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Abstract
Long-period fiber gratings (LPGs) have been demonstrated to be inscribed independently of each other into two separate cores of a twin-core fiber (TCF) by using point-by-point CO2 laser irradiation. The TCF is hydrogen-loaded to reduce the energy density of the CO2 laser required in the inscribing process of the grating, so that each core of TCF can be addressed individually. The field distributions and effective refractive indices of the core and cladding modes were calculated theoretically. The measured results coincide well with calculated results. An integrated TCF-LPG-assisting coupler is proposed and a peak coupling efficiency of 48% is achieved experimentally. The point-by-point core-independent inscription of LPGs in the TCF provides a flexible platform to fabricate integrated fiber devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Multicore fibers have received much attention in spatial division multiplexing (SDM), which can increase the capacity of optical fiber communication systems. The multicore fiber based devices that can achieve optical amplification, transverse coupling between cores and the connection between fibers are urgently needed. Some devices based on multicore fiber such as filters, sensors and fan-in/fan-out device have been demonstrated [1–3]. Long period fiber gratings (LPGs) have received much attention due to their high sensitivity, easy fabrication and integration. Several methods have been proposed to fabricate the LPGs, such as amplitude mask [4], femtosecond laser writing [5], point-by-point CO2 laser irradiation [6] and electric arc discharge [7]. The femtosecond laser can already inscribe parallel-integrated Bragg gratings in one core [8]. However among them point-by-point CO2 laser irradiation is popular and frequently used owing to its low cost and high efficiency [9]. Nowadays, LPGs have been demonstrated to be successfully inscribed into many kinds of optical fibers for sensing temperature, strain and refractive index, including single-mode fibers (SMFs), D-shaped cladding fibers [10,11], eccentric core fibers [12], and multicore fibers [13]. The most common fiber couplers are manufactured by the fusion and tapering technique [14–17]. Recently, a grating-assisting coupler has been demonstrated. K. S. Chiang et al analyzed the coupling characteristics between two parallel identical LPGs, two parallel non-uniform LPGs, and two long-period waveguide gratings (LPWGs) [18–21]. Y. Q. Liu et al have demonstrated experimentally the coupling phenomenon between two parallel LPGs written by CO2 laser irradiation in two adjacent SMFs and achieved a coupling efficiency of up to 86% by using a suitable surround refractive index and offset distance [5,22]. However, suitable surround refractive index and offset distance are difficult during actual device packaging. Recently, LPGs have also been fabricated in multicore fibers [13,23,24]. A. M. Rocha et al theoretically analyzed the power transfer in the multicore fiber with LPGs [13]. The LPG-assisted selective coupling between cores in a 4-core fiber has been demonstrated experimentally [23]. A LPG coupler in asymmetric nonlinear dual-core fiber has also been proposed [24]. However, LPGs in each core in a multicore fiber are simultaneously inscribed by CO2 laser and cannot be inscribed selectively as well due to large size and high energy density of CO2 laser spot.
In this work, the twin-core fiber (TCF) is hydrogen-loaded to reduce the energy density of the CO2 laser required in the fabrication process of the grating, so that each core of the TCF can be addressed individually. The point-by-point core-independent inscription of LPGs in the TCF provides a flexible platform to fabricate integrated fiber devices. A novel fiber coupler consisting of two LPGs in the TCF is experimentally demonstrated. Different from the two single fiber based-coupler, the TCF-LPG-assisting coupler couples light from the input core to the other core through the common cladding mode at specific wavelength instead of the evanescent-field coupling. Two cores of TCF in our experiment are symmetrically distributed in the cladding and the homogeneous cores can better satisfy the phase-matching condition. Due to ease packing, the proposed TCF couplers have a promising application in space division multiplexing (SDM) systems.
2. Twin-core optical fibers
Figure 1 shows the cross section of the TCF sample. Two cores with the identical diameter of 8.93 μm locate symmetrically with respect to the center of the cladding, which are defined as core 1 and core 2. The thickness of the isolation layer around the core is ~2.5 μm. The diameter of the fiber is 122.86 μm and the distance between two cores (so-called core spacing) is represented by d = 63.93 μm. The measured refractive index difference between the core and the cladding is 0.0053 by using a RI profiler (S14, Photon Kinetics, Inc.). The cutoff wavelength of the lowest high-order mode is about 1200 nm.
