Multicore Fiber Technology

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 34, NO. 1, JANUARY 1, 2016 55

Multicore Fiber TechnologyKunimasa Saitoh, Member, OSA and Shoichiro Matsuo, Member, OSA

(Tutorial Review)

Abstract—Multicore fibers (MCFs) are expected as a good can-didate for overcoming the capacity limit of a current optical com-munication system. This paper describes the recent progress onthe MCFs for space-division multiplexing to be utilized in futurelarge capacity long-distance transmission systems. Tradeoff issuebetween low crosstalk and high core density in MCFs is presentedand prospect of large-space multiplicity of MCFs is discussed.

Index Terms—Few-mode fiber, multicore fiber, multimode fiber,space division multiplexing.

I. INTRODUCTION

W E experienced Internet traffic growth of about 100 timesevery 10 years, and this trend is estimated to proceed [1].

The transmission capacity of conventional single-mode single-core fiber (SM-SCF) has also been exponentially increased inthe past few decades by a variety of advanced technologiesincluding the expansion of the optical bandwidth of transmis-sion window and enhancement of the spectral efficiency. RecentSM-SCF transmission systems have achieved transmission ca-pacity up to about 100 Tb/s and capacity-distance product over100 Pb/s·km as shown in Fig. 1 [2]–[7]. However, the capacityof existing standard SM-SCF may no longer satisfy the grow-ing capacity demand and is approaching its fundamental limitaround 100 Tb/s owing to the limitation of amplifier bandwidth,nonlinear noise, and fiber fuse phenomenon. Therefore, it is es-timated that the current trends of traffic growth will result incapacity crunch in the near future [8].

In order to further increase the fiber capacity or spatial ca-pacity - the capacity per cross-sectional area of the fiber, spacedivision multiplexing (SDM) has been proposed [9] and at-tracted intensive research efforts as a solution to the problem ofsaturation of the capacity of conventional SM-SCFs. In SDMtransmission systems, several different signals are transmittedsimultaneously by providing multiple spatial paths with costeffective ways. From the SDM fiber point of view, there are ba-sically two approaches to introduce multiple spatial paths intoa fiber. The first approach is to incorporate multiple separatecores with sufficiently low crosstalk between neighboring coresin a single fiber, which is known as a weakly-coupled multi-

Manuscript received June 15, 2015; revised August 5, 2015; accepted August6, 2015. Date of publication August 19, 2015; date of current version January 24,2016. This work was supported in part by the National Institute of Informationand Communications Technology, Japan, and the Ministry of Internal Affairsand Communication, of Japan, and Horizon 2020 of EU.

K. Saitoh is with the Graduate School of Information Science and Tech-nology, Hokkaido University, Sapporo 060-0814, Japan (e-mail: [email protected]).

S. Matsuo is with the Advanced Technology Laboratory, Fujikura Ltd., Chiba285-8550, Japan (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JLT.2015.2466444

Fig. 1. Recently reported transmission capacity and transmission distance byusing single-mode single-core fibers and single-mode multicore fibers.

core fiber (MCF). The second approach is to utilize multipledifferent modes in a fiber, which is a few-mode fiber (FMF) ormultimode fiber (MMF). From the spatial density perspective,MMF approach is a promising scheme since the spatial channelcount (SCC) can be scaled up to more than 30 theoretically witha standard cladding diameter of 125 μm [10], [11], however,the control of group velocity difference between each channelbecomes a challenging issue due to structural parameter fluctu-ation during fabrication if the number of modes increases. Onthe other hand, from the total SCC perspective, MCF approachis expected as a good candidate since the core multiplicity andmode multiplicity can be combined in MCFs, however, the sup-pression of crosstalk between neighboring cores becomes anissue if the number of cores increases in a limited cladding size.

