We successfully fabricated the long-period fiber gratings in few-mode fibers (FMF-LPFGs) with micro-tapered method, which are different from the traditional LPFGs that only couple the fundamental mode to different cladding modes to obtain multiple resonant dips. There are two resonant dips on the transmission spectrum of the FMF-LPFGs, which are induced by the coupling between the fundamental mode and the low-order cladding mode LP03 (dip 1) and the coupling between the fundamental mode and the high-order core mode LP11 (dip 2). Due to the difference of the coupling mechanism involved in two dips, the shift of resonant wavelengths has different characteristics with the variation of the external environment parameter. The corresponding wavelength of dip 1 exhibits a red shift as the temperature increased. But for dip 2, the resonant wavelength has a blue shift. In addition, the two dips have different temperature and strain sensitivities. Therefore, discriminative determination of temperature and strain is realized by establishing the cross coefficient matrix, and the relative measurement error is less than 3%. What’s more, we theoretically analyzed the reason why the two resonant wavelengths shift toward opposite direction with the increase of temperature and toward the same direction with the increase of strain.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Long-period fiber gratings (LPFGs) have received much attention since their appearance . LPFGs have many well-known advantages over electronic based sensors, such as compact size, robust construction, immunity to electromagnetic interference and remote sensing capability. Therefore, LPFGs have a wide range of applications including gain-flattening filters, wavelength rejection filters and optical fiber sensors for physical parameters such as temperature, strain, refractive index and curvature [2–9]. In the past decades, many methods have been developed to fabricate LPFGs. Nevertheless, most of light-based methods need sophisticated fabrication platform and pretreatment procedure. For example, the UV laser exposure through the amplitude mask needs amplitude or phase masks , CO2 or femtosecond laser direct point-to-point irradiation requires high power laser system at specific wavelength and long-time hydrogen loading , while the chemical etching needs precise control . In recent years, a micro-taper based method has been proposed and experimentally demonstrated to fabricate LPFGs by periodically tapering with heating source [13–15]. The immense attention has been increasingly focused on this new type of LPFGs, because its fabrication is simple and does not need expensive laser equipment. The micro-tapered LPFGs usually have some special sensing applications, such as high-strain sensitivity and high-temperature sensing [16,17].
At present, most of LPFGs fabricated by the micro-tapered method are based on single-mode fibers (SMFs). However, LPFGs based on SMFs usually can only couple the core mode to the forward propagating cladding modes, inducing resonant dips in the transmission spectrum . LPFGs inscribed in SMFs can discriminate concurrently strain and temperature by measuring the shift of resonant wavelength and the variation of transmission power . But there may be a correlation between them with one resonant dip. LPFGs based on multicore fibers (MCFs) with parallel transmission can solve the correlation caused by one dip . However, it is only the fundamental mode that is coupled to the cladding mode in the LPFGs inscribed in MCFs. The sensitivity of the outer cores is almost the same and the spatial multiplexing advantage of MCFs cannot be fully utilized. On the other hand, few-mode fibers (FMFs) have been widely used in optical communication  and optical fiber sensors . Compared to SMFs, FMFs can support a small number of modes in the fiber core and it can enhance the capability of the optical transmission system. FMF-LPFGs can couple the fundamental mode to the high-order core mode [22–24]. It can make full use of the characteristic that the FMFs can support multiple modes transmission. In , the LPFGs based on FMFs are quite sensitive to strain and slightly insensitive to temperature, which is quite different from LPFGs fabricated in common SMFs. However, it only achieved single parameter sensing due to the coupling between the fundamental mode and the high-order core mode.
In this paper, the LPFG is fabricated on a 4-mode fiber by the micro-tapered method with electric arc discharges. There are two resonant dips on the transmission spectrum of the FMF-LPFGs. The resonant wavelength of dip 1 can be controlled from 1475 nm to 1525 nm when the grating period changes from 344 μm to 350 μm. While for dip 2, the corresponding wavelength can shift from 1571 nm to 1615 nm when the grating period changes from 346 μm to 340 μm. Then the mechanism of the mode coupling at two resonant dips is discussed. In addition, we measured the temperature and strain sensitivity of two dips respectively and theoretically analyzed the reason of the difference of temperature and strain sensitivity between two dips. Due to the different sensitivities of temperature and strain, the cross coefficient matrix is established and dual-parameter discrimination determination is realized.
2. Fabrication of FMF-LPFGs
We utilized a 4-mode fiber with the step-index profile. Figures 1(a) and 1(b) demonstrate the refractive index difference profile and the end view of the FMF, respectively. The refractive index of core and cladding are 1.4635 and 1.4588, respectively. The core diameter is 20 μm and the cladding diameter is 125 μm. The initial guiding modes in the FMFs are calculated by the finite-element method. The effective refractive index of the first four linear polarization modes (LP01, LP11, LP21, LP02) are shown in Fig. 2.
