We designed and fabricated a low-crosstalk seven-core fiber with transmission losses of 0.17 dB/km or lower, effective areas larger than 120 μm2, and a total mean crosstalk to the center core of –53 dB after 6.99-km propagation (equivalent to −42.5 dB after 80 km), at 1550 nm. We also investigated the signal-to-noise ratio (SNR) achievable in uncoupled multi-core transmission systems by regarding the crosstalk as a virtual additive white Gaussian noise. The SNR under existence of crosstalk in the fabricated multi-core fiber (MCF) was estimated to be 2.4 dB higher than that in a standard single-mode fiber (SSMF) in the case of 80-km span, and 2.9 dB higher in the case of 100-km span; which are the best values among MCFs ever reported, to the best of our knowledge. The SNR penalties from crosstalk in this MCF were calculated to be 0.4 dB for 80-km span and 0.2 dB for 100-km span. We also investigated SNR penalty from crosstalk in the more ordinary case of an MCF with SSMF cores, and found that the total mean crosstalk to the worst core after one 80-km span should be less than about −47 dB for 0.1-dB penalty, about −40 dB for 0.5-dB penalty, and about −36 dB for 1-dB penalty.
©2012 Optical Society of America
Spatial division multiplexing using a multi-core fiber (MCF) is a strong candidate technology to overcome the capacity limit of single-core fiber transmission systems . Inter-core crosstalk (XT) is one of the most important properties of uncoupled MCFs, and the suppression of the XT has been actively studied [2–5]. As a high-capacity and long-distance transmission medium, transmission loss and effective area (Aeff) are also important optical properties for improving signal-to-noise ratio (SNR) in each core . However, no reported MCFs have realized low loss and large Aeff simultaneously superior to standard single-mode fiber (SSMF) [5,7–11]. Furthermore, the effect of the XT on the SNR has not been investigated well; therefore, it has been unclear whether enlarging of Aeff is effective to improving the SNR or not.
In this paper, we report the design and fabrication of a seven-core MCF that achieves low loss and large Aeff simultaneously. The transmission loss of the fabricated MCF was observed to be 0.163–0.172 dB/km (average: 0.168 dB/km), which is the lowest among MCFs to the best of our knowledge. In addition, we discuss how this result enhances the SNR in uncoupled multi-core transmission systems, which is an expansion of .
2. Fiber design
We designed an uncoupled seven-core MCF that has identical and hexagonally-arranged pure-silica cores. A trench-assisted core design was employed to confine the power strongly into the core for achieving both large Aeff and low XT. Figure 1 shows the designed relative refractive index difference (Δ) profile of the core. The core was designed to have Aeff of ~130 µm2, cable cutoff wavelength (λcc) of 1460 nm, and the Rayleigh scattering coefficient lower than that of the MCF in . As for the design of the XT, the statistical mean of the XT (mean XT, µXT) between two adjacent cores of a homogeneous MCF can be expressed as :Eq. (1), Λ of the MCF was designed to be 52 μm so that µXT from six outer cores to the center core (center-core µXT ( = 6ηL)) can be less than −30 dB after 80-km propagation at 1625 nm when the MCF are wound on a 140-mm-radius bobbin. The cladding diameter was designed to be 187.5 μm so that excess loss of the outer cores (loss induced by coupling to coating modes) can be lower than 0.001 dB/km at 1625 nm.
We should pay attention to the XT of uncoupled MCF also for lowering loss. The power coupling from Core n to other cores can be understood as power loss of Core n due to the XT:Fig. 2 . To suppress αXT,dB lower than 0.001 dB/km, 6η should be less than 2.30 × 10−4 /km (corresponding to the center-core µXT less than −17.3 dB at L = 80 km) so that the XT target was appropriate in terms of loss.