In this paper, the state-of-the-art of MCFs as a future largecapacity long-distance transmission media for SDM is pre-sented. Firstly, crosstalk estimation and crosstalk suppressiontechniques in MCFs are described. Next, the core density inMCFs is discussed based on the recently fabricated single-modeMCFs (SM-MCFs). It is shown that there is a tradeoff relation-ship between low crosstalk and high space multiplicity, thereforethe maximum number of cores and the core arrangement have tobe carefully determined based on the allowable crosstalk leveland upper cladding size. In addition, in order to further increasethe space multiplicity in SDM fibers, recently developed MCFswith supporting a few spatial modes in each core, which arefew-mode MCFs (FM-MCFs), are also presented.

II. LOW CROSSTALK MULTICORE FIBERS

A. Classification of Multicore Fibers

MCFs for SDM application were firstly proposed in 1979[12], [13], however, they have not been commercialized thensince other cost- and space-efficient network for the subscriber

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56 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 34, NO. 1, JANUARY 1, 2016

Fig. 2. Classification of multicore fibers for SDM.

lines was utilized. In the late 2000s, the SDM approach withMCFs had come to attract much attention again [9] because thefuture capacity crunch became an issue with reality [8].

MCFs can be fundamentally classified into two different cat-egories as shown in Fig. 2. The first type is a weakly-coupledMCF, in which each core is used as an individual waveguidewith sufficiently low interference between neighboring cores.In weakly-coupled MCFs, the optical crosstalk between adja-cent cores is an important problem, since a part of the opticalpower launched into one of the core is coupled with neigh-boring cores during the propagation, and the crosstalk (XT) isdefined as XT = 10log10 (P’/P) [dB], where P and P’ are theoutput power from the input core and that from the neighbor-ing core, respectively. In order to keep crosstalk level lowerthan −30 dB, the coupling coefficient κ between neighboringcores should be lower than around 10−2 m−1 [14] for trans-mission distance of longer than 10 km by sacrificing the coredensity and its typical core-to-core distance is around 40 μm. Inthis case, multiple-input multiple-output (MIMO) digital signalprocessing (DSP) is not needed at the receiver side for recov-ering the signals. The second type is a strongly-coupled MCF,in which the crosstalk between cores is intentionally introducedby decreasing the core-to-core distance, resulting in the coredensity improvement. In theory, the strongly-coupled MCF sup-ports several super-modes and it can be considered a form ofMMFs. In practice, these super-modes are strongly mixed due tostructural parameter fluctuations and/or bending effect, if the ef-fective index difference Δneff between each mode is relativelysmall (typically Δneff < 10−5). In MMF transmission, groupdelay spread originating from the modal dispersion is one of themajor problems since the magnitude of group delay spread de-termines the complexity of MIMO receiver (and hence, systemreach) [15]. The strong mode mixing in strongly-coupled MCFsis beneficial for reducing the group delay spread and the groupdelay spread is proportional to the square root of the trans-mission distance [16]. Recently, this square root dependenceof group delay spread was experimentally reported by using awell-designed coupled 3-core fiber up to 4200 km [17], [18]and a coupled 6-core fiber up to 1705 km [19]. The coupling co-efficient κ between neighboring cores in the strongly-coupledMCFs is in the order of 10−1 m−1 or more and the typical

core-to-core distance is less than 30 μm. In this case, MIMODSP with low complexity is needed at the receiver side to undothe signals. It should be noticed that the mode coupling dur-ing the propagation between super-modes becomes weak if thecoupling between cores is too strong, since the effective indexdifference Δneff between each mode becomes large (typicallyΔneff > 10−4). In this case, it can be used as an MMF similarto a single-core MMF with high spatial density [20], however,its group delay spread is proportional to the transmission dis-tance and complex MIMO DSP is required as increasing thetransmission distance.

Among these two categories of MCFs, SDM based on weakly-coupled MCFs is a simple and promising approach for increas-ing SCC, resulting in improvement of transmission capacityper fiber. Various kinds of weakly-coupled MCFs have beendeveloped to achieve high-capacity long-distance transmission.Recent SM-MCF transmission experiments have achieved thetransmission capacity well beyond the fundamental limit ofSM-SCF as shown in Fig. 1 [21]–[32]. The current maximumtransmission capacity per fiber is 1.01 Pb/s [28], the maximumcapacity-distance product is 1.032 (0.516+0.516) Eb/s/fiber·km[32], and the maximum number of spatial multiplicity is 19 [25],[26] in SM-MCF transmission. The longest span length of MCFtransmission reported so far is about 75 km [23], [27].

