A large effective area multi-core fibre with an optimised cladding thickness

The cladding-thickness of trench-assisted multi-core fibres was investigated in terms of excess losses. The MCF with an effective area of 110 μm<sup>2</sup> at 1.55 μm and 181-μm cladding diameter was realised without any excess loss.


Introduction
A multi-core fiber (MCF) is expected to be a next generation transmission fiber that overcomes the capacity limit by space-division multiplexing technique. Many types of MCFs have been proposed [1][2][3][4][5]. Crosstalk between cores is a critical issue for MCF. Additionally, low attenuation and large effective area (A eff ) characteristics are also important for a transmission fiber to improve OSNR. A MCF with A eff of about 110 µm 2 at 1.55 µm has been reported [3]. However, the cladding diameter of the MCF was about 220 µm for suppressing a micro-bending loss. The large cladding diameter is undesirable in terms of a reliability issue and a high density core arrangement.
In this paper, we investigate cladding thickness effect on a micro-bending loss and an excess loss of outer cores to realize a large A eff and small-cladding MCF. The cladding thickness is determined in consideration of the micro-bending loss and the excess loss of outer cores. The micro-bending characteristic of MCFs is compared to that of single-core fibers (SCFs) for various cladding thicknesses. It is confirmed that the tolerance for the microbending loss of a multi-core fiber is larger than that of the single core fiber. The excess loss is estimated by the confinement loss of cores and experimentally confirmed. We clarify that the limit of the cladding thickness in the case of the large A eff MCF is about 40 µm. Our fabricated MCF with a trench index profile realizes A eff of more than 110 µm 2 , cladding diameter of 181-µm and crosstalk of lower than −30 dB at 100 km, simultaneously.

Fiber design
We employed a trench-assisted MCF (TA-MCF) design to realize a low crosstalk and dense core arrangement simultaneously. The trench-assisted fiber (TAF) can reduce not only a macro-bending loss [6] but also a micro-bending loss [7]. Figure 1 shows a cross section of a seven-core TA-MCF and an index profile of a core element. The TA-MCFs with A eff of 80 µm 2 have been reported [4]. We targeted the TA-MCF with A eff of about 110 µm 2 for long transmission lines. The fiber parameters were determined to achieve A eff of 110 µm 2 and crosstalk of lower than −30 dB at 100 km. An outer cladding thickness (OCT) affects microbending loss characteristics and excess loss of outer cores. We fabricated MCFs with OCTs of about 30 µm and 50 µm based on the following consideration on micro-bending loss and excess loss.  Figure 2 shows the measurement results of micro-bending loss of SCFs. Three types of fibers were prepared for the measurement. The coating thicknesses of the fibers were set to be same as the standard single-mode fiber. A Step80 is a conventional single-mode fiber with a step index profile and A eff at 1.55 µm of 80 µm 2 . A Step110 and a TAF110 realize A eff at 1.55 µm of 110 µm 2 with a step profile and a trench-assisted profile, respectively. The step110 is a conventional large A eff fiber. We fabricated the TAF110 to verify the micro-bending reduction due to a trench. The OCT of a SCF corresponds to half of a cladding diameter. The microbending loss is a loss increase at 1.625 µm when the fiber was wound on a bobbin whose surface is covered with a sand paper (grade 40 µm) based on the IEC standard [8]. The tension on the fiber during winding was 100 gf. The length of the fiber was 400 m.

Micro-bending loss
The micro-bending loss of Step80 was about 0.1dB/km. The micro-bending loss reduction thanks to a trench was clearly observed from the measurement data of Step110 and TAF110. The micro-bending loss of TAF110 with 50-µm OCT is the similar level with that of Step110 with 62.5-µm OCT.

Excess loss in outer cores
In the case of transmission fibers, the refractive index of the coating n co is larger than that of glass region of a fiber. The high index coating causes the excess loss in outer cores for small OCT [5]. To estimate the excess loss in outer cores is important in terms of homogeneous optical properties of all cores. The excess loss can be evaluated with the difference of confinement loss between cores. We simulate the confinement loss of a center core (CL c ) and an outer core (CL o ) with full vector finite element method [9] and define a simulated excess loss in outer cores (EL sim ) by the following equation. (1) Figure 3 shows simulation results of CL o and CL c as a function of OCTs. r 1 = 5.13 µm, r 2 = 11.10 µm, r 3 = 16.00 µm, Λ = 40.7 µm, ∆ 1 = 0.260%, ∆ 2 = 0.00%, ∆ 3 = −0.70% and n co = 1.486. The wavelength of the simulation was 1.625 µm. The simulated CL o was about sixdigit larger than the CL c for the simulated structure. Figure 4 shows EL sim as a function of OCT. The OCT dependence of EL sim was well fitted with an exponential function. The OCT should be larger than 38 µm to suppress EL sim less than 0.001 dB/km.