The FMF-LPFGs are fabricated by the micro-tapered method. Figure 3 shows the fabrication platform of the FMF-LPFGs based on the specialty fiber fusion splicer (Fujikura FSM 100P + ). SMFs are spliced at both ends of the FMFs. First, the fusion splicer preheats FMFs by electric arc discharge, and then the left and right motors move to both sides at a speed of 0.04 μm/ms to conduct the taper. Second, the left and right motors which take the whole FMFs move to the next micro-tapered position along “Y” direction. The grating period Λ of the FMF-LPFGs is determined by the moving distance. Finally, the above two steps are repeated N times to induce periodic refractive index modulation and obtain the FMF-LPFGs.
During the fabrication of FMF-LPFGs, a super-continuum optical source (SCS) and an optical spectrum analyzer (OSA) are used to monitor the evolution of transmission spectra. Figure 4(a) shows the FMF-LPFGs transmission spectra evolving with the grating period number N when the grating period Λ equals to 340 μm. It clearly shows extinction ratio of two resonant dips grow with the increase of grating period number N. When the grating period number N is 49, the total length of the FMF-LPFGs is 16.66 mm. There are two distinct resonant dips in the transmission spectrum, and the corresponding wavelengths are 1470.19 nm of dip 1 and 1615.15 nm of dip 2, respectively. The dip 1 approaches to extinction ratio about 28 dB and extinction ratio about 14 dB is obtained of dip 2. The insertion loss is around 5 dB, which is caused by the uneven heating with electric arc discharge and micro-tapered method. The microscopic photograph of the fabricated FMF-LPFGs with a period of 340 μm is shown in Fig. 4(b).
In order to obtain two dips at the same time, the transmission spectra of FMF-LPFGs with the grating periods from 340 μm to 350 μm are shown in Figs. 5(a) and 5(b), respectively. The largest extinction ratio about 38 dB is achieved of dip 1 when the grating period is 350 μm. The corresponding wavelength of dip 1 can shift from 1475 nm to 1525 nm with different grating periods. As the grating period changed, the corresponding wavelength of dip 2 shifts from 1615 nm to 1571 nm. The relationship between the resonant wavelength and grating period is indicated in Figs. 5(c) and 5(d). The corresponding wavelength of dip 1 increases with the growing of grating period. However, with the growing of grating period, the corresponding wavelength of dip 2 decreases.
In order to confirm the mechanism of the mode coupling at the resonant wavelengths, we use a tunable laser diode (1480 nm~1650 nm) and a CCD camera to measure the output field profile at the end of the fabricated FMF-LPFGs. Figures 6(a)–6(c) show the mode profiles around dip 1 with grating period of 348 μm at different wavelengths of 1485 nm, 1513 nm, 1530 nm, respectively. From Fig. 6(b), it indicates that the dip 1 appears on account of the fundamental mode LP01 coupled to the low-order cladding mode LP03. The field profile of the cladding mode LP03, which only has two rings in the radial, is different from that of the ordinary LP03, because the central part of the measured radial distribution contains the partially transmitted fundamental mode and the fundamental mode field masks the inner rings of the cladding mode . When the wavelength increases, the fundamental mode reappears in FMFs. Finally, it completely becomes the fundamental mode LP01 at the wavelength of 1530 nm. The mode profiles around dip 2 with grating period of 346 μm at different wavelengths of 1552 nm, 1571 nm, 1593 nm are shown in Figs. 6(d)–6(f), respectively. The dip 2 originates from the coupling between the fundamental mode LP01 and the high-order core mode LP11, as shown in Fig. 6(e). When the light transmits from FMF to SMF, the high-order core modes are dissipated. Therefore, the resonant dip appears at the wavelength of 1571 nm. Because two resonant dips have different coupled modes, the resonant wavelengths shift to different directions with the change of grating period. For dip 1, the effective refractive index difference of two coupled modes is basically unchanged with the increase of wavelength. The length of grating period determines the corresponding wavelength of dip 1 moving direction. For dip 2, the effective refractive index difference of two coupled modes has a significant change with the increase of wavelength from Fig. 2. As the period increased, the phase matching condition is satisfied at a shorter wavelength. Therefore, the corresponding wavelength of dip 2 shifts to shorter wavelength with the increase of grating period.
