the cladding, , after the CO2-laser radiated, is,18]. On the basis of the Eq. (1), the refractive index modulation is proportional to the tilt angle . In the experiments, the researchers fabricated three ACLPFGs and their values of the reference grid tilt angles were 1°, 2° and 3° to be compared to the normal LPFG. To acquire a narrow spectrum and match the measurement range of the optical spectrum analyzer (OSA), the researcher selected the grating with a period of 580μm and 41 grids in the experiments. The transmission spectra of the normal LPFG and the three ACLPFGs with 1° (ACLPFG-1), 2° (ACLPFG-2), 3° (ACLPFG-3) tilt angles are presented in Figs. 3(a) and 3(b). When the tilt angle is small, the transmission spectrum of the fabricated device is similar to the transmission spectrum of a normal LPFG. As the value of the tilt angle increases, the refractive index modulation becomes deeper and stimulates the cladding modes. This is because of the adiabatic angle characteristics of the proposed ACLPFG, the Berry phase is introduced into the core mode and the cladding mode’s optical path difference, and, further produces an additional influence when the twist is applied. However, if the tilt angle is large excessively, the fiber possesses a higher risk of breaking during torsion and further affects the measurement range. Taking into account the practical application, the structure of the tilt angle was selected at 3° (ACLPFG-3).
In the experiments, when the input reaches the ACLPFG, it is split into two light paths. One part of the light is propagated as the cladding mode while the other part still propagates as the fundamental core mode. Moreover, one part of the cladding modes is coupled back to the core mode when it propagates at the end of the ACLPFG. According to the interference theory, the interference intensity can be expressed as,
In general, the normal LPFG possesses a linear refractive index modulation . While the proposed ACLPFG, the change of the refractive index is adiabatic along the light propagation. Therefore, the optical path becomes difference, since the Berry phase can be written as,20] when the torsion is applied.
3. Experiments and discussion
The experimental setup for torsion measurement is shown in Fig. 1. The torsion characteristics of the sensors were investigated experimentally. One end of the fiber was fixed to a stationary holder, and the other end was fixed to the center of a rotatable holder that provided the twist to the device. A ~20 g mass was attached to the fiber to apply a constant external tension. The broadband light source (BBS) and the OSA were used to record the transmission spectra when the grating was twisted. The twist rate is defined as , where L is the distance between two holders.
In the experiments, four gratings were fabricated, these are: the ACLPFG-1, ACLPFG-2, ACLPFG-3 and normal LPFG. Figure 4 shows the experimental results when the clockwise or anticlockwise twist was applied. The green and red curves are the sine function fitting with R2 = 0.99 for the torsion ranging from −15 to 15 rad/m for the ACLPFG-2 and ACLPFG-3, and the wavelength of the selected dips shift 6.9 nm and 14.05 nm, respectively. The torsion sensitivity is up to ~0.252 nm/ (rad/m) for ACLPFG-2, which is ~4 folds higher than that of the normal LPFG. However, with the same applied torsion, no remarkable wavelength shifts were observed for the normal LPFG and ACLPFG-1, which maintain the same with the previous report . The sine function torsion response verifies that the proposed device introduces the Berry phase when twist is applied. As a contrast, the normal LPFG situation only has low linear torsion sensitivity. For the proposed sensor (ACLPFG-3), Dip A at 1453.4 nm and Dip B at 1591.65 nm were selected as an indicator, because the laser source and OSA are well developed and econimical in the communication wavelength band. These two resonances are stable in the large measurement range and have a high contrast, while the other dips will decrease in the process of twisting. Dip B was firstly tracked in order to monitoring the torsion. The twist sensitivity is ~0.593 nm/ (rad/m) in the particular region, which is an order magnitude higher than that of the normal CO2-laser written LPFGs. In contrast, Dip A shifted to the opposite direction compared to Dip B, and this phenomenon is similar to the “resonance mode splitting” and “dual resonance” in LPFGs in step-index fibers . The twist responses are directionally sensitive and possess a sine function response with the twist rate, as shown in Fig. 5. The as-achieved twist sensitivity is ~0.94 nm/ (rad/m) in the torsion range of ± 10 rad/m by using the relative measurement technology finally, which is ~16 folds higher than that of the normal LPFG. In the small range a linear function approximation can be used to fit any physics phenomenon. But the linear phenomenon is highly rear in the real word, and the higher order component should be expected. The berry phase is a nonlinear processing, and it also has a linear component. If one ignores its higher order component like the common sensor application , the response should be lower compared to sum all the components’ response. Therefore, if the higher order component is considered, the nonlinear response function, i.e., sine function, should have a large rate of change compared to that of the linear function. The experimental data show that the sine function did better than the linear function response in Figs. 4 and 5(b).
In practical applications, it is beneficial to avoid the cross-sensitivity of temperature in torsion measurements. Some experiments were carried out to investigate the temperature response of the sensor. The proposed sensors were placed in a heating stove. By gradually increasing the ambient temperature from 25 to 80 °C, the transmission spectra under different temperatures were recorded by the OSA. Figure 6 shows the wavelength shift of the Dips A and B respectively without any twist. Under different temperature conditions, both the Dips A and B shifted to the longer wavelength and the temperature sensitivities of attenuation peaks-A and B are 0.057 and 0.051 nm/°C, respectively. However, if the post process was employed, i.e., considering the relative shift between Dips A and B, the temperature crosstalk could be almost eliminated. The temperature sensitivity decreases as low as 0.006 nm/°C, which is about one-tenth of the temperature sensitivity of the normal LPFG written by a CO2 laser . The maximum wavelength variation with temperature changes is less than 0.209 nm and the shaded sections represent the uncertainty of the experimental system.
In conclusion, this research proposes and experimentally demonstrates a novel ACLPFG inscribed in SMF. The responses of the three samples to torsion and temperature were investigated. For the normal LPFG, the resonance wavelength shift has a linear response to the applied twist, while the refractive index change of the ACLPFG is adiabatic compared to the normal LPFG. Hence the interference fringes shift has a sine relation with the torsion after taking the first order of the refractive index response for the fiber torsion into account. By using the relative measurement technology, the proposed sensor decreases the cross sensitivity of temperature and increases the twist sensitivity. Its temperature crosstalk (~0.006 nm/°C) is one order of magnitude lower than that of the normal LPFG and the twist sensitivity is ~16 folds (~0.94 nm/ (rad/m)) higher than that of the normal LPFG. Therefore, the proposed device has a promising application as a high-performance torsion sensor.
Natural Science Foundation of Tianjin (15JCZDJC3980); National Natural Science Foundation of China (NSFC) (11274181, 10974100, 61405179); Doctoral Scientific Fund Project of the Ministry of Education (20120031110033); Open fund of the Key Laboratory of Optical Information Science &Technology (Nankai University).
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