Large-effective-area uncoupled few-mode multi-core fiber

Characteristics of few-mode multi-core fiber (FM-MCF) were numerically analyzed and experimentally confirmed. Fabricated fibers supported two-mode transmission over C-band and L-band with the effective area of about 110 μm2 at 1550 nm. The crosstalks of the fibers were estimated to be smaller than -30 dB at 1550 nm after 100-km propagation.


Introduction
Space division multiplexing (SDM) is expected as a new advanced technology that overcomes the capacity limit of the current optical communication systems [1]. The SDM is realized by multi-core fiber (MCF) and few-mode fiber (FMF). To improve space multiplicity, 10-core fiber with large effective area (A eff ) [2], 19-core fiber with small A eff [3], and five-mode fiber [4] have been proposed. However, there are limits in improvement of spacial multiplicity only by using those teqnichues each other from the perspective of inter-core crosstalk or inter-mode crosstalk. The combination of MCF and FMF will improve the multiplicity furthermore.
In this paper, we present the characteristics of few-mode multi-core fiber (FM-MCF) that suports LP 01 and LP 11 modes over C-band and L-band. The fabricated fibers based on simulations realized the A eff of LP 01 mode which is about 110 μm 2 at 1550 nm, propagation of both LP 01 and LP 11 modes over the bands, and 100-km inter-core crosstalk of smaller than −30 dB at 1550 nm. Finally the crosstalk dependence on wavelength was measured and compared with simulated results.

FM-MCF design for two-mode transmission
It is effective to enlarge A eff in order to suppress the non-linearity. Figure 1 shows the calculated results of A eff of LP 01 and LP 11 modes at 1550 nm as functions of relative refractive index difference Δ and core radius a [5]. The full-vector finite-element method was used for the calculation [6]. The lower side of a black line is where the bending loss of LP 21 mode is larger than 1 dB/m at 1530 nm and a bending radius of 140 mm. The upper side of a white line is where the bending loss of LP 11 mode is smaller than 0.5 dB/100 turn at 1625 nm and a bending radius of 30 mm. The areas which satisfy both conditions support LP 01 and LP 11 modes over C-band and L-band and realize the A eff of both modes which is larger than 100 μm 2 at 1550 nm.
The small inter-core crosstalk of MCFs is preferable to reduce the load of signal processing. In the case of FM-MCF, we should concern crosstalk related to higher order mode such as LP 11 -LP 11 inter-core crosstalk  ) and LP 01 -LP 11 inter-core crosstalk (XT 01-11 ) in addition to LP 01 -LP 01 inter-core crosstalk (XT 01-01 ) that is only crosstalk for a single-mode MCF. Figure 2 shows the simulated 100-km inter-core crosstalk at 1550 nm among modes as a function of core pitch, assuming a = 6.47 μm and Δ = 0.45% [5]. The core supports twomode propagation as shown in Fig. 1. The 1550-nm A eff of LP 01 and LP 11 modes would be 110 μm 2 and 170 μm 2 , respectively. The XT 11-11 and the XT 01-11 depend on the angle of LP 11 mode of adjacent cores because LP 11 mode is composed from two spatial degenerated modes and shows asymmetry field distribution. We define LP 11 mode related crosstalk such as XT XT . Simulated inter-core 100-km crosstalk as a function of core pitch assuming a = 6.47 μm and Δ = 0.45%.

