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Fabrication and sensing characterization of thermally induced long period fiber gratings in few mode fibers
Optik 158 (2018) 71–77
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Fabrication and sensing characterization of thermally induced long period fiber gratings in few mode fibers Ri-Qing Lv, Qi Wang, Hai-Feng Hu ∗ , Jin Li College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China
a r t i c l e
i n f o
Article history: Received 10 October 2017 Received in revised form 7 December 2017 Accepted 8 December 2017 Keywords: Few mode fibers Long period fiber gratings Sensor Temperature Stress
a b s t r a c t In this work, the long period fiber gratings (LPFGs) in few mode fibers are investigated systematically. A simple but effective method is employed to fabricate the thermally induced LPFG with asymmetric structure. When few mode fibers with LPFG are spliced between two single mode fibers, the obvious dip can be observed in the transmission spectrum. The mechanism of the transmission dip can be explained by the mode conversion process from LP01 to LP11 , which is identified by both theoretical analysis and the mode field measurements in FMF. The resonance wavelength of FMF-based LPFG is sensitive to applied strain and temperature. The sensitivities of strain and temperature measurements are 5.4 pm/ and 58.9 pm◦ C respectively. Because cladding modes are not involved in the mode conversion process, the LPFGs fabricated in this method are not sensitive to the environmental refractive index. It is suitable for the measurements of temperature and strain in the environment with variable refractive index. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction In the last two decades, few mode fibers (FMFs) have been intensively studied due to their potential to overcome the capacity limit of the optical communication based on standard single mode fibers (SMFs) [1,2]. Because the FMFs support a small number of modes in core layer, they provide more capacities and flexibilities than SMFs in optical communication by utilizing the space division multiplexing technology. Moreover, FMFs can also be employed to develop fiber optical sensors [3–7]. By exploring the unique properties of high order modes of FMFs, the optical fiber sensors can be developed with high sensing performance [4]. For this purpose, how to excite high order mode in FMFs becomes an important issue. The core offset splice between standard SMFs and FMFs is employed in order to generate the high order modes of FMFs under the incidence from SMFs [8]. However, the generation efficiency for each mode is difficult to control. In most cases, some modes in FMFs are excited by the offset splice structure simultaneously. The selective excitation of a specific high order mode in FMFs can be achieved by using planar phase plates [4]. In this technology, the alignment of the optical devices is difficult in free space optical system. Compared with this method, long period fiber gratings (LPFGs) are more compact and flexible in practical applications due to their all-fiber structures [9–11]. The mode conversion between two fiber modes can be achieved with high efficiency when the resonance condition is fulfilled. In fact, the LPFGs on FMFs can be fabricated by some different kinds of technologies, including acoustic wave [12], mechanical micro-bending [13] and CO2 laser pulse [14]. However, in most of these works, the sensing properties of these grating structures have not been fully explored. According
∗ Corresponding author. E-mail address: [email protected] (H.-F. Hu). https://doi.org/10.1016/j.ijleo.2017.12.022 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
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Fig. 1. The schematic of the LPFG written in FMF segment of the SMF-FMF-SMF structure. The insets show the electric field distribution of LP01 and LP11 modes in FMF.
to the previous work [7], the resonance wavelength of the LPFG on FMF is sensitive to strain and temperature applied on four-mode FMFs. When the four-mode FMF is inserted between two single mode fibers, the mode interference between LP01 and LP02 modes in the FMF may influence sensing results of the LPFG in FMF. In order to solve this problem, two-mode fiber has been employed in this work. The LPFGs in few mode fibers are fabricated to realize the mode conversion between LP01 and LP11 mode by a low-cost heating method. When the FMF segment with LPFGs is inserted between two SMFs, the formed structure can be developed for strain and temperature measurements. The sensing performance of the structure is characterized numerically and experimentally. Compared with the LPFGs in SMF, the FMF-based LPFGs proposed in this work are insensitive to the environmental refractive index, because only the core modes are involved in the mode conversion process. FMF-based LPFG is suitable for the measurement of temperature or strain in the environment with variable refractive index. 