## Abstract

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 μm^{2}, 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

## 1. Introduction

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 [1]. 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 (*A*_{eff}) are also important optical properties for improving signal-to-noise ratio (SNR) in each core [6]. However, no reported MCFs have realized low loss and large *A*_{eff} 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 *A*_{eff} 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 A_{eff} 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 [12].

## 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 *A*_{eff} and low XT. Figure 1
shows the designed relative refractive index difference (Δ) profile of the core. The core was designed to have *A*_{eff} of ~130 µm^{2}, cable cutoff wavelength (*λ*_{cc}) of 1460 nm, and the Rayleigh scattering coefficient lower than that of the MCF in [5]. As for the design of the XT, the statistical mean of the XT (mean XT, *µ*_{XT}) between two adjacent cores of a homogeneous MCF can be expressed as [5]:

*η*is the power coupling coefficient,

*κ*the mode coupling coefficient,

*R*the bending radius,

*β*the propagation constant, Λ the core pitch, and

*L*the fiber length. Based on Eq. (1), Λ of the MCF was designed to be 52 μm so that

*µ*

_{XT}from six outer cores to the center core (center-core

*µ*

_{XT}( = 6

*ηL*)) 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:

*α*

_{XT}

*is the power loss coefficient [/unit length], and the*

_{,n}*η*is the power coupling coefficient [/unit length] from Core

_{mn}*n*to Core

*m*. In the homogeneous seven-core fiber, the power loss coefficient due to the XT in the center core can be approximated to be 6

*η*(the sum of the power coupling coefficients to six outer cores). Thus, the XT-induced power loss coefficient

*α*

_{XT,dB}in the unit of [dB/unit length] of the center core can be represented aswhose relationship is shown in Fig. 2 . To suppress

*α*

_{XT,dB}lower than 0.001 dB/km, 6

*η*should be less than 2.30 × 10

^{−4}/km (corresponding to the center-core

*µ*

_{XT}less than −17.3 dB at

*L*= 80 km) so that the XT target was appropriate in terms of loss.

## 3. Fabrication

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. *A*_{eff}s of the cores were slightly smaller than the design target but all of the *A*_{eff}s exceeded 120 μm^{2}. The *λ*_{cc}s 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 *µ*_{XT}s between adjacent two cores of the MCF, which were measured as wavelength averages of the XTs by using the wavelength scanning technique described in [13]. Values of averages, maximums, and minimums of the *µ*_{XT}s between the adjacent two cores, and of total *µ*_{XT}s 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 *µ*_{XT}s for *L* = 80 km are also shown in Table 2, which were calculated based on the linear accumulation of the XT. The center-core *µ*_{XT}s can be less than −30 dB for *L* shorter than 1.4 × 10^{3} km at 1550 nm, 8.7 × 10^{2} km at 1565 nm, and 2.0 × 10^{2} km at 1625 nm.

## 4. Discussion

#### 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 *A*_{eff} 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 [6]:

*P*

_{Tx,ch},

*P*

_{ASE},

*P*

_{NLI}are the average powers of transmitted power per channel, of the ASE noise within the OSNR noise bandwidth

*B*

_{n}, and of the nonlinear interference (NLI) within

*B*

_{n}, respectively, and where

*N*

_{s}is the number of spans,

*F*the EDFA noise figure,

*α*the power loss per unit length,

*L*

_{s}the span length, h the Planck’s constant,

*ν*the center frequency of WDM comb,

*γ*= 2π

*n*

_{2}/(

*λA*

_{eff}) is the nonlinear coefficient,

*n*

_{2}the nonlinear refractive index,

*L*

_{eff}= [1−exp(−

*αL*)]/

_{s}*α*is the effective length,

*β*

_{2}= −

*λ*

^{2}

*D*/(2πc) is the chromatic dispersion in [(unit time)

^{2}/(unit length)],

*B*

_{WDM}=

*N*

_{ch}

*R*

_{s}is the WDM bandwidth,

*N*

_{ch}the number of WDM channels, and

*R*the symbol rate.