B. Crosstalk Estimation in Weakly-Coupled Multicore Fibers

The estimation of crosstalk in MCFs is a very important issuefor determining its structural parameters. In order to evaluatecrosstalk in MCFs theoretically, coupled-mode theory (CMT)has been introduced [33], [34]. The coupled mode equations forMCFs are written as [35]

dAm

dz= −j

∑

n �=m

κmnAn (z) exp(jΔβ′mnz)f(z) (1)

where Am is the mode amplitude in core m, z is the propagationdirection, κmn is the mode-coupling coefficient from core nto core m, and Δβ′

mn is the propagation-constant differencebetween core m and core n expressed as

Δβ′mn = Δβcore,mn + Δβbend,mn (z) (2)

SAITOH AND MATSUO: MULTICORE FIBER TECHNOLOGY 57

with Δβcore,mn being the intrinsic propagation constant dif-ference between core m and core n and Δβbend,mn being thebending and twisting induced propagation constant difference.f(z) is the phase function and is given by

f(z) = exp [j(φm − φn )] δf(z) (3)

where φm and φn are the phase in core m and core n, respectively,and δf(z) is the random part. If the random part is missing, Eq.(1) becomes a well-known conventional coupled mode equa-tion. On the other hand, the crosstalk in actual MCFs showsstatistical characteristics and this random part δf(z) has to beconsidered accordingly, since there is random fluctuation in lon-gitudinal direction. In order to consider the random part of phasefunction, δf , the total fiber length is divided into finite segmentsof arbitrary but equal length, ds , and random phase-offsets ofexp(jφrnd) are applied to all cores at every segment. It has beenreported that the segment length ds used in CMT is a stochas-tic parameter corresponding to the correlation length of phasefunction [36]. By solving Eq. (1), crosstalk between core m andcore n in MCFs can be evaluated, however, in order to obtainsufficiently accurate average values of crosstalk, a large num-ber of simulations are required, since the crosstalk obtained byCMT with random phase-offset shows statistical characteristics.

To evaluate crosstalk in MCFs more easily, coupled-powertheory (CPT) has also been introduced [36]–[38]. The coupledpower equations for MCFs are written as [39]

dPm

dz=

∑

n �=m

hmn [Pn (z) − Pm (z)] (4)

where Pm is the average power in core m and hmn is the power-coupling coefficient. The averaged power Pm in core m at apoint z close to z = 0 is given by using the solution of Eq. (1)as

Pm (z) =⟨|Am (z)|2

⟩

=⟨[

κmnAn (0)∫ z

0exp(jΔβ′

mnξ)δf(ξ)dξ

]

[κmnA∗

n (0)∫ z

0exp(−jΔβ′

mnη)δf ∗(η)dη

]⟩

= κ2mnPn (0)

∫ z

0dη

∫ z

0exp [jΔβ′

mn (ξ − η)]

〈δf(ξ)δf ∗(η)〉 dη

= κ2mnPn (0)

∫ z

0dη

[∫ z−η

−η

exp(jΔβ′mnζ)

〈δf(η + ζ)δf ∗(η)〉 dζ] (5)

where the asterisk and the symbol 〈〉 indicate complex conju-gation and an ensemble average, respectively. The random partof phase function, δf , is a stationary random process and there-fore, it has an autocorrelation function R(ζ), and Eq. (5) can berewritten as

Pm (z) = κ2mnPn (0)z

∫ z−η

−η

exp(jΔβ′mnζ)R(ζ)dζ (6)

Since the two quantities, η and ζ, are not independent, it isdifficult to evaluate rigorously the integral in Eq. (6). If thecorrelation length of δf is much smaller than the increment z offiber length, the bounds of the integral in Eq. (6) can be neglectedand therefore, the upper and the lower integration limits, z−ηand −η, are replaced by +∞ and, −∞ respectively, and thepower-coupling coefficient hmn (z) is written as [36]

hmn (z) =Pm (z)zPn (0)