2. Theoretical analysis The designed structure of the FMF-based LPFG is shown in Fig. 1 . A segment of FMF with LPFG is spliced between two SMFs (SMF-28e, Corning). The FMF employed in this work is a step-index two mode fiber, which only supports the LP01 and LP11 modes. The SMF and FMF are well aligned without any core-offset during the splicing processes. The incident light is from the input SMF. Due to the restriction by mode orthogonal characteristic, the LP01 mode in the input SMF cannot couple with the LP11 mode in FMF, and only the LP01 mode in FMF is excited at the first joint. At the resonance wavelength of the LPFG, the LP01 mode can be converted to LP11 mode. At the second joint between FMF and the output SMF, the excited LP11 mode cannot couple into output SMF fiber in the form of LP01 mode. In this case, the transmission loss of the proposed structure can be caused by the mode conversion process. The power loss of the transmitted light is related to the conversion process of LPFG. According to the coupled mode theory, the z-dependent mode amplitudes for LP01 (A01 ) and LP11 (A11 ) in LPFGs should fulfill the differential equations as follows: dA01 j = j01−01 A01 + 01−11 A11 e−jız , 2 dz
(1a)
j dA11 = j11−11 A11 + 11−01 A01 ejız , 2 dz
(1b)
where ı is the detuning parameter, defined as ı = ˇ01 -ˇ11 -2/. ˇ01 and ˇ11 are the propagation constants of LP01 and LP11 modes in FMF. represents the grating period. The coupling coefficient - between mode and mode can be calculated by Eq. (2). − =
ε(r, )E (r, ) · E (r, )ds,
(2)
S1
In Eq. (2), ε(r, ) represents the perturbation of the grating region. E (r,) and E (r, ) are the field distributions of fiber modes. The mode conversion efficiency can be expressed as the ratio between the converted mode (LP11 ) power and incident mode (LP01 ) power. For a LPFG with length L, the conversion efficiency can be calculated by |A11 (z = L)|2 /|A01 (z = 0)|2 . The insets of Fig. 1 show the field distributions of these two modes when = 1550 nm. By calculating the integral in Eq. (2), one can prove that coupling coefficient is zero if the grating perturbation is independent with the azimuthal angle
(i.e. circular symmetry). In this work, the asymmetric LPFGs, like the periodical multi-notch structure as shown in Fig. 1, is designed and fabricated to realize the mode conversion between core modes in FMFs. In order to determine the resonance condition of LPFG, mode analysis should be carried out for the FMF fiber. In this work, the core diameter of the FMF is 15 m. The refractive index of the core layer and the cladding layer is n1 = 1.465 and n2 = 1.46. By solving the eigen-equation of the FMF, the effective indices of LP01 and LP11 modes in the wavelength range of 1300 nm ∼ 1800 nm are shown by the black and blue curves in Fig. 2(a) respectively. It can be proved that the
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Fig. 2. (a) The wavelength-dependent effective index of LP01 and LP11 modes in FMF. (b) The predicted LPFG period versus the resonance wavelength for the mode conversion between LP01 and LP11 modes.
Fig. 3. The schematic of LPFGs fabrication system.
corresponding grating period at the resonance wavelength of res can be determined by the zero detuning condition (i.e. ı = 0) as expressed in Eq. (3). =
res nLP01 − nLP11
(3)
In Eq. (3), nLP01 and nLP11 represent the index refractive index of LP01 mode and LP11 modes respectively. The calculated grating period for resonance coupling between the LP01 and LP11 modes versus res is shown Fig. 2(b). When the grating period is 830 m, the resonance wavelength is predicted to be at = 1550 nm. 3. Fabrication There existed several methods to fabricate LPFGs, such as ultraviolet laser, femtosecond laser pulse and CO2 laser heating. As discussed above, to convert LP01 mode to LP11 mode, the perturbation of grating ε(r, ) should has the asymmetric distribution in the fiber cross section. In this work, a simple but effective method is employed to fabricate LPFGs with low cost [15]. The fabrication system is shown in Fig. 3. A platinum-rhodium wire with a diameter of 0.5 mm is the heating element. The two ends of FMF segment along the horizontal direction are fixed on the translation stage by the fiber holders. Two pulleys with the v-shaped grooves are employed to guarantee that the position of the FMF fiber is unchanged during the grating fabrication. The vertical heating wire is mounted on a micro-displacement platform to adjust the tightness of the contact between fiber and heating wire. The broadband light source (ASE) and the optical spectrum analyzer (OSA) are employed to monitor the transmission spectrum of LPFG during the fabrication process. When the current through the heating wire is 18.5 A, a notch on fiber can be formed at the contact point between fiber and heating wire after 10 s. Then the fiber is moved to the next period within 1 s to write the next notch on fiber. Both of the two stages are moved to the same direction. The period can be controlled by the moving distance of the translation stage. When LPFG with 20 periods are written in FMF, the transmission spectrum through the sensing structure is shown in Fig. 4(a). The grating period is = 830 m. A transmission dip can be recognized at the wavelength of = 1536 nm. The slight deviation of the resonance wavelength between the experimental and theoretically predicted results may be introduced
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Fig. 4. (a) The Transmission spectrum of LPFGs in FMF segment of SFS structures. (b) The measured field distribution after passing through the LPFG at the resonance wavelength ( = 1536 nm). (c) The measured field distribution emitted from FMF without LPFG at = 1536 nm.