_{s}Based on the characteristics of XT in MCF shown in [13], 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 as

*P*

_{XT}is the power of the XT from or to the certain core. In Eq. (8),

*P*

_{Tx,ch}s equivalent between all cores and losses equivalent between all cores are assumed. “−

*P*

_{XT}” in the numerator represents the XT from the certain core to other cores, and “+

*P*

_{XT}” in the denominator represents the XT from other cores to the certain core. However, “−

*P*

_{XT}” is negligible in the case of low XT (

*P*

_{Tx,ch}>>

*P*

_{XT}). Depending on system capability,

*P*

_{XT}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,

*P*

_{XT}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,

*P*

_{XT}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.,

*μ*

_{XT}< ~0.01),

*P*

_{XT}can be related to

*P*

_{Tx,ch}by

*μ*

_{XT}asIn the following discussion, we discuss the case of a core (the worst core) to which total

*μ*

_{XT}from other cores is highest. When the XT is adequately low and XT between non-adjacent cores is negligible, the total

*μ*

_{XT}(

*μ*

_{XT,WC}) to the worst core can be approximated as

*η*

_{WC}is the aggregate power coupling coefficient to the worst core, and

*N*is the maximal number of the adjacent cores.

_{c}Equations (4), (8)–(10) yield

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 *P*_{Tx,ch} = [*P*_{ASE}/(2*a*_{NLI})]^{1/3}. Therefore, the maximal SNR (SNR_{SC,max}) achievable in a SC system can be derived as

_{system}/

*N*

_{s}includes the second and third bracket terms in the second line. When assuming moderately high |

*β*

_{2}| and adequately broad

*B*

_{WDM}, C

_{system}/

*N*

_{s}can be cancelled out by taking a ratio of SNR

_{SC,max}s in the same system between different fibers. Accordingly, a figure of merit of a single-core fiber can be expressed only by the bracket term in the last line. Especially in case that ${e}^{\alpha {L}_{\text{s}}}>>1$, SNR

_{SC,max}s in [dB] can be approximately obtained as

_{SC}) between SNR

_{SC,max,dB}between different fibers can be expressed only with the fiber parameters and

*L*

_{s}.

From Eqs. (12) and (14), the maximal SNR (SNR_{MC,max}) in a MC system can be expressed as

_{MC}) of SNR

_{MC,max}in [dB] between different fibers cannot be expressed only with the fiber parameters and

*L*

_{s}. Only

*N*

_{s}can be cancelled out in ΔSNR

_{MC}and other system parameters (C

_{system}) cannot be cancelled out. However, in both SC and MC cases, we can obtain ΔSNR independent of

*N*

_{s}, and SNR penalty due to XT independent of

*N*

_{s}:

#### 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 SNR_{SC,max} and the worst-core *µ*_{XT} after one span affect SNR penalty due to XT and ΔSNR_{MC} in cases of *L*_{s} = 80 km and *L*_{s} = 100 km. In Fig. 6, the SNR_{SC,max}s and the *µ*_{XT}s of the various reported MCFs and the fabricated MCF—their characteristics are listed in Table 3
— are plotted as red diamonds, and the SNR_{SC,max} of SSMF are plotted as dashed lines. The SNR_{SC,max}s were calculated using Eq. (14) in case of *B*_{WDM} = 10 THz and *F*_{dB} = 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, SNR_{SC,max}s—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 ΔSNR_{MC} unaffected by XT, *µ*_{XT} per *L*_{s} of the MCF have to be suppressed adequately lower than ASE and NLI noises per *L*_{s}. Based on the SNR_{SC,max} and the SNR penalty, or on Eq. (16), ΔSNR_{MC} from the SSMF can be obtained and are plotted as solid curves. The XT of the fabricated MCF was well suppressed, and ΔSNR_{MC} of the MCF can be achieved to be 2.4 dB for *L*_{s} = 80 km and 2.9 dB for *L*_{s} = 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 *L*_{s} = 80 km and 0.2 dB for *L*_{s} = 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 *µ*_{XT} after one span and the SNR penalty due to XT in an MCF with SSMF core (ΔSNR_{SC} = 0 dB), for combinations of system parameters of *F*_{dB} = 3, 4, 5, 6 dB and *B*_{WDM} = 5, 10 THz, in the case of *L*_{s} = 80 km, which is more severe than *L*_{s} = 100 km. In these traces, the case of *F*_{dB} = 3 dB and *B*_{WDM} = 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 *µ*_{XT} 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 SNR_{SC,max} is cancelled by a decrease in XT. Accordingly, horizontal offsets of the curves in Fig. 7 are equivalent to the difference in the SNR_{SC,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 SNR_{SC,max} for *L*_{s} = 80 km was increased by 2.8 dB from the SSMF (ΔSNR_{SC} = 2.8 dB), we need to suppress the worst-core *µ*_{XT} 2.8 dB further from the above values.

## 5. Conclusions

We designed and fabricated an MCF simultaneously achieving transmission losses of 0.17 dB/km or lower, effective areas larger than 120 μm^{2}, 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.

## Acknowledgment

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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