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Long period fiber gratings (LPGs) in a two-core hollow eccentric fiber (TCHF) have been demonstrated experimentally. Two LPGs have been fabricated into the respective core of the TCHF by a high frequency CO2 laser. The coupling characteristics in the TCHF-LPG have been studied using the coupling mode theory (CMT). The resonant peak is mainly caused by the coupling between the core mode LP01 and cladding mode LP81. The experimental results agree well with the simulation results. Furthermore, the sensing properties of the TCHF-LPG have been investigated with respect to bending, temperature and axial strain. Compared with the LPG in the single mode fiber (SMF), the experimental results indicate that the sensitivity of the TCHF-LPGs to bending curvature is low and even very small at some bending directions. In addition, TCHF-LPGs are insensitive to the axial strain while sensitive to the temperature. Therefore, the proposed TCHF-LPGs can efficiently sense the changing temperature that is independent of the strain. Moreover, the TCHF-LPGs can also be applied to two-channel filters without signal crosstalk between two cores.
© 2015 Optical Society of America
1. Introduction
In recent years, long period fiber gratings (LPGs) have received much attention because of their versatile advantages such as their high sensitivity [1,2], easy fabrication and integration. For inscribing the LPGs, UV-writing method is time-consuming to load hydrogen (H2) into many kinds of fibers without photosensitivity. Many other methods, including femtosecond laser writing [3], point-by-point CO2 laser irradiation [4,5] or electric arc discharge [6] and etching [7], have been proposed to replace the UV exposure. Among these methods, the CO2 laser irradiation is popular owing to their high repetition, convenience and simple operation. At present, plenty of LPGs have been written in special fibers such as polymer optical fibers [8], D-shaped cladding fibers [9,10], optical microfibers [11,12], eccentric core fibers [13,14], and photonic crystal fibers (PCFs) [15–19]. More importantly, holey fibers (HFs) can provide a strong evanescent field in the air holes and also offer great potentials for designing grating-based photonic devices [20–22]. For the multi-core HFs, the air holes can prevent the signal crosstalk between the cores [23]. The holey PCF- LPGs [16–19] have been used for temperature, strain, and gas pressure and curvature sensors. Z. Wang et al. [24] have fabricated the LPG in simplified hollow-core photonic crystal fibers (HC-PCFs) by using the CO2-laser irradiation technology and analyzed theoretically the mode-coupling characteristics of the LPG. Y. G. Han et al. have reported the LPGs [25] and the Bragg fiber gratings (FBGs) [26] inscribed in the six-hole fibers and investigated experimentally the effect of the holes’ size on the properties of the gratings. The FBGs and LPGs have been inscribed in the two-hole fiber by C. M. Jewart et al. [27] and J. Kang et al. [20]. However, there are few literatures about the HFs with few holes and multi-cores. The LPGs in the single air hole fiber with two cores have not been reported yet.
In this work, we propose a two-core hollow eccentric fiber (TCHF), in which two cores are positioned symmetrically in inner wall of the annular cladding with a big air hole. The LPGs are written in this fiber and their sensing characteristics are investigated including the axial strain, temperature and bending. Compared with the D-shaped fibers and microfibers, the TCHF is simple fabrication, low cost and stable. On the other hand, the two cores separated by the air hole can prevent the signal from cross talking. Therefore, the TCHF-LPGs could be promising to realize the two-channel filters in optical communications.
2. Two-core hollow eccentric fiber
As shown in Fig. 1, the investigated TCHF has a diameter of about 118 μm, a big air hole with a diameter of 70 μm and an annular cladding with a thickness of 24 μm. The two quasi-elliptical cores with a major axis 2a ≈7.18 μm and a minor axis 2b ≈3.58 μm are embedded symmetrically in the annular cladding. They are labeled by core 1 and core 2. There is a thin cladding between the air and cores and its thinnest section () is about 1.85~2 μm. The refractive index difference between the cladding and cores is 0.0049.
Fig. 1 Cross-section of the two-core hollow eccentric fiber (TCHF). (a) Sample picture and (b) its schematic diagram.
3. Fabrication of TCHF-LPGs
Figure 2 shows the schematic of the grating fabrication. The single mode pigtail from Super-K supercontinuum laser (NKT Photonics) and one end of the TCHF are together butted by two multi-axis platforms, which are used to adjust two fibers position slightly in order to launch the light into one core of the TCHF. The two coaxially rotatable fiber clamps with a resolution of 2° support the TCHF at the focal plane of the high-frequency CO2 laser. The CO2 laser beam with a maximum average output power of 10 W is focused into a spot of ~50 μm diameter. The computer can command the scanning speed across the fiber and the energy density of the laser radiation. The optical spectrum analyzer (OSA) is applied to record the transmission spectra of the TCHF-LPG and the 5 g weight provides a constant tension during the LPG fabrication process.
Fig. 2 Schematic of the TCHF-LPG fabrication by a high-frequency CO2 laser. Insets: (a) conventional diagram of fiber grating, (b) observed lateral image of the TCHF, and (c) the exposure direction and the initial position of TCHF.