= κ2mn

∫ ∞

−∞exp(jΔβ′

mnζ)R(ζ)dζ

= κ2mnS(Δβ′

mn (z)) (7)

where S(Δβ′mn ) is the Fourier transform of the autocorrela-

tion function. The autocorrelation function R(ζ) is an unknownfunction, but it has been reported that the experimental resultsof crosstalk in MCFs can be well fitted by using exponentialautocorrelation function [36], [40] given by

R(ζ) = exp (− |ζ| /d) (8)

where d is the correlation length and its corresponding powercoupling coefficient is a Lorenzian function as

hmn (z) =2κ2

mnd

1 + [Δβ′mn (z)d]2

. (9)

If we assume that an MCF is bent at a constant radius R andis twisted continuously at a constant rate γ, the power couplingcoefficient is averaged over a twist pitch as

h̄mn =γ

2π

∫ 2π/γ

0hmn (z)dz (10)

and the analytical expression of the averaged power couplingcoefficient has been derived [40]. Notice that, in this case, thepower coupling coefficient is independent of the twist rate γ,and the crosstalk (XT) between two cores with length L is easilyestimated as

XT = tanh(h̄mnL). (11)

From Eq. (9), we can see that the power coupling coefficientbecomes peak value when Δβ′

mn is zero at a particular bendingradius, and this critical bending radius Rc is given as

Rc =βm Λ

Δβcore,mn=

nef f,m ΛΔnef f,mn

(12)

where βm and nef f,m is the propagation constant and the ef-fective index of the propagating mode in core m, respectively,Δnef f,mn is the intrinsic effective index difference betweencore m and core n, and Λ is the core-to-core distance. In the caseof homogeneous MCFs (Δβcore,mn = 0) with small bendingradii, Eq. (9) can be approximated as [35], [36]

h̄mn =2κ2

mnR

βm Λ. (13)

It is clear that, when the mode-coupling coefficient κ is ob-tained, the averaged crosstalk can be easily estimated in homo-geneous MCFs. For example, if we target a crosstalk level of−50 dB/km with Λ<40 μm and R<300 mm, the κ has to belowered to around 0.002 m−1 or less.


Fig. 3. Cross sectional view of a fabricated trench-assisted MCF [30], [32]and its index profile.

C. Crosstalk Suppression Techniques

In order to decrease crosstalk in MCFs, the coupling coeffi-cient κ between cores has to be reduced. Trench-assisted MCFs[41]–[43] and hole-assisted MCFs [44]–[47] have been pro-posed for reducing the coupling coefficient. Fig. 3(a) shows anexample of cross sectional view of a fabricated trench-assistedMCF with 12 cores [30], [32], where each core has low-indextrench layer around the core. In Fig. 3(b), the schematic dia-gram of an index profile with trench-assisted structure [48] isshown. The relative refractive index differences between coreand cladding, trench and cladding are Δ1 and Δ2 , respectively,and r1 , r2 , and W are the core radius, the distance from the corecenter to the inner edge of trench layer, and the trench width,respectively. Due to the existence of low index trench layer withthe thickness of W, the overlap of the electromagnetic fieldsbetween cores can be greatly suppressed, resulting in the sup-pression of crosstalk compared with that in an MCF withouttrench.

Recently, simple analytical expression for crosstalk estima-tion in trench-assisted MCFs [49] was reported. The crosstalkin a trench-assisted MCF, XTtrench , can be accurately approxi-mated as

XTtrench = XTstepΓ exp[−4 (W2 − W1)