3. Fabrication of TCF-LPG
The schematic of the grating fabrication is shown in Fig. 2. The CO2 laser (CO2 -H10) is controlled by a computer and periodically modulates the refractive index of the cores of the TCF. The SMF pigtail of the supercontinuum light source (NKT Photonics) is aligned to one core of the TCF by a commercial fiber fusion splicer through the manual mode. The other end of the TCF is connected to the optical spectrum analyzer (OSA), which can real-time monitor the transmission spectrum. The TCF is supported by two coaxially rotatable fiber clamps and is placed on the focal plane of the CO2 laser. The beam waist of the CO2 laser in the focal plane is ~50 μm. A 5g weight provides a constant tension to keep the fiber straight during the LPG fabrication process. Before the fabrication of the grating, in order to reduce the energy density of the CO2 laser and more effectively excite cladding modes, the TCF was placed in a hydrogen clamber under the pressure of 10 MPa for approximately one week at room temperature. The orientation of the two cores is rather difficult to observe clearly using the microscope directly due to small refractive index difference between the core and the cladding. In our experiment, a few drops of pine oil were dripped upon the fiber to observe the TCF more clearly. For inscribing gratings on the two cores individually, the positions of the two cores were adjusted to the orientation as shown in Fig. 2(b) by simultaneously rotating two coaxially rotatable fiber clamps. The plane with the two cores is perpendicular to the focal plane of the laser and the upper core is as close as possible to the focal plane as shown in Fig. 2(c). Since the TCF is hydrogen-loaded, the required average energy density of the CO2 laser is only 1.11 J/mm2 that is lower than that of SMF-LPG (~1.88 J/mm2) [5]. Due to the low energy density, the exposure operation upon the upper core hardly affects the lower core since only 0.2 dB loss is introduced in the lower core. Therefore, we can individually inscribe the gratings with different parameters in two cores. The transmission spectrum is recorded once the grating written on one core is completed. Then two coaxially rotatable fiber clamps are rotated by 180° simultaneously and the light from the source is launched into the second core by adjusting the position of the TCF at the fusion splicer. The identical or different gratings can be inscribed upon the second core according to the same procedure again.
Fig. 2 (a) Schematic of the TCF-LPG fabrication. (b) Lateral image of the TCF and (c) the exposure direction and the orientation of two cores in the TCF.
The transmission spectra of two cores in the hydrogen loaded TCF are shown in Fig. 3(a), when the grating was written into the core 1. The period and period number of the grating are 560 μm and 50, respectively. The exposure direction of two cores is shown in the inset. The loss due to the grating writing is ~3 dB. The LPG 1 (blue line) has a resonant dip with an amplitude of 19.8 dB and half bandwidth of 15 nm at ~1540 nm, while the core 2 is not affected. After the fiber was rotated 180° and the core 2 was written, the transmission spectra are shown in Fig. 3(b). The two gratings have the same period and period number. The LPG 2 (red line) has a resonant dip with an amplitude of 13.2 dB and half bandwidth of 23 nm at ~1544 nm, while the spectrum of LPG 1 remains unchanged. Therefore, each core of TCF can be addressed individually. It is worth noting that there is a difference between the center wavelengths of resonant peaks of two LPGs, which can be attributed to the fact that the parameters of these two cores are not exactly identical during the fiber fabrication process and there is a little difference of refractive index modulation introduced by the power instability of CO2 laser. However, the resonance peaks of the two gratings can be identical by adjusting finely the period during grating writing process. The minimal distance between the cores for core-independent inscription depends on the energy density and beam waist of the laser. The minimal distance is ~50 μm for the energy density of 1.11 J/mm2. For comparison, the gratings are also written in the non-hydrogen loaded fiber in the same exposure direction. In order to obtain a grating with a deep resonant dip, the laser energy density of 1.84 J/mm2 is required, which is much larger than that of hydrogen-carrying fiber. The transmission spectra of two gratings for x-polarized light in non-hydrogen loaded fiber are shown in Fig. 3(c), in which only single inscription program was used. The loss of LPGs in the non-hydrogen loaded fiber is slightly larger than that in the hydrogen loaded fiber. Although the distance between the cores and the focal plane is different, two cores are simultaneously modulated due to the high laser energy density. Therefore, the grating cannot be written independently in two cores. The resonance peaks of two gratings are located at 1250 nm and 1260 nm, respectively. Obviously, the resonance peaks of LPGs in hydrogen loaded and non-hydrogen loaded TCFs are different and they are induced by the coupling between the fundamental mode and different order cladding modes. This phenomenon can be interpreted since the hydrogen-carrying optical fiber can excite effectively more cladding modes. The polarization characteristics of LPGs in the non-hydrogen loaded DCF were also measured as shown in Fig. 3(c). The measured results show that although the fiber is an asymmetric waveguide structure, LPGs only exhibit a weak polarization dependence.
Fig. 3 The transmission spectra of the LPGs in hydrogen loaded TCF (a)-(b) and the polarization dependence of the two LPGs in non-hydrogen loaded TCF (c).