Fabricated fiber
We have fabricated three kinds of four-core FM-MCF (Fiber A, B and C) with stack and draw method. The core pitch of Fiber A was scaled to be 52 μm for XT 11-11 at 1550 nm to be smaller than −30 dB. And the core pitch of Fiber B was scaled to be 44 μm for XT 11-11 at 1550 nm to be about −10 dB. Fiber A, Fiber B and Fiber C had almost the same profile. A eff of Fiber C was designed to be about 120 μm 2 . Figure 3 shows a cross sectional view of Fiber A. Table 1 and Table 2 summarize the structural parameters and optical properties of LP 01 mode of fabricated fibers, respectively. The core pitch of fabricated Fiber A and Fiber B, and A eff of Fiber C were as we had designed. The near field pattern (NFP) was measured to confirm two mode transmissions directly. Figure 4(a) is the NFP of Fiber B at 1550 nm, which shows the propagating mode was mainly LP 11 mode. By adding bends of 20 turns whose diameter was 10 mm, the NFP has changed to Fig. 4(b), which shows the propagating mode was mainly LP 01 mode. Those results shows both LP 11 and LP 01 modes are propagated at 1550 nm. We also measured cable cutoff wavelength of LP 11 mode and next higher order LP 21 mode. The definition of cable cutoff wavelength of LP 11 mode was applied to that of LP 21 mode. The cutoff wavelength of LP 21 mode was smaller than 1530 nm and that of LP 11 mode was larger than 2000 nm. Those results indicate that Fiber A, Fiber B and Fiber C realized LP 01 and LP 11 mode operation over C-band and L-band as we had designed. The differential mode group delay (DMGD) between LP 01 mode and LP 11 mode, which was measured with OFDR [7], was about 3000 ps/km. Intra-core mode coupling between LP 01 and LP 11 modes will be fully suppressed.   Figure 5 shows a setup for XT 11-11 measurement. We reconsidered the measurement system which we use to measure crosstalk in the case of single mode MCF. A single-mode fiber (SMF) connected to light source was offset spliced to a core of a FM-MCF to excite both LP 01 mode and LP 11 mode. Output power from cores on another end face was measured with a two-mode fiber (TMF) which has almost the same profile as the FM-MCF.  Figure 6 explains the measurement procedure of XT 11-11 . At first, we measure P j which is an output power of an offset excited core (core j) without bend as shown in Fig. 6(a). The P j is the sum of the power of LP 01 and LP 11 modes: P j = P j-LP01 + P j-LP11 . Then, P j ' is measured with bends of 20 turns whose diameter was 10 mm to eliminate LP 11 mode as shown in Fig.  6(b): P j ' = P j-LP01 . The difference of the power (P j -P j ') indicates P j-LP11 . Finally, the output power of core k P k , which core is not the excited core, is measured without bend condition as shown in Fig. 6(c). The most of P k is comprised of the power of LP 11 mode because the crosstalk between few-mode cores is dominated by LP 11 -LP 11 crosstalk as shown in Fig. 2: P k = P k-LP11 . Accordingly, we obtain:  Figure 7 shows results of measured XT 11-11 of Fiber A, Fiber B and Fiber C, respectively. The lengths of Fiber A, Fiber B and Fiber C were 3709 m, 2730 m and 4403 m, respectively. The fibers were wound on spools with a diameter of 210 mm. The horizontal axis denotes the excited core number and the graph legends denote the measured core number as shown in Fig.  3. The left side is measured crosstalk at 1550 nm and the right side is at 1625 nm. In the case of Fiber A, the crosstalk of the cores that located at the diagonal positions from the excited cores were about −80 dB, which were the lower limit of the measurement setup. On the other hand, in the case of Fiber B and Fiber C, crosstalk was detected even for the diagonal cores. The direct crosstalk between the diagonal cores is estimated to be very small compared to the measured crosstalk because of the large diagonal core pitch of 62 μm. The measured crosstalk of the diagonal cores may originate from the repeat of the crosstalk between adjacent cores. Figure 8 shows the 100-km inter-core crosstalk estimated from the measured crosstalk with the coupled-power theory [8] and simulated XT 11-11 for comparison as a function of core pitch. Lines are simulated results. Deep blue and red lines correspond to Fiber A and Fiber B. The pale blue and red lines correspond to Fiber C. The parameters used in the simulations are also shown. The symbols indicate the averaged crosstalk and the error bars indicate the maximum and the minimum values. The blue ones are at 1550 nm and red ones are at 1625 nm. In the case of Fiber B and Fiber C, estimations match well with simulated results. In the case of Fiber A, there were discrepancies between estimations and simulated results. We think there are two reasons. The first is the simulations were based on the worst case where the overlap of fields of LP 11 mode between adjacent cores gets to be maximum. The second is these simulations did not take into account of crosstalk dependence on bending diameter [9]. Although, the averaged 100-km crosstalk of Fiber A was −42 dB at 1550 nm and −32 dB at 1625 nm, which means Fiber A realized 100-km crosstalk of smaller than −30 dB over Cband and L-band as we had expected.   Figure 9(a) and 9(b) shows the wavelength dependence of crosstalk from core 1 to core 2 and core 1 to core 4 of Fiber B. We measured the wavelength dependence, which is denoted as a black line in Fig. 9, by using supercontinuum wideband light source and spectrum analyzer as shown in Fig. 10. The fiber length was 22 m and a bending diameter was 280 mm. In Fig. 9, solid symbols indicate the estimated 22-m crosstalk from measured crosstalk, which is already shown in Fig. 7(b), with the conventional measurement setup shown in Fig. 5. A blue line and a red line indicate simulated results of XT 11-11 and XT 01-01 as a function of wavelength. Simulated inter-core crosstalk is dominated by XT 11-11 over the wavelength from LP 21 cutoff wavelength of about 1530 nm to LP 11 cutoff wavelength of about 2000 nm because XT 11-11 is much larger than XT 01-01 by 40 dB. In this area, the measured wavelength dependence of crosstalk matched with the simulated wavelength dependence of XT 11-11 . The measured crosstalk gradually converged to the simulated XT 01-01 over the wavelength longer than LP 11 cutoff wavelength of about 2000 nm. The change of the measured crosstalk around 1400 nm originates from the crosstalk that relates to the next higher modes such as LP 21 mode. The results indicate that FM-MCF should be designed with the careful consideration of crosstalk of higher-modes. Simulation of XT  (b) Fig. 9. Wavelength dependence of inter-core crosstalk (a) from core 1 to core 2 and (b) from core 1 to core 4.

Conclusion
We have designed and fabricated few-mode multi-core fibers which support both LP 01 and LP 11 modes over C-band and L-band. The fibers had the A eff of LP 01 mode of about 110 μm 2 at 1550 nm. Inter-core crosstalk characteristics of the fibers were numerically analyzed. Large-effective-area uncoupled few-mode multi-core fiber whose inter-core 100-km crosstalk is smaller than −30 dB at 1550 nm was realized.