Before inscribing gratings, we should ensure that the plane including two cores is perpendicular to the focal plane of the CO2 laser. Meanwhile, the one core is as close to the focal plane of the laser as possible shown in Figs. 2(b) and 2(c). During fabricating the grating, the frequency, the scan speed and the average output power of the CO2 laser are 5 kHz, 5.41 mm/s and 0.2 W, respectively. The corresponding energy density of the CO2 laser is 0.741 J/mm2 and is particularly lower than that required during the fabrication of SMF-LPGs (~1.8 J/mm2). The low energy density is attributed to the thin annular cladding of the TCHF that leads to easy modulation of the refractive indices of the cores. Because of the weak energy of CO2 laser and the big air hole, the exposure operation on the upper core rarely affects the other core. Therefore, we can record the spectrum of this grating when one grating writing is completed, and then two rotatable fiber clamps are rotated 180° synchronously by controlling the stepping motors on the clamps. Afterwards, it is necessary to launch light into the other core by regulating the multi-axis platforms. Consequently, we can write the second grating according to the same procedure.
The transmission spectra of two gratings in a TCHF are shown in Fig. 3. Both of them have the same period of 405 μm and the same period number of 50. It is noted that the spectra of two LPGs are quite different. The most probable cause is a subtle difference between the two cores’ sizes due to the fabrication error during drawing the fiber process. The blue transmission curve (LPG1) has a resonant peak with its amplitude of ~25 dB and half bandwidth of ~7.15 nm at ~860.8nm, while the red one (LPG2) has a resonant peak with its amplitude of ~21 dB and half bandwidth of ~7.18 nm at ~864.8nm.
4. Coupling characteristics of the TCHF-LPG
The LPG, which is formed by periodic perturbation of the refractive index or geometry along a fiber, can couple a guided mode with a co-propagating cladding mode. The coupling characteristics of the TCHF-LPG can be studied theoretically. On the basis of the coupled mode theory (CMT), the transverse coupling coefficient between two modes is defined by
where is the perturbation of the permittivity induced by the exposure of CO2 laser, is angular frequency, and and stand for the transverse electric field components of the modes k and j. For a small index perturbation (), the permittivity perturbation can be approximated as, in which is the permittivity of vacuum. Then will be simplified asThe Finite Element Method (FEM, COMSOL4.3a) is used for calculating the electric field distributions (and ) and the propagation constants (and) of the fundamental and cladding modes. In consideration of a tiny difference of two core’s sizes, the size of core 2 is set to slightly larger than core 1 in the TCHF model (2a1 = 7.18 μm and 2b1 = 3.58 for core 1, while 2a2 = 7.186 μm and 2b2 = 3.584 μm for core 2). The effective index of the fundamental mode LP01 in core 2 is 0.000013 bigger than that of LP01 in core 1. The transverse coupling coefficient between LP01 and LP81 modes is much larger than that between LP01 and other modes at 860nm. Their effective refractive index difference () agrees well with the experimental result (). Actually, either of TCHF-LPGs has the only resonant peak in the wavelength range from 800 to 1000 nm in the experiment, therefore LP81 mode can be identified as the only cladding mode coupling with LP01 mode. The field distributions of LP01 and LP81 modes are shown in Fig. 4.
Fig. 4 Field distributions of LP01 modes in (a) core 1 and (b) core 2, and (c) LP81 mode. White arrows represent amplitudes of the electric field.
Then Eq. (2) can give the coupling coefficient () between LP01 and LP81 modes. Substituting, and into the coupled equations [28], we get
where,and are the forward wave amplitudes of LP01 mode in the core and LP81 mode in the cladding, respectively. Then using the boundary conditions and, and can be calculated. The transmission spectrum of the TCHF-LPG can be obtained by the formula . Figures 5(a) and 5(b) show the measured and calculated transmission spectra of the gratings in two cores for different effective index modulations. The resonance peaks become deeper with the increasing refractive index modulation. The calculated transmission spectra agree well with the experimental results. Therefore, it can be inferred that the refractive index modulation of the TCHF in the experiment is 9.5 × 10−5 approximately, which is much less than that of the SMF-LPGs (7.12 × 10−4) [29]. Because the only one cladding mode is considered to couple with the fundamental mode, the bandwidths of the calculated transmission spectra are narrower than that of the measured one for each grating in two cores.Fig. 5 Experimental and calculated transmission spectra of the gratings in core 1 (a) and core 2 (b) for different effective index modulations.