W

r1

](14)

where XTstep is the crosstalk in a step-index MCF. The param-eter Γ is given by

Γ = W1/ [W1 + (W2 − W1) W/Λ] , (15)

in which W1 ≈1.1428V1 − 0.996 for 1.5 ≤ V1 ≤ 2.5 with V1 =2πr1ncore

√2Δ1/λ, λ is the wavelength, Λ is the core-to-

core distance, and W2 =√

V 22 + W 2

1 with V2 = 2πr1nclad√2 |Δ2 |/λ, where ncore and nclad are the core index and

cladding index, respectively. As shown in Eq. (14), the trenchwidth W and the trench depth Δ2 are key parameters for crosstalkreduction. Fig. 4 shows the crosstalk between two cores as afunction of the core-to-core distance in a step-index MCF andtrench-assisted MCFs with various relative trench widths ofW/r1 at a wavelength of 1550 nm with R = 140 mm, wherer1 = 4.5 μm, r2/r1 = 2.0, Δ1 = 0.35%, and Δ2 = −0.70%,as an example. The crosstalk decreases linearly as increasingthe core-to-core distance and the amount of crosstalk reductionin trench-assisted structure relative to step-index structure is

Fig. 4. Crosstalk between two cores as a function of the core-to-core distancein a step-index MCF and trench-assisted MCFs with various relative trenchwidths of W/r1 at a wavelength of 1550 nm with R = 140 mm, where r1 =4.5 μm, r2 /r1 = 2.0, Δ1 = 0.35%, and Δ2 = −0.70%.

Fig. 5. The averaged power coupling coefficient as a function of the intrinsiceffective index difference Δneff between cores and the bending radius R at1550 nm wavelength, where the core-to-core distance is Λ = 40 μm and thecoupling coefficient is κ = 0.01 m−1.

core-to-core distance independent [49]. It can be seen that morethan 30 dB crosstalk reduction is achievable with a typical trenchwidth of W/r1 = 1.0.

The second approach to suppress the crosstalk is to introduceintrinsic index difference between adjacent cores [50], [51],which is called heterogeneous MCFs. The heterogeneous MCFconsists of several kinds of cores whose propagation constantsare different from each other, and the bending perturbation playsan important role for predicting the crosstalk in heterogeneousMCFs [33], [34]. Fig. 5 shows the averaged power couplingcoefficient as a function of the intrinsic effective index differ-ence Δneff between cores and the bending radius R at 1550 nmwavelength obtained from Eqs. (9) and (10), where the core-to-core distance is Λ = 40 μm and the coupling coefficient isκ = 0.01 m−1 as an example. Notice that the bending radius ofthe MCF in a cable will be depending on the cable design andit can be assumed to be from several tens of mm to 1000 mm[52]. It is shown that, when the bending radius is smaller thana critical bending radius Rc given by Eq. (12), there is a linearrelation between a bending radius in a logarithmic scale and acrosstalk values [51]. On the other hand, over the bending radius


Fig. 6. (a) Schematic structure, (b) cross-sectional view, and (c) index profilesfor a fabricated 30-core fiber with heterogeneous core arrangement [54].

larger than the critical bending radius, the crosstalk decreasesrapidly. This is because, if the bending radius is smaller thanRc , the bent induced effective index variation is larger than theintrinsic index difference Δneff between heterogeneous cores,namely Max|Δβbend(z)| > Δβcore , and large crosstalk degra-dation occurs many times during the propagation at the phasematching points of Δβ′

mn (z) = 0. On the other hand, in the non-phase-matching region of bending radii > Rc , the bent inducedeffective index variation is smaller than the intrinsic index differ-ence Δneff , namely Max|Δβbend(z)| < Δβcore , therefore thecrosstalk is dominated by the statistical properties [33], [36],[53], [54]. In this non-phase-matching region, the heteroge-neous MCFs can be used as a bending insensitive fiber in termsof crosstalk. If the effective index difference between cores issufficiently large, the value of Rc can be pushed toward smallrange lower than an effective bending radius in MCF cables.