Fig. 5. (a) The measured transmission spectra of FMF-based LPFG under different strains. (b) The relationship between the measured resonance wavelength and strain. (c) The measured transmission spectra of FMF-based LPFG under different temperatures. (d) The relationship between the measured resonance wavelength and temperature.
by the variation of the fiber refractive index during the heating treatment process. To verify the excitation of LP11 mode at = 1536 nm, the output field profiles from FMF are measured by infrared couple charge device (CCD) camera. The tunable distributed feedback (DFB) laser is employed as the light source, which has a wavelength tuning range from 1529 nm to 1569 nm. The FMF segment of the SMF-FMF-SMF structure is cut off after the grating end. When the linear polarized light from DFB laser passes through the LPFG in FMF, the field profile is recorded by the camera as shown in Fig. 4(b). By contrast, the field profile from FMF without LPFG structure is also measured in Fig. 4(c). The field of LP11 mode and LP01 mode can be identified from the two field profiles in Fig. 4(b) and (c) respectively, by comparing with the theoretical results in the insets of Fig. 1. Based on the measurements of transmission spectrum and mode profiles, the mode conversion process in LPFG can be identified at the resonance wavelength. 4. Sensing characterization Similar with the LPFGs in SMF, the resonance wavelength of the proposed FMF-based LPFGs also exhibit high sensitivity to the variation of strain and temperature. The transmission spectra of LPFG under different strains are measured in Fig. 5(a). The resonance wavelength experiences a blue shift with the applied strain increasing obviously. The relationship between the resonance wavelength and strain can be fitted by a linear function in Fig. 5(b). The strain sensitivity of the resonance wavelength is 5.4 pm/, which is slightly larger with the FMF-based LPFG fabricated by high frequency CO2 laser pulse [7]. The temperature sensing characteristic of the FMF-based LPFG is also characterized experimentally. The transmission
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Fig. 6. The simulated transmission spectra of LP01 mode through LPFGs with different periods. The inset shows the perturbation region of LPFG in the theoretical model.
spectra under different temperatures are shown in Fig. 5(c). By carrying out linear fitting, the temperature sensitivity is determined to be 58.9 pm/◦ C in Fig. 5(d), which is comparable with that of LPFG in single mode fiber. In order to analyze the strain and temperature characteristics of LPFGs written in FMF, the two-layered numerical model based on coupled mode theory (CMT) is employed to determine the conversion efficiency between LP01 and LP11 by LPFG. During the thermal process, the geometry of FMF in grating region has been modified. Additionally, the variation of refractive index caused by residual stress relaxation can also affect the optical properties of LPFG. In order to simplify the numerical model, the periodical perturbation of the grating is equivalently considered as the semicircle region with the refractive index variation of n as shown by the inset of Fig. 6. In our theoretical model, the number of grating period is 20 and n is 4.3 × 10−3 . The calculated spectra for LPFGs with the periods from 825 m to 835 m are shown in Fig. 6. When the grating period is increased, the resonance wavelength experiences blue shift, which is consistent with the theoretical prediction in Fig. 2 (b). According to the elasto-optic effect, the fibers become uniaxial crystal, when strain is applied on LPFGs. In this case, the anisotropic optical properties of fiber should be taken into account in the theoretical model. The transverse and longitudinal refractive indices can be expressed as functions of strains in Eqs. (4a) and (4b). nit = ni −
1 3 − (pi,11 + pi,12 )]s n [p 2 i i,12
(4a)
niz = ni −
1 3 − 2pi,12 ]s n [p 2 i i,11
(4b)
In Eq. (4), subscript i denotes the core layer (i = 1) and cladding layer (i = 2) of the fiber. nit and niz represent the transverse and longitudinal refractive indices. pi, 11 and pi, 12 are the Pockel coefficients of fiber and is Poisson ratio. For silica, pi, 11 = 0.113, pi, 12 = 0.252 (i = 1, 2) and = 0.16 [16]. In Fig. 7(a), the transmission spectra are calculated when the strain is varied from 0 to 840 when period is 830 m. The theoretical strain sensitivity is 4.5 pm/ in Fig. 7(b), which is close to the experimental results. The temperature sensitivity of LPFG is mainly caused by the thermal expansion and thermo-optic effect. The period and the refractive index can be expressed as the functions of temperature in Eqs. (5a) and (5b). = 0 [1 + ˛(T − T0 )]
(5a)
ni = ni0 [1 + (T − T0 )]
(5b)
For silica optical fiber [17], the thermal expansion coefficient and thermo-optical coefficient are ˛ = 5.5 × 10−7 /◦ C and
= 7.5 × 10−6 /◦ C. When temperature is varied from 20 ◦ C to 80 ◦ C, the calculated transmission spectra are shown in Fig. 7(c). By carrying out the linear fitting of the simulated data in Fig. 7(d), the theoretical temperature sensitivity is 61 pm/◦ C, which is close to the experimental result. However, the resonance wavelengths between the experiments and simulations are obviously different. The transmission losses at the resonance wavelengths from the simulation results are much larger than that of the measured results. The deviation may be attributed to the variations of the refractive index of fiber after the thermal process in the LPFG fabrication. Moreover, the approximate model is employed to analysis the sensing principle of LPFG. In this model, many factors are not taken into account, including the accurate perturbation distribution of refractive index, the complex geometrical shape and the change of fiber characteristics (such as thermal expansion coefficient, thermo-optical coefficient and elasto-optic coefficient) caused by high-temperature processing. More effective theoretical model should be built to obtain a better analysis for LPFGs fabricated by the metal wire heating method.