3. Experimental results and discussions
In order to realize discriminative determination of temperature and strain, we chose the FMF-LPFGs with grating period of 340 μm and 49 periods as the sensor head. The experimental setup for temperature and strain measurement is shown in Fig. 7. To measure the strain, both ends of the FMF-LPFGs are fixed on two translation stages with interval of 26.5 cm. The strain measurement region is controlled by the translation stages. In order to measure the temperature, the whole FMF-LPG is placed between two copper plates. The temperature of the measurement region is controlled by a thermoelectric cooler (TEC) with the temperature resolution of 0.1 °C. The SCS is used as the light source and the OSA is used to monitor the change of transmission spectra.
When the strain is fixed at 0.0 με, the spectra characteristics of temperature change are studied. The temperature is changed from 20 °C to 70 °C with a step of 10 °C. The wavelength shift of dip 1 and dip 2 are shown in Figs. 8(a) and 8(b), respectively. With the increase of temperature, the corresponding wavelengths of dip 1 and dip 2 linearly shift to opposite direction. Figures 8(c) and 8(d) are the linear fitting of two dips. The temperature sensitivity is 38.7 pm/°C for dip 1 and −12.6 pm/°C for dip 2. The R-square values of the linear fitting are all above 0.99. The spectra characteristics with various strain are studied when the temperature is fixed at 30 °C. The axial strain increased from 0.0 με to 2264.2 με with the step of 377.3 με. Figures 9(a) and 9(b) show the wavelength shift of dip 1 and dip 2, respectively. For both dips, they all linearly shift to shorter wavelength with the increase of axial strain. Figures 9(c) and 9(d) are the linear fitting results. The strain sensitivity is −0.9 pm/με for dip 1 and −2.0 pm/με for dip 2. The R-square values of Figs. 9(c) and 9(d) are 0.9966 and 0.9945, respectively.
The temperature and strain responses are quite different between dip 1 and dip 2. The resonant wavelength of dip 2 has a blue shift with the increase of temperature, which is opposite to dip 1. And the strain sensitivity of dip 2 is about double that of dip 1. The following formulas give an explanation of the shift of wavelength with temperature and strain :Eqs. (4) and (5).
The sensitivities to the temperature and strain are affected by the thermos-optic and elasto-optic coefficient of the fiber material. The dip 1 originates from the fundamental mode coupled to the low-order cladding mode. and are the effective index of the fundamental mode and the low-order cladding mode. We can get = 2.16 based on Fig. 5(c). For standard fiber,the and are positive values, < −1 . We can calculate that is a positive value and is a negative value. Therefore, with the increase of temperature, the corresponding wavelength of dip 1 shifts to longer wavelength and shifts to shorter wavelength with the increase of strain. While for dip 2, it is the fundamental mode coupled to the high-order core mode. Therefore, the sensitivities to the temperature and strain of dip 2 are determined by the material of the fiber core. and are the effective index of the fundamental mode and the high-order core mode. We can deduce that = −5.82 from Fig. 5(d) and the dispersion curves in the Fig. 2. Due to the coupling between two core modes, Eqs. (4) and (5) can be simplified as and . When we assume that the material of the core is pure silica, the , and can be set to /°C, and −0.22 respectively . We can deduce that and are both negative values. With the increase of temperature and strain, the corresponding wavelength of dip 2 both shift to shorter wavelength.
Discriminative determination can be achieved with two dips because two dips have different sensitivities to the temperature and strain. Variations in the external environment parameters can lead to different responses. Therefore, the cross sensitivities of dual-physical parameters based on the micro-tapered FMF-LPFGs can be distinguished effectively. A cross coefficient matrix can describe the cross sensitivities of temperature and axial strain, as shown below :Eq. (6) can be re-written as:Table 1. The relative errors of temperature and strain measuring are 3.00% and 1.98%, respectively.
In summary, we successfully fabricated FMF-LPFGs by using the micro-tapered method with arc discharge technology. There are two resonant dips on the transmission spectrum of the FMF-LPFGs. The corresponding wavelength of dip 1 can shift from 1475 nm to 1525 nm and the corresponding wavelength of dip 2 can shift from 1571 nm to 1615 nm with different grating periods. Two dips originate from the fundamental mode coupled to the low-order cladding mode and the high-order core mode, which is confirmed by experiment. We realized the temperature and strain discriminative determination with the cross coefficient matrix. And the relative measurement error is less than 3%, which shows excellent accuracy. In addition, two resonant dips shifting toward opposite direction with the increase of temperature and toward the same direction with the increase of strain are analyzed theoretically. It’s believed that the LPFGs in FMFs have attractive potentials for multi-parameter discrimination determination and filters.
National Key R&D Program of China (2018YFB1801002); National Natural Science Foundation of China (NSFC) (61722108); Innovation Fund of WNLO.
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