5. Sensing properties of the TCHF-LPGs
In order to understand the characteristics of the TCHF-LPGs, we studied their responses to bending, temperature and axial strain. As shown in Fig. 6, the resonant wavelengths shift linearly in bending directions of 0°, 90° and 180°. According to the data in [5], when the grating is bent in different directions, the difference between the effective refractive indices of the cladding and the core will increase or decrease, resulting in the resonant wavelength shift towards longer or shorter wavelengths. For the direction of 90°, both the LPGs in core 1 and core 2 drift hardly with relatively low sensitivities, because the LPGs bear a little squeeze and stretch in this direction and then the difference between the effective refractive indices of the cores and the cladding modes is hardly changed. However, for the direction of 0° (or 180°), in core 1 and core 2 the resonant wavelengths show distinct redshift and blueshift (or blueshift and redshift), respectively. Figure 6(b) shows the resonant wavelength shifts with changing curvature in the bending direction of 180°, where the LPG in core 1 is stretched and the resonant peak shifts towards shorter wavelength, while the LPG in core 2 is squeezed and the resonant peak shifts towards longer wavelength. As a consequence, the TCHF-LPGs can distinguish the directions of 0° and 180°. However, the bending response of the TCHF-LPGs has a maximum sensitivity of 0.63nm/m−1 and is much lower than that of SMF-LPGs (6.4 nm/m−1) [5], D-shaped fiber-LPG (12.55 nm/m−1) [10], and eccentric core fiber LPG (2.2 nm/m−1) [14]. The big air hole facilitates that the effective refractive indices difference between the core and the cladding modes suffers little fluctuation when TCHF-LPGs are bent, which leads to small bending sensitivity of TCHF-LPGs. The bending sensitivity of the TCHF-LPGs can be very small for the bending direction of 90°, and the TCHF-LPGs can be applied to bending resistance.
Fig. 6 (a) Measured resonant wavelength dependent on the curvature for the directions of 0°, 90°, 180°. (b) The transmission spectra in the bending direction of 180° for different curvatures.
Figure 7 reveals the responses of the TCHF-LPGs to the temperature in a range of 0~225 °С. Like others LPGs, the TCHF-LPGs show a linear redshift with a sensitivity of ~55 pm/°С, which is the same magnitude as the SMF-LPG [2]. In addition, the heating and cooling responses of the TCHF-LPG exhibit a good repeatability shown in Fig. 7, where the measured results of core 1 are only shown. Meanwhile, the resonant wavelengths of the TCHF-LPGs shift linearly but hardly with the increasing strain. Figures 8(a) and 8(b) shows the shifts of the resonant peaks of two gratings for the axial strain of 0 ~2140 με. The shifts of the resonant peaks of the TCHF-LPG are only about 0.2 nm (−0.091 pm/με) for core 1 and 0.18 nm (−0.074 pm/με) for core 2 in the strain range from 0 με to 2140 με. The strain sensitivity of the TCHF-LPGs is much lower than that of conventional SMF-LPGs (0.42 pm/με) [2] and PCF-LPGs (0.797 pm/με) [18]. The larger shape change of the fiber induced during the LPGs fabrication can cause a high strain sensitivity. For example, PCF-LPGs (5.6 pm/με) [17] and SMF-LPGs (102.89 pm/με) [30] with obvious periodic shape change have a high sensitivity. For TCHF-LPGs, the exposure energy density is much lower than that of other LPGs, whichcannot induce any shape change in the TCHF. On the other hand, the small strain sensitivity also originates from small waveguide dispersion [31] of the HEOF due to the big air hole. Therefore, the TCHEOF-LPFGs are almost completely immune to the axial strain and much more stable than the SMF-LPFGs.
Fig. 7 Temperature sensitivities for core 1 (red points for heating and blue points for cooling) and core 2 (green points for heating).
Fig. 8 (a) The shifts of two peaks of the TCHF-LPGs for different axial strains. (b) Measured resonant wavelength of the TCHF-LPGs with increasing the axial.
6. Conclusions
In conclusion, we proposed a novel TCHF-LPG and fabricated an LPG in each core by using the high frequency CO2 laser. To study its coupling characteristics, the transmission spectra of the TCHF-LPGs are simulated and the corresponding results show the resonant peaks occur owing to the coupling between the core mode (LP01) and the cladding mode (LP81). The simulation results agree well with the experimental results. In addition, we have investigated the responses of TCHF-LPGs to bending, temperature and axial strain. Because of the large air hole and thin cladding in the TCHF, the TCHF-LPGs are sensitive to the temperature (~55 pm/°С) while insensitive to the bending curvatures (~0.6 nm/m−1). In the meantime, the TCHF-LPGs are immune to the strain since the maximum shift of the resonant wavelengths is only ~0.2nm under the strain of 2140 με. Therefore, the TCHF-LPGs can be applied to sense the changing temperature and are independent of the strain. Furthermore, the signal cross talk in the TCHF can be prevented due to the two separated cores by the large air hole. The proposed TCHF-LPGs can be applied in the two-channel filters, which will be important in optical fiber communication systems.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. U1231201, 61275094, 61411130152 and 61405043, partly by the Natural Science Foundation of Heilongjiang Province in China under Grant Nos. LC201424 and A2015014, by the Special Foundation for Harbin Young Scientists under Grant No. 2013RFQXJ099, by Foundation for University Key Teacher by Heilongjiang province under Grant No. 1254G014, by the 111 project (B13015) to the Harbin Engineering University. T. T. Yuan and X. Zhong contributed equally to this work.
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