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Fig. 7. (a) The simulated transmission spectra of LP01 mode through LPFGs under different strains. (b) The relationship between the simulated resonance wavelength and strain. (c) The simulated transmission spectra of LP01 mode through LPFGs under different temperatures. (d) The relationship between the simulated resonance wavelength and temperature.
5. Conclusion We have experimentally demonstrated thermally induced LPFGs in FMF for achieving the mode conversion between LP01 and LP11 . The LPFG structures consist of the periodical multi-notches, which are formed at the contact points between fiber and heating metallic wire. When the FMF with LPFG is inserted between two SMFs, the transmission loss at the resonance wavelength is increased, because the LP11 mode converted by LPFG cannot couple with the LP01 mode in the output SMF. The sensing performance of FMF-based LPFG is investigated experimentally and numerically. The measured temperature and strain sensitivities of the proposed structure are 5.4 pm/ and 58.9 pm/◦ C, which are both close to the numerical simulations based on coupled mode theory. Acknowledgements This work was supported by the National Nature Science Foundation of China (61403074); the Fundamental Research Funds for the Central Universities (N160405001, N160404002), and the Natural Science Foundation of Liaoning Province (201602262). References [1] R. Ryf, A.H. Randel, C. Gnauck, A. Bolle, Sierra, Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing, J. Lightw. Technol. 30 (2012) 521–531. [2] F. Yaman, N. Bai, B.Y. Zhu, T. Wang, G.F. Li, Long distance transmission in few-mode fibers, Opt. Exp. 18 (2010) 13250–13257. [3] A. Kumar, N.K. Goel, R.K. Varshney, Studies on a few-mode fiber-optic strain sensor based on LP01-LP02 mode interference, J. Lightw. Technol. 19 (2001) 358–362. [4] A. Li, Y.F. Wang, Q.W. Hu, Shieh, Few-mode fiber based optical sensors, Opt. Exp. 23 (2015) 1139–1150. [5] T. Mizunami, T.V. Djambova, T. Niiho, S. Gupta, Bragg gratings in multimode and few-mode optical fibers, J. Lightw. Technol. 18 (2000) 230–235. [6] E. Salik, M. Medrano, G. Cohoon, J. Miller, C. Boyter, J. Koh, SMS fiber sensor utilizing a few-mode fiber exhibits critical wavelength behavior, IEEE Photon. Technol. Lett. 24 (2012) 593–595. [7] B.A. Wang, W.G. Zhang, Z.Y. Bai, L. Wang, L.Y. Zhang, Q. Zhou, L. Chen, T.Y. Yan, CO2-laser-induced long period fiber gratings in few mode fibers, IEEE Photon. Technol. Lett. 27 (2015) 145–148. [8] Y.H. Qi, Z.X. Kang, J. Sun, L. Ma, W.X. Jin, Y.D. Lian, S.S. Jian, Wavelength-switchable fiber laser based on few-mode fiber filter with core-offset structure, Opt. Laser Technol. 81 (2016) 26–32. [9] S. Ramachandran, Z.Y. Wang, M. Yan, Bandwidth control of long-period grating-based mode converters in few-mode fibers, Opt. Lett. 27 (2002) 698–700. [10] C. Schulze, R. Bruning, S. Schroter, M. Duparre, Mode coupling in few-mode fibers induced by mechanical stress, J. Lightw. Technol. 33 (2015) 4488–4496.