We fabricated a pure-silica-core homogeneous seven-core fiber based on the design. Figure 3 shows a cross-section of the fabricated MCF. The core pitch was 51 μm. The cladding diameter was 188 μm. The coating diameter was 334 μm. The fiber length was 6.99 km. Figure 4 and Table 1 show transmission loss spectra and optical properties of the MCF. The transmission losses of the individual cores were observed to be very low values of 0.163–0.172 dB/km (average: 0.168 dB/km), thanks to the low-loss design and pure-silica core technology. Aeffs of the cores were slightly smaller than the design target but all of the Aeffs exceeded 120 μm2. The λccs were 1460 ± 10 nm and successfully fabricated as designed. The chromatic dispersions (D) were 21.7 ps/(nm∙km). The bending losses were also well suppressed.
Figure 5 shows the µXTs between adjacent two cores of the MCF, which were measured as wavelength averages of the XTs by using the wavelength scanning technique described in . Values of averages, maximums, and minimums of the µXTs between the adjacent two cores, and of total µXTs to the center core are shown in Table 2 . The measured MCF was 6.99 km long and wound on a 140-mm-radius bobbin. The center-core µXTs for L = 80 km are also shown in Table 2, which were calculated based on the linear accumulation of the XT. The center-core µXTs can be less than −30 dB for L shorter than 1.4 × 103 km at 1550 nm, 8.7 × 102 km at 1565 nm, and 2.0 × 102 km at 1625 nm.
4.1. Effects of fiber parameters, system parameters, and XT on SNR
To realize high-capacity and long-distance transmission, SNRs in MCF cores is an important factor as with single-core fibers. However, a proper suppression level of XT, where the lowering loss and/or enlarging Aeff can be effective, has not been investigated yet. So, in this section, we will discuss the effects of system parameters and fiber parameters including the XT on SNRs in uncoupled MCF systems, and investigate how the SNR can be improved in the MCF systems.
When assuming an ideal filtering (a noise bandwidth is equivalent to a signal bandwidth) and Nyquist limit of WDM, SNR of dispersion-uncompensated single-core (SC) transmission link can be expressed as :
Based on the characteristics of XT in MCF shown in , XT in MCFs may be regarded as a virtual additive white Gaussian noise by assuming adequately broad bandwidth of signal light. Thus, SNR in a certain core in dispersion-uncompensated multi-core (MC) transmission link with uncoupled MCF can be simply expressed asEq. (8), PTx,chs equivalent between all cores and losses equivalent between all cores are assumed. “−PXT” in the numerator represents the XT from the certain core to other cores, and “+PXT” in the denominator represents the XT from other cores to the certain core. However, “−PXT” is negligible in the case of low XT (PTx,ch >> PXT). Depending on system capability, PXT may have some different definitions. If skew between cores is small and thus pulse broadening due to multipath interference (MPI) can be mitigated by digital signal processing, PXT can simply be the power of light that is input to all cores except the certain core and output from the certain core. If the skew is very large and thus the MPI cannot be mitigated, PXT can be the power of light that is input to all cores, coupled between cores, and output from the certain core. But in either case, if the XT is adequately low (i.e., μXT < ~0.01), PXT can be related to PTx,ch by μXT as
Figures of merit of fibers can be evaluated by comparing maximal SNRs achievable in the same system using the different fibers. In both of the SC and MC cases, SNRs are maximized at PTx,ch = [PASE/(2aNLI)]1/3. Therefore, the maximal SNR (SNRSC,max) achievable in a SC system can be derived asEqs. (14) and (15), a difference (ΔSNRSC) between SNRSC,max,dB between different fibers can be expressed only with the fiber parameters and Ls.Eq. (16), a difference (ΔSNRMC) of SNRMC,max in [dB] between different fibers cannot be expressed only with the fiber parameters and Ls. Only Ns can be cancelled out in ΔSNRMC and other system parameters (Csystem) cannot be cancelled out. However, in both SC and MC cases, we can obtain ΔSNR independent of Ns, and SNR penalty due to XT independent of Ns:
4.2. Comparison of SNRs between SSMF, reported MCFs, and the fabricated MCF
Based on the above consideration, we can evaluate the effects of the fiber parameters (including the XT) on SNR. Figure 6 shows how the SNRSC,max and the worst-core µXT after one span affect SNR penalty due to XT and ΔSNRMC in cases of Ls = 80 km and Ls = 100 km. In Fig. 6, the SNRSC,maxs and the µXTs of the various reported MCFs and the fabricated MCF—their characteristics are listed in Table 3 — are plotted as red diamonds, and the SNRSC,max of SSMF are plotted as dashed lines. The SNRSC,maxs were calculated using Eq. (14) in case of BWDM = 10 THz and FdB = 4 dB. The SNR penalty due to XT was calculated using Eqs. (14) and (17), and shown as blue dot-dashed isolines. As shown in the graphs, SNRSC,maxs—that is, SNR without XT— of many of the reported MCFs were calculated to be improved from that of the SSMF. However, SNR in uncoupled MCFs can be degraded by XT as is shown in the blue dot-dashed lines. In order to preserve the ΔSNRMC unaffected by XT, µXT per Ls of the MCF have to be suppressed adequately lower than ASE and NLI noises per Ls. Based on the SNRSC,max and the SNR penalty, or on Eq. (16), ΔSNRMC from the SSMF can be obtained and are plotted as solid curves. The XT of the fabricated MCF was well suppressed, and ΔSNRMC of the MCF can be achieved to be 2.4 dB for Ls = 80 km and 2.9 dB for Ls = 100 km compared to the SSMF, which are the highest in reported MCFs, to the best of our knowledge. The SNR penalties due to XT were calculated to be 0.4 dB for Ls = 80 km and 0.2 dB for Ls = 100 km.
The appropriate suppression level of the XT may also depend on the system parameters. Figure 7 shows the relationships between the worst-core µXT after one span and the SNR penalty due to XT in an MCF with SSMF core (ΔSNRSC = 0 dB), for combinations of system parameters of FdB = 3, 4, 5, 6 dB and BWDM = 5, 10 THz, in the case of Ls = 80 km, which is more severe than Ls = 100 km. In these traces, the case of FdB = 3 dB and BWDM = 5 THz is the most severe for the SNR penalty suppression, since the ASE and NLI noises are the lowest. In the most severe case, the worst-core µXT should be less than −46.8 dB after one 80-km span for suppressing the SNR penalty less than 0.1 dB, −39.6 dB for 0.5-dB penalty, and −36.3 dB for 1-dB penalty. Based on Eq. (17), the SNR penalty can be constant if an increase in an SNRSC,max is cancelled by a decrease in XT. Accordingly, horizontal offsets of the curves in Fig. 7 are equivalent to the difference in the SNRSC,max between the cases, which can be induced by the SNR improvement from the system parameters or fiber parameters. For example, in the case of the fabricated MCF, since the SNRSC,max for Ls = 80 km was increased by 2.8 dB from the SSMF (ΔSNRSC = 2.8 dB), we need to suppress the worst-core µXT 2.8 dB further from the above values.
We designed and fabricated an MCF simultaneously achieving transmission losses of 0.17 dB/km or lower, effective areas larger than 120 μm2, and a total mean crosstalk to the center core equivalent to −42.5 dB after 80 km, at 1550 nm. We investigated SNR in uncoupled MCF (under existence of crosstalk), and found that the SNR in the fabricated MCF can be estimated to be improved more than 2 dB from SSMF even under the existence of crosstalk. Based on the investigation, the total mean crosstalk to worst core of an MCF should be less than about −47 dB after 80 km for SNR penalty due to crosstalk less than 0.1 dB, about −40 dB for 0.5-dB penalty, and about −36 dB for 1-dB penalty, even in the case of an MCF with SSMF cores.
Further SNR enhancement in each core of the MCF can be realized by improving transmission loss and by finding a good balance between large effective area and low crosstalk, so that the SNR under crosstalk can be maximized.
This research is supported by the National Institute of Information and Communications Technology (NICT), Japan under “Research on Innovative Optical Fiber Technology”.
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