Characteristics of few-mode multi-core fiber (FM-MCF) were numerically analyzed and experimentally confirmed. The cores of FM-MCF were designed to support transmission of LP01 and LP11 modes from the point of bending loss of LP11 and LP21 modes. Inter-core crosstalk between LP11 mode was calculated to determine core pitch of fibers. It was confirmed that the fabricated fibers was two-mode transmission over C-band and L-band with the effective area of LP01 mode of about 110 μm2 at 1550 nm. The crosstalk of the fibers was estimated to be smaller than −30 dB at 1550 nm after 100-km propagation. The crosstalk dependence on wavelength was also measured and matched well with the simulated results.
©2012 Optical Society of America
Space division multiplexing (SDM) is expected as a new advanced technology that overcomes the capacity limit of the current optical communication systems . 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 (Aeff) , 19-core fiber with small Aeff , and five-mode fiber  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 LP01 and LP11 modes over C-band and L-band. The fabricated fibers based on simulations realized the Aeff of LP01 mode which is about 110 μm2 at 1550 nm, propagation of both LP01 and LP11 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.
2. FM-MCF design for two-mode transmission
It is effective to enlarge Aeff in order to suppress the non-linearity. Figure 1 shows the calculated results of Aeff of LP01 and LP11 modes at 1550 nm as functions of relative refractive index difference Δ and core radius a . The full-vector finite-element method was used for the calculation . The lower side of a black line is where the bending loss of LP21 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 LP11 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 LP01 and LP11 modes over C-band and L-band and realize the Aeff of both modes which is larger than 100 μm2 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 LP11-LP11 inter-core crosstalk (XT11-11) and LP01-LP11 inter-core crosstalk (XT01-11) in addition to LP01-LP01 inter-core crosstalk (XT01-01) 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% . The core supports two-mode propagation as shown in Fig. 1. The 1550-nm Aeff of LP01 and LP11 modes would be 110 μm2 and 170 μm2, respectively. The XT11-11 and the XT01-11 depend on the angle of LP11 mode of adjacent cores because LP11 mode is composed from two spatial degenerated modes and shows asymmetry field distribution. We define LP11 mode related crosstalk such as XT11-11 as the worst crosstalk over various angles. A red line, a green line and a blue line indicate XT01-01, XT01-11 and XT11-11, respectively. The worst is XT11-11, because the power of LP11 mode distributes more extensively than that of LP01 mode. We can realize 100-km XT11-11 smaller than −30 dB for a core pitch of larger than 52 μm.
3. 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 XT11-11 at 1550 nm to be smaller than −30 dB. And the core pitch of Fiber B was scaled to be 44 μm for XT11-11 at 1550 nm to be about −10 dB. Fiber A, Fiber B and Fiber C had almost the same profile. Aeff of Fiber C was designed to be about 120 μm2. Figure 3 shows a cross sectional view of Fiber A. Table 1 and Table 2 summarize the structural parameters and optical properties of LP01 mode of fabricated fibers, respectively. The core pitch of fabricated Fiber A and Fiber B, and Aeff 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 LP11 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 LP01 mode. Those results shows both LP11 and LP01 modes are propagated at 1550 nm. We also measured cable cutoff wavelength of LP11 mode and next higher order LP21 mode. The definition of cable cutoff wavelength of LP11 mode was applied to that of LP21 mode. The cutoff wavelength of LP21 mode was smaller than 1530 nm and that of LP11 mode was larger than 2000 nm. Those results indicate that Fiber A, Fiber B and Fiber C realized LP01 and LP11 mode operation over C-band and L-band as we had designed. The differential mode group delay (DMGD) between LP01 mode and LP11 mode, which was measured with OFDR , was about 3000 ps/km. Intra-core mode coupling between LP01 and LP11 modes will be fully suppressed.
4. Measurement of inter-core crosstalk
4.1 Measuring higher mode crosstalk
Figure 5 shows a setup for XT11-11 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 LP01 mode and LP11 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 XT11-11. At first, we measure Pj which is an output power of an offset excited core (core j) without bend as shown in Fig. 6(a). The Pj is the sum of the power of LP01 and LP11 modes: Pj = Pj-LP01 + Pj-LP11. Then, Pj’ is measured with bends of 20 turns whose diameter was 10 mm to eliminate LP11 mode as shown in Fig. 6(b): Pj’ = Pj-LP01. The difference of the power (Pj –Pj’) indicates Pj-LP11. Finally, the output power of core k Pk, which core is not the excited core, is measured without bend condition as shown in Fig. 6(c). The most of Pk is comprised of the power of LP11 mode because the crosstalk between few-mode cores is dominated by LP11-LP11 crosstalk as shown in Fig. 2: Pk = Pk-LP11. Accordingly, we obtain:
4.2 Results of measured crosstalk and comparison with simulated results
Figure 7 shows results of measured XT11-11 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  and simulated XT11-11 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 LP11 mode between adjacent cores gets to be maximum. The second is these simulations did not take into account of crosstalk dependence on bending diameter . 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 C-band and L-band as we had expected.
4.3 Wavelength dependence of crosstalk
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 XT11-11 and XT01-01 as a function of wavelength. Simulated inter-core crosstalk is dominated by XT11-11 over the wavelength from LP21 cutoff wavelength of about 1530 nm to LP11 cutoff wavelength of about 2000 nm because XT11-11 is much larger than XT01-01 by 40 dB. In this area, the measured wavelength dependence of crosstalk matched with the simulated wavelength dependence of XT11-11. The measured crosstalk gradually converged to the simulated XT01-01 over the wavelength longer than LP11 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 LP21 mode. The results indicate that FM-MCF should be designed with the careful consideration of crosstalk of higher-modes.
We have designed and fabricated few-mode multi-core fibers which support both LP01 and LP11 modes over C-band and L-band. The fibers had the Aeff of LP01 mode of about 110 μm2 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.
This work was partially supported by National Institute of Information and Communication Technology (NICT), Japan under “Research on Innovative Optical fiber Technology”.
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