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[11] J.L. Dong, K.S. Chiang, Temperature-insensitive mode converters with CO2-laser written long-period fiber gratings, IEEE Photon. Technol. Lett. 27 (2015) 1006–1009. [12] W. Zhang, L. Huang, K. Wei, P. Li, B. Jiang, D. Mao, F. Gao, T. Mei, G. Zhang, J. Zhao, Cylindrical vector beam generation in fiber with mode selectivity and wavelength tunability over broadband by acoustic flexural wave, Opt. Express 24 (2016) 10376–10384. [13] I. Giles, A. Obeysekara, R. Chen, D. Giles, F. Poletti, D. Richardson, Fiber LPG mode converters and mode selection technique for multimode SDM, IEEE Photon. Technol. Lett. 24 (2012) 1922–1925. [14] J. Dong, K.S. Chiang, Temperature-insensitive mode converters with CO2 -laser written long-period fiber gratings, IEEE Photon. Technol. Lett. 27 (2015) 1006–1009. [15] L. Gruner-Nielsen, J.O. Olsen, Systems and techniques for fabricating optical fiber gratings. U.S. Patent 20140238080A1, (2014). [16] O.V. Ivanov, L.A. Wang, Wavelength shifts of cladding-mode resonance in corrugated long-period fiber gratings under torsion, Appl. Opt. 42 (2003) 2264–2272. [17] Y.J. Kim, U.C. Paek, B.H. Lee, Measurement of refractive-index variation with temperature by use of long-period fiber gratings, Opt. Lett. 27 (2002) 1297–1299.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Fabrication and sensing characterization of thermally induced long period fiber gratings in few mode fibers Ri-Qing Lv, Qi Wang, Hai-Feng Hu ∗ , Jin Li College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China
a r t i c l e
i n f o
Article history: Received 10 October 2017 Received in revised form 7 December 2017 Accepted 8 December 2017 Keywords: Few mode fibers Long period fiber gratings Sensor Temperature Stress
a b s t r a c t In this work, the long period fiber gratings (LPFGs) in few mode fibers are investigated systematically. A simple but effective method is employed to fabricate the thermally induced LPFG with asymmetric structure. When few mode fibers with LPFG are spliced between two single mode fibers, the obvious dip can be observed in the transmission spectrum. The mechanism of the transmission dip can be explained by the mode conversion process from LP01 to LP11 , which is identified by both theoretical analysis and the mode field measurements in FMF. The resonance wavelength of FMF-based LPFG is sensitive to applied strain and temperature. The sensitivities of strain and temperature measurements are 5.4 pm/ and 58.9 pm◦ C respectively. Because cladding modes are not involved in the mode conversion process, the LPFGs fabricated in this method are not sensitive to the environmental refractive index. It is suitable for the measurements of temperature and strain in the environment with variable refractive index. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction In the last two decades, few mode fibers (FMFs) have been intensively studied due to their potential to overcome the capacity limit of the optical communication based on standard single mode fibers (SMFs) [1,2]. Because the FMFs support a small number of modes in core layer, they provide more capacities and flexibilities than SMFs in optical communication by utilizing the space division multiplexing technology. Moreover, FMFs can also be employed to develop fiber optical sensors [3–7]. By exploring the unique properties of high order modes of FMFs, the optical fiber sensors can be developed with high sensing performance [4]. For this purpose, how to excite high order mode in FMFs becomes an important issue. The core offset splice between standard SMFs and FMFs is employed in order to generate the high order modes of FMFs under the incidence from SMFs [8]. However, the generation efficiency for each mode is difficult to control. In most cases, some modes in FMFs are excited by the offset splice structure simultaneously. The selective excitation of a specific high order mode in FMFs can be achieved by using planar phase plates [4]. In this technology, the alignment of the optical devices is difficult in free space optical system. Compared with this method, long period fiber gratings (LPFGs) are more compact and flexible in practical applications due to their all-fiber structures [9–11]. The mode conversion between two fiber modes can be achieved with high efficiency when the resonance condition is fulfilled. In fact, the LPFGs on FMFs can be fabricated by some different kinds of technologies, including acoustic wave [12], mechanical micro-bending [13] and CO2 laser pulse [14]. However, in most of these works, the sensing properties of these grating structures have not been fully explored. According
∗ Corresponding author. E-mail address: [email protected] (H.-F. Hu). https://doi.org/10.1016/j.ijleo.2017.12.022 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
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Fig. 1. The schematic of the LPFG written in FMF segment of the SMF-FMF-SMF structure. The insets show the electric field distribution of LP01 and LP11 modes in FMF.