Recently, a heterogeneous MCF with 30 cores has been re-ported [55]. Fig. 6(a) and (b) show a schematic structure andcross-sectional view of the fabricated 30-core fiber with het-erogeneous core arrangement, respectively. The fiber structureis based on a hexagonal closed-pack structure (HCPS) with 37cores. Six outermost cores were removed to reduce the claddingdiameter. The center core was also removed because the cutoffwavelength lengthening of the center core due to the trench-assisted structure was unavoidable. Four kinds of cores wereused to produce a heterogeneous relation for all the adjacentcores under the limitation of the similar effective area (Aeff ) forall the cores. Cores 1, 2, and 3 employed a trench-assisted indexprofile shown in Fig. 3(b) to reduce the crosstalk, whereas Core4 has a step-index profile without trench layer to avoid the cutoffwavelength lengthening of the inner cores surrounded by trench-assisted cores. Their core parameters were determined based onthe effective index difference as shown in Fig. 7, where the nor-malized trench position is r2/r1 = 1.7 and Δ2 = −0.7% fortrench-assisted cores. All the cores were selected so that the ef-fective index difference between adjacent cores becomes largerthan 0.0005 with the similar Aeff of 80 μm2.

The fabricated fiber length was 9.6 km, and it had the core-to-core distance of 29.7 μm, the cladding diameter of 228 μm,and the averaged Aeff of 77.3 μm2 at 1550 nm wavelength. Inaddition, the critical bending radius Rc was less than 100 mm forall the core combinations. The measured crosstalk was less than−50 dB. Fig. 8 shows the characteristics of the fan-in/fan-out

Fig. 7. Relationship between core parameters and effective indices in trench-assisted and step-index cores.

Fig. 8. (a) Insertion loss and (b) crosstalk of FI/FO device for the 30-corefiber [56].

(FI/FO) device for the 30-core fiber [56]. The averaged insertionloss of a set of FI/FO was 6.1 dB and the averaged link crosstalkwas−36.6 dB, which is dominated by the crosstalk of the FI/FO.

Another option for crosstalk suppression in MCFs is to utilizepropagation-direction interleaving (PDI) technique [57]–[59],


Fig. 9. Crosstalk in Core m from Core n in (a) unidirectional propagationscheme and (b) bidirectional propagation scheme of PDI.

where adjacent cores are assigned to opposite direction. We canreduce the number of adjacent core in which the signal propa-gates to the same direction to one for all cores by using PDI.Accordingly, effective crosstalk is expected to be reduced. Inthe unidirectional propagation scheme, the inputted power inexcited core is coupled to adjacent cores and the crosstalk givenby Eq. (11) is forward propagated crosstalk, XTf , as shown inFig. 9(a). On the other hand, in the bidirectional propagationscheme, the crosstalk from the adjacent cores is generated whenthe back-scattered light is coupled with the opposite direction asshown in Fig. 9(b), and the dominant factor in back-propagatingsignals is Rayleigh backscattering [59]. The backward propa-gated crosstalk, XTb , is given by

XTb =SαR

2α h̄mn

[1−exp(−2αL)

α − 2L exp(−2αL)]

exp(−h̄mnL) cosh(h̄mnL) exp(−αL)(16)

where S and αR are the recapture factor of the Rayleigh scatter-ing component into the backward direction and the attenuationcoefficient due to Rayleigh scattering, respectively. α and L arethe fiber attenuation coefficient and fiber length, respectively.Fig. 10 shows the forward propagated crosstalk, XTf , and thebackward propagated crosstalk, XTb , as a function of the fiberlength in a trench-assisted MCF at a wavelength of 1550 nm withR = 140 mm, where r1 = 4.5 μm, r2/r1 = 2.0, W/r1 = 1.0,Δ1 = 0.35%, Δ2 = −0.70%, and the core-to-core distance is40 μm, as an example. The Rayleigh backscattering coefficient(SαR/2α) and the fiber attenuation coefficient were assumedto be −32 dB [60] and 0.2 dB/km, respectively. XTb is smallerthan XTf by more than 18 dB for the fiber length of 100 km orless, however, it can be seen that the crosstalk reduction effectof PDI becomes weaker as the fiber length increases and it islimited by Rayleigh scattering.

By adopting combination of these crosstalk suppressiontechniques, low crosstalk and high core count MCFs can bedesigned, such as heterogeneous trench-assisted MCFs [55] andtrench-assisted MCFs with PDI [59]. The allowable crosstalk is

Fig. 10. Forward propagated crosstalk and backward propagated crosstalkas a function of the fiber length in a trench-assisted MCF at a wavelength of1550 nm with R = 140 mm, where r1 = 4.5 μm, r2 /r1 = 2.0, W/r1 = 1.0,Δ1 = 0.35%, and Δ2 = −0.70%.