Characteristics of fabricated fibers
We fabricated three kinds of 7-core TA-MCF. Table 1 shows measurement results of fabricated fibers. Figure 5 shows a cross sectional view of a fabricated fiber (Fiber A). The OCTs of Fiber A, Fiber B and Fiber C were 31.6 µm, 33.6 µm and 47.7 µm, respectively. The coating thicknesses of the fabricated fibers were set to be same as the standard single-mode fiber. The outer-core crosstalk at 1.55 µm was measured on a fiber wound on a spool with a diameter of 210 mm according to the same measurement setup with Ref [1]. Figure 6(a) shows simulated cutoff wavelength as a function of core pitch Λ. The FEM [9] was used for the simulation. We selected Λ to be as small as possible while suppressing the lengthening of the cable cutoff wavelength [4]. Figure 6(b) shows 100-km crosstalk as a function of Λ. Three lines are the simulation results by the coupled power theory [10] for each fabricated MCF. Symbols indicate 100-km crosstalks that are estimated from the measured crosstalks on the fabricated fibers of a few km lengths by the coupled power theory. All the fibers have crosstalks of less than −30 dB at 100 km as designed.    Figure 7 shows measured micro-bending losses of the fabricated MCFs and SCFs. The microbending losses were measured at the condition as described in section 2.1. Open symbols were averaged micro-bending losses between outer cores and error bars denote maximum and minimum micro-bending losses of outer cores. The measured micro-bending losses of MCFs were smaller than those of SCFs with the same OCT and A eff . No significant loss increase was observed even at the OCT of about 30 µm. We think that large glass diameter and the twisting along the longitudinal direction of MCFs would play a role in the reduction of micro-bending losses with comparison to SCFs. The micro-bending losses of the fabricated MCFs were slightly larger than that of a standard single-mode fiber (Step80, cladding diameter = 125 µm) and were smaller than that of a commercially available large A eff fiber (Step110, cladding diameter = 125 µm). As the results, we can conclude that fabricated MCFs have enough performance for actual use in terms of micro-bending performance. The variations with micro-bending of crosstalk values were smaller than 2dB at the condition as described in section 2.1.

Excess loss in outer cores
where α outer is an attenuation of an outer core and α center is an attenuation of a center core. The dashed line is the approximated line of simulated results in Fig. 4. The solid line is an approximate line on the measured data with the same slope as the simulation line. Large excess loss was observed on outer cores of the MCFs with the OCT less than 35 µm and the trend of the measured excess loss well agreed with the simulation results. The reduction of OCT is probably limited around 40 µm in terms of the excess loss.

Core multiplicity factor
We introduce a core multiplicity factor (CMF) to compare the core density of MCFs. The CMF is given by where n is a number of core with A eff in a cladding and D is a cladding diameter. The CMF indicates the core area ratio in a cladding. Figure 9 shows the contour plot of relative CMF (RCMF) on a 7-core MCFs for various A eff and cladding diameter. The RCMF is ratio between CMF of a MCF and a standard single core single mode fiber with A eff = 80 µm 2 at 1.55 µm and cladding diameter = 125 µm. The RCMF of the MCF in [3,11] was about 3 because of the large cladding diameter. The RCMFs of Fiber A, Fiber B and Fiber C were 7.3, 6.7 and 4.7, respectively. Fiber A and Fiber B realize the RCMF larger than 6.5. However, the OCTs of the fibers are not applicable because the excess losses were observed on the fibers. The RCMF of a TA-MCF with A eff about 110 µm 2 and OCT of 40 µm will reach to six without any excess loss. The RCMF of six is two times larger than the previously reported large A eff MCF. Fig. 9. Contour plot of RCMF on a 7-core MCF for various Aeff and cladding diameter: Red symbols are measured data presented in this paper. Green symbols are previously reported data. Solid lines indicate counter lines of RCMF.

Conclusion
We investigated required cladding thickness of a MCF in terms of a micro-bending loss and an excess loss of outer cores theoretically and experimentally. No significant micro-bending loss increase was observed on MCFs with the cladding thickness of about 30 µm. The tolerance for the micro-bending loss of a MCF is larger than that of the SCF. However, the cladding thickness will be limited by the occurrence of the excess loss on outer cores. Our fabricated MCF realized a RCMF of 4.7 without any excess loss of outer cores. The RCMF of six, which is about two times larger than that of the previously reported large A eff MCF, will be attainable on a TA-MCF with an optimized cladding thickness.