to the previous work [7], the resonance wavelength of the LPFG on FMF is sensitive to strain and temperature applied on four-mode FMFs. When the four-mode FMF is inserted between two single mode fibers, the mode interference between LP01 and LP02 modes in the FMF may influence sensing results of the LPFG in FMF. In order to solve this problem, two-mode fiber has been employed in this work. The LPFGs in few mode fibers are fabricated to realize the mode conversion between LP01 and LP11 mode by a low-cost heating method. When the FMF segment with LPFGs is inserted between two SMFs, the formed structure can be developed for strain and temperature measurements. The sensing performance of the structure is characterized numerically and experimentally. Compared with the LPFGs in SMF, the FMF-based LPFGs proposed in this work are insensitive to the environmental refractive index, because only the core modes are involved in the mode conversion process. FMF-based LPFG is suitable for the measurement of temperature or strain in the environment with variable refractive index. 2. Theoretical analysis The designed structure of the FMF-based LPFG is shown in Fig. 1 . A segment of FMF with LPFG is spliced between two SMFs (SMF-28e, Corning). The FMF employed in this work is a step-index two mode fiber, which only supports the LP01 and LP11 modes. The SMF and FMF are well aligned without any core-offset during the splicing processes. The incident light is from the input SMF. Due to the restriction by mode orthogonal characteristic, the LP01 mode in the input SMF cannot couple with the LP11 mode in FMF, and only the LP01 mode in FMF is excited at the first joint. At the resonance wavelength of the LPFG, the LP01 mode can be converted to LP11 mode. At the second joint between FMF and the output SMF, the excited LP11 mode cannot couple into output SMF fiber in the form of LP01 mode. In this case, the transmission loss of the proposed structure can be caused by the mode conversion process. The power loss of the transmitted light is related to the conversion process of LPFG. According to the coupled mode theory, the z-dependent mode amplitudes for LP01 (A01 ) and LP11 (A11 ) in LPFGs should fulfill the differential equations as follows: dA01 j = j01−01 A01 + 01−11 A11 e−jız , 2 dz
(1a)
j dA11 = j11−11 A11 + 11−01 A01 ejız , 2 dz
(1b)
where ı is the detuning parameter, defined as ı = ˇ01 -ˇ11 -2/. ˇ01 and ˇ11 are the propagation constants of LP01 and LP11 modes in FMF. represents the grating period. The coupling coefficient - between mode and mode can be calculated by Eq. (2). − =
ε(r, )E (r, ) · E (r, )ds,
(2)
S1
In Eq. (2), ε(r, ) represents the perturbation of the grating region. E (r,) and E (r, ) are the field distributions of fiber modes. The mode conversion efficiency can be expressed as the ratio between the converted mode (LP11 ) power and incident mode (LP01 ) power. For a LPFG with length L, the conversion efficiency can be calculated by |A11 (z = L)|2 /|A01 (z = 0)|2 . The insets of Fig. 1 show the field distributions of these two modes when = 1550 nm. By calculating the integral in Eq. (2), one can prove that coupling coefficient is zero if the grating perturbation is independent with the azimuthal angle
(i.e. circular symmetry). In this work, the asymmetric LPFGs, like the periodical multi-notch structure as shown in Fig. 1, is designed and fabricated to realize the mode conversion between core modes in FMFs. In order to determine the resonance condition of LPFG, mode analysis should be carried out for the FMF fiber. In this work, the core diameter of the FMF is 15 m. The refractive index of the core layer and the cladding layer is n1 = 1.465 and n2 = 1.46. By solving the eigen-equation of the FMF, the effective indices of LP01 and LP11 modes in the wavelength range of 1300 nm ∼ 1800 nm are shown by the black and blue curves in Fig. 2(a) respectively. It can be proved that the
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Fig. 2. (a) The wavelength-dependent effective index of LP01 and LP11 modes in FMF. (b) The predicted LPFG period versus the resonance wavelength for the mode conversion between LP01 and LP11 modes.
Fig. 3. The schematic of LPFGs fabrication system.
corresponding grating period at the resonance wavelength of res can be determined by the zero detuning condition (i.e. ı = 0) as expressed in Eq. (3). =
res nLP01 − nLP11
(3)
In Eq. (3), nLP01 and nLP11 represent the index refractive index of LP01 mode and LP11 modes respectively. The calculated grating period for resonance coupling between the LP01 and LP11 modes versus res is shown Fig. 2(b). When the grating period is 830 m, the resonance wavelength is predicted to be at = 1550 nm. 3. Fabrication There existed several methods to fabricate LPFGs, such as ultraviolet laser, femtosecond laser pulse and CO2 laser heating. As discussed above, to convert LP01 mode to LP11 mode, the perturbation of grating ε(r, ) should has the asymmetric distribution in the fiber cross section. In this work, a simple but effective method is employed to fabricate LPFGs with low cost [15]. The fabrication system is shown in Fig. 3. A platinum-rhodium wire with a diameter of 0.5 mm is the heating element. The two ends of FMF segment along the horizontal direction are fixed on the translation stage by the fiber holders. Two pulleys with the v-shaped grooves are employed to guarantee that the position of the FMF fiber is unchanged during the grating fabrication. The vertical heating wire is mounted on a micro-displacement platform to adjust the tightness of the contact between fiber and heating wire. The broadband light source (ASE) and the optical spectrum analyzer (OSA) are employed to monitor the transmission spectrum of LPFG during the fabrication process. When the current through the heating wire is 18.5 A, a notch on fiber can be formed at the contact point between fiber and heating wire after 10 s. Then the fiber is moved to the next period within 1 s to write the next notch on fiber. Both of the two stages are moved to the same direction. The period can be controlled by the moving distance of the translation stage. When LPFG with 20 periods are written in FMF, the transmission spectrum through the sensing structure is shown in Fig. 4(a). The grating period is = 830 m. A transmission dip can be recognized at the wavelength of = 1536 nm. The slight deviation of the resonance wavelength between the experimental and theoretically predicted results may be introduced
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Fig. 4. (a) The Transmission spectrum of LPFGs in FMF segment of SFS structures. (b) The measured field distribution after passing through the LPFG at the resonance wavelength ( = 1536 nm). (c) The measured field distribution emitted from FMF without LPFG at = 1536 nm.