4. The coupling between TCF-LPGs
Figure 4 illustrates the schematic of a TCF-LPGs-assisted coupler. The power transfer between two cores can be achieved by two identical parallel LPGs. The two LPGs are identical and satisfy the same phase matching condition, they share the common cladding mode. λ1 = (ncore1-nclad)Λ1 = λ2 = (ncore2-nclad)Λ2, λ denotes resonance wavelength, Λ is the period of the LPGs, ncore and nclad are the refractive indices of the core and cladding. When light is launched into core 1, LPG 1 couples the fundamental mode in core 1 to the co-propagating cladding mode at the resonance wavelength. The excited cladding mode is further coupled into the fundamental mode in core 2 by LPG 2. The center wavelengths of the resonance peaks of two gratings in non-hydrogen loaded TCF are distinctly different, thus two LPGs in Fig. 3(c) cannot satisfy the same phase matching condition. However, two gratings can be independently written in hydrogen loaded TCF, so they can satisfy the same phase matching condition to realize grating-assisted coupler. The output optical spectra are shown in Fig. 5(a) as the light was launched into the core 1. Core 1 (blue line) and core 2 (red line) represent band-rejection and band-pass characteristics, respectively. The maximum coupling efficiency is −3.3 dB (48%) at 1540 μm. In contrast, when core 2 is used as the input core, core 2 has band-rejection characteristic and core 1 has the band-pass characteristic as shown in Fig. 5(b). The maximum coupling efficiency is −6.7 dB. The different coupling efficiency of the transmission band in both cases can be attributed to different attenuation dips (19.8 dB and 13.2 dB), and more energy is coupled into the cladding from the core with LPG 1. In theory, the transmission spectrum of the output core should be complementary to that of the input core, i.e., the attenuation band of the input core corresponds to the transmission band of the output core.
Fig. 5 The transmission spectra of the two cores when light was launched into core 1 (a) and core 2 (b).
5. Theoretical analysis of coupling characteristic of TCF-LPGs
The coupling characteristics of TCF-LPGs can be analyzed theoretically based on the coupled mode theory (CMT). Around the resonant wavelength, LPG 1 couples the power of the fundamental mode in core 1 to the cladding mode, and then the excited cladding mode is coupled to the fundamental mode in core 2 by LPG 2. Here, the electric field distributions and effective refractive indices of the modes in the TCF are analyzed by using the finite element method (COMSOL Multiphysics 5.2a). In simulation, the diameters of the two cores and the cladding are 9 μm and 122 μm, respectively, the distance between two cores is 64 μm, and the refractive index difference between the core and the cladding is 0.0053. According to the CMT, the transverse coupling coefficient between the k- and j-order modes is given by
where ω is angular frequency, ekt and ejt represent the transverse field components of the k- and j- order modes, respectively. Δε is the change of permittivity, which can be approximated as Δε~2ε0n × Δn because of weak index perturbation, ε0 is the permittivity of vacuum. Sowill be further simplified asBased on Eq. (2), the coupling efficiencies between the fundamental mode and various order cladding modes can be calculated. The calculated results indicate that the coupling efficiency between the fundamental mode LP01 and the cladding mode LP11 is the maximum at the 1540 nm and their field distributions are shown in Fig. 6. The effective refractive index difference between LP01 and the LP11 modes is 0.0027, which coincides well with measured result (1.540/560 = 0.00275).The coupling equations between the fundamental mode and various order cladding modes in the co-propagating direction in TCF-LPGs can be expressed as
where Aco and Acl represent the amplitudes of the fundamental and cladding modes. δcl-co = , βco and βcl are propagation constants of the fundamental and cladding modes, . Using the boundary condition Aco(z = 0) = 1 and Acl(z = 0) = 0, Aco and Acl can be calculated based on Eqs. (3) and (4). The transmission spectrum of the LPG in core 1 can be expressed asThe calculated transmission spectrum of core 1 is shown in Fig. 7, where the index perturbation is 5 × 10−4. The resonance wavelength of core 1 is basically consistent with the measured result. In simulation, only the coupling between the fundamental mode and a cladding mode is considered, therefore the bandwidth of the transmission spectra is narrower than the measured result. The coupling between two gratings can be calculated by the formula , in which it is assumed that the power in the cladding is fully coupled into the fundamental mode of core 2. In theory, the transmission spectra of core 1 and core 2 are completely complementary to each other at 1550 nm and the coupling efficiency reaches 100% as shown in Fig. 7. Therefore, a complete power transfer in a grating-assisted TCF coupler can be achieved. The measured coupling efficiency only reaches 48%, which results from incomplete excitation of the cladding mode, incomplete coupling between the cladding mode and fundamental mode in core 2 and the loss of the cladding mode as well.
Fig. 7 Calculated the transmission spectra of the input core (core 1) and the coupling core (core 2).
6. Conclusion
In conclusion, two identical LPGs are inscribed successfully into each core of a TCF by using point-by-point CO2 laser irradiation technique. To ensure that each core can be addressed individually, the TCF needs to be hydrogen-loaded. The grating-assisted coupler in hydrogen-loaded TCF is demonstrated with 48% coupling efficiency. The coupling characteristics between two cores of TCF-LPGs are theoretically analyzed, and the measured results coincide well with the calculated results. In our experiment, the two gratings are in the same longitudinal position and there is no offset distance between them, leading to the incomplete coupling of the power from one core to other core. The suitable offset distance between the two gratings in the TCF will can further improve the coupling efficiency. The point-by-point core-independent inscription of LPGs in the TCF provides a flexible platform to fabricate integrated fiber devices. The proposed TCF-LPG coupler is compact and easy to package, and has a great potential to be used as an add-drop filter and optical multiplexer in DWDM systems.
Funding
National Natural Science Foundation of China (NSFC) (61675054, 91750107 and 61875044); Natural Science Foundation of Heilongjiang Province in China (ZD2018015); 111 project to the Harbin Engineering University (B13015).
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