Fig. 11. Relation between the achievable transmission distance and the allow-able crosstalk level for different modulation format.

depending on the transmission distance as well as the modula-tion format to be used. In Ref. [61], the effect of the crosstalkon the optical signal to noise ratio was numerically investigatedby assuming the crosstalk as a static coupling, and experimen-tally by realizing the crosstalk as an effectively static couplingusing optical couplers and variable optical attenuators. It hasbeen reported that the crosstalk-induced penalty at the bit-errorrate of 10−3 is less than 1 dB, when the crosstalk is less than–18 dB for quadrature phase-shift keying (QPSK), –24 dB for16 quadrature amplitude modulation (QAM), and –32 dB for64 QAM [61]. Similarly, in Ref. [59], the crosstalk penalty inQ-factor for QPSK, 16 QAM, and 32 QAM signals were exper-imentally measured by using 50-km 12-core fiber. It has beenreported that the allowable crosstalk for 0.3-dB Q-penalty was –18 dB for QPSK, –25 dB for 16 QAM, and –29 dB for 32 QAM.Based on these relations between the allowable crosstalk leveland the modulation format, a relation between the achievabletransmission distance and the allowable crosstalk level for differ-ent modulation format can be plotted as shown in Fig. 11. If themodulation format is QPSK, the crosstalk level of −40 dB/kmis acceptable for 100 km transmission. On the other hand, ifthe modulation format is 64 QAM, the crosstalk level of around−55 dB/km is required for 100 km transmission. Therefore,


Fig. 12. Crosstalk increment due to nearest neighbor cores (ΔXT) for hexag-onally close-pack structure (HCPS), one ring structure (ORS), and dual ringstructure (DRS).

the crosstalk level in MCFs should be carefully designed basedon the transmission distance and the modulation format for thetransmission experiment.

We should also notice that the crosstalk given by Eq. (11) isthe averaged crosstalk between two cores and it is not the worstcase crosstalk. In actual MCFs, each core generally has severaladjacent cores and it is affected by all the nearest cores [23]. Ifall cores carry equal signal power, the worst case crosstalk ofinner cores is larger than that of outer cores, since the numberof nearest neighbor cores is larger for inner cores. For example,in the case of the HCPS, the inner core has six nearest neighborcores, while the outer cores have three or four nearest neighborcores. The worst crosstalk, XTworst , in [dB] is given by

XTworst = XT − 10 log n (17)

where XT is the crosstalk between two cores in [dB], and n isthe number of nearest neighbor cores. Fig. 12 shows the crosstalkincrement due to nearest neighbor cores (ΔXT) for HCPS, onering structure (ORS), and dual ring structure (DRS), whereΔXT = XTworst − XT = 10logn. In HCPS, the ΔXT of innercores is 7.8 dB and that of outer cores is 4.8 dB for three nearestneighbor cores or 6.0 dB for four nearest neighbor cores. On theother hand, in ORS, ΔXT is 3 dB for all the cores. The allowablecrosstalk level in MCFs should be determined by consideringXTworst .

D. Core Density and Spatial Channel Count

MCFs for SDM applications should have high spatial effi-ciency (SE) compared with a conventional SM-SCF. The num-ber of cores to be multiplexed in a fiber is related to the core-to-core distance, and the core-to-core distance can be determinedby considering the allowable crosstalk based on the transmis-sion distance and the modulation format. The upper limit ofthe core number is also limited by a cladding diameter (CD),since a small cladding diameter is preferable for maintaininghigh mechanical reliability for bending. Fig. 13 shows the fail-ure probability after 20 years as a function of cladding diameterfor bending diameters of D = 30 mm and D = 60 mm [62],where the proof level is 1% and the number of bending is 100turns. The failure probability of a standard single-mode fiberwith 125 μm cladding diameter and 30 mm bending diameter

Fig. 13