Fig. 5. (a) The measured transmission spectra of FMF-based LPFG under different strains. (b) The relationship between the measured resonance wavelength and strain. (c) The measured transmission spectra of FMF-based LPFG under different temperatures. (d) The relationship between the measured resonance wavelength and temperature.
by the variation of the fiber refractive index during the heating treatment process. To verify the excitation of LP11 mode at = 1536 nm, the output field profiles from FMF are measured by infrared couple charge device (CCD) camera. The tunable distributed feedback (DFB) laser is employed as the light source, which has a wavelength tuning range from 1529 nm to 1569 nm. The FMF segment of the SMF-FMF-SMF structure is cut off after the grating end. When the linear polarized light from DFB laser passes through the LPFG in FMF, the field profile is recorded by the camera as shown in Fig. 4(b). By contrast, the field profile from FMF without LPFG structure is also measured in Fig. 4(c). The field of LP11 mode and LP01 mode can be identified from the two field profiles in Fig. 4(b) and (c) respectively, by comparing with the theoretical results in the insets of Fig. 1. Based on the measurements of transmission spectrum and mode profiles, the mode conversion process in LPFG can be identified at the resonance wavelength. 4. Sensing characterization Similar with the LPFGs in SMF, the resonance wavelength of the proposed FMF-based LPFGs also exhibit high sensitivity to the variation of strain and temperature. The transmission spectra of LPFG under different strains are measured in Fig. 5(a). The resonance wavelength experiences a blue shift with the applied strain increasing obviously. The relationship between the resonance wavelength and strain can be fitted by a linear function in Fig. 5(b). The strain sensitivity of the resonance wavelength is 5.4 pm/, which is slightly larger with the FMF-based LPFG fabricated by high frequency CO2 laser pulse [7]. The temperature sensing characteristic of the FMF-based LPFG is also characterized experimentally. The transmission
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Fig. 6. The simulated transmission spectra of LP01 mode through LPFGs with different periods. The inset shows the perturbation region of LPFG in the theoretical model.
spectra under different temperatures are shown in Fig. 5(c). By carrying out linear fitting, the temperature sensitivity is determined to be 58.9 pm/◦ C in Fig. 5(d), which is comparable with that of LPFG in single mode fiber. In order to analyze the strain and temperature characteristics of LPFGs written in FMF, the two-layered numerical model based on coupled mode theory (CMT) is employed to determine the conversion efficiency between LP01 and LP11 by LPFG. During the thermal process, the geometry of FMF in grating region has been modified. Additionally, the variation of refractive index caused by residual stress relaxation can also affect the optical properties of LPFG. In order to simplify the numerical model, the periodical perturbation of the grating is equivalently considered as the semicircle region with the refractive index variation of n as shown by the inset of Fig. 6. In our theoretical model, the number of grating period is 20 and n is 4.3 × 10−3 . The calculated spectra for LPFGs with the periods from 825 m to 835 m are shown in Fig. 6. When the grating period is increased, the resonance wavelength experiences blue shift, which is consistent with the theoretical prediction in Fig. 2 (b). According to the elasto-optic effect, the fibers become uniaxial crystal, when strain is applied on LPFGs. In this case, the anisotropic optical properties of fiber should be taken into account in the theoretical model. The transverse and longitudinal refractive indices can be expressed as functions of strains in Eqs. (4a) and (4b). nit = ni −
1 3 − (pi,11 + pi,12 )]s n [p 2 i i,12
(4a)
niz = ni −
1 3 − 2pi,12 ]s n [p 2 i i,11
(4b)
In Eq. (4), subscript i denotes the core layer (i = 1) and cladding layer (i = 2) of the fiber. nit and niz represent the transverse and longitudinal refractive indices. pi, 11 and pi, 12 are the Pockel coefficients of fiber and is Poisson ratio. For silica, pi, 11 = 0.113, pi, 12 = 0.252 (i = 1, 2) and = 0.16 [16]. In Fig. 7(a), the transmission spectra are calculated when the strain is varied from 0 to 840 when period is 830 m. The theoretical strain sensitivity is 4.5 pm/ in Fig. 7(b), which is close to the experimental results. The temperature sensitivity of LPFG is mainly caused by the thermal expansion and thermo-optic effect. The period and the refractive index can be expressed as the functions of temperature in Eqs. (5a) and (5b). = 0 [1 + ˛(T − T0 )]
(5a)
ni = ni0 [1 + (T − T0 )]
(5b)
For silica optical fiber [17], the thermal expansion coefficient and thermo-optical coefficient are ˛ = 5.5 × 10−7 /◦ C and
= 7.5 × 10−6 /◦ C. When temperature is varied from 20 ◦ C to 80 ◦ C, the calculated transmission spectra are shown in Fig. 7(c). By carrying out the linear fitting of the simulated data in Fig. 7(d), the theoretical temperature sensitivity is 61 pm/◦ C, which is close to the experimental result. However, the resonance wavelengths between the experiments and simulations are obviously different. The transmission losses at the resonance wavelengths from the simulation results are much larger than that of the measured results. The deviation may be attributed to the variations of the refractive index of fiber after the thermal process in the LPFG fabrication. Moreover, the approximate model is employed to analysis the sensing principle of LPFG. In this model, many factors are not taken into account, including the accurate perturbation distribution of refractive index, the complex geometrical shape and the change of fiber characteristics (such as thermal expansion coefficient, thermo-optical coefficient and elasto-optic coefficient) caused by high-temperature processing. More effective theoretical model should be built to obtain a better analysis for LPFGs fabricated by the metal wire heating method.
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Fig. 7. (a) The simulated transmission spectra of LP01 mode through LPFGs under different strains. (b) The relationship between the simulated resonance wavelength and strain. (c) The simulated transmission spectra of LP01 mode through LPFGs under different temperatures. (d) The relationship between the simulated resonance wavelength and temperature.
5. Conclusion We have experimentally demonstrated thermally induced LPFGs in FMF for achieving the mode conversion between LP01 and LP11 . The LPFG structures consist of the periodical multi-notches, which are formed at the contact points between fiber and heating metallic wire. When the FMF with LPFG is inserted between two SMFs, the transmission loss at the resonance wavelength is increased, because the LP11 mode converted by LPFG cannot couple with the LP01 mode in the output SMF. The sensing performance of FMF-based LPFG is investigated experimentally and numerically. The measured temperature and strain sensitivities of the proposed structure are 5.4 pm/ and 58.9 pm/◦ C, which are both close to the numerical simulations based on coupled mode theory. Acknowledgements This work was supported by the National Nature Science Foundation of China (61403074); the Fundamental Research Funds for the Central Universities (N160405001, N160404002), and the Natural Science Foundation of Liaoning Province (201602262). References [1] R. Ryf, A.H. Randel, C. Gnauck, A. Bolle, Sierra, Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing, J. Lightw. Technol. 30 (2012) 521–531. [2] F. Yaman, N. Bai, B.Y. Zhu, T. Wang, G.F. Li, Long distance transmission in few-mode fibers, Opt. Exp. 18 (2010) 13250–13257. [3] A. Kumar, N.K. Goel, R.K. Varshney, Studies on a few-mode fiber-optic strain sensor based on LP01-LP02 mode interference, J. Lightw. Technol. 19 (2001) 358–362. [4] A. Li, Y.F. Wang, Q.W. Hu, Shieh, Few-mode fiber based optical sensors, Opt. Exp. 23 (2015) 1139–1150. [5] T. Mizunami, T.V. Djambova, T. Niiho, S. Gupta, Bragg gratings in multimode and few-mode optical fibers, J. Lightw. Technol. 18 (2000) 230–235. [6] E. Salik, M. Medrano, G. Cohoon, J. Miller, C. Boyter, J. Koh, SMS fiber sensor utilizing a few-mode fiber exhibits critical wavelength behavior, IEEE Photon. Technol. Lett. 24 (2012) 593–595. [7] B.A. Wang, W.G. Zhang, Z.Y. Bai, L. Wang, L.Y. Zhang, Q. Zhou, L. Chen, T.Y. Yan, CO2-laser-induced long period fiber gratings in few mode fibers, IEEE Photon. Technol. Lett. 27 (2015) 145–148. [8] Y.H. Qi, Z.X. Kang, J. Sun, L. Ma, W.X. Jin, Y.D. Lian, S.S. Jian, Wavelength-switchable fiber laser based on few-mode fiber filter with core-offset structure, Opt. Laser Technol. 81 (2016) 26–32. [9] S. Ramachandran, Z.Y. Wang, M. Yan, Bandwidth control of long-period grating-based mode converters in few-mode fibers, Opt. Lett. 27 (2002) 698–700. [10] C. Schulze, R. Bruning, S. Schroter, M. Duparre, Mode coupling in few-mode fibers induced by mechanical stress, J. Lightw. Technol. 33 (2015) 4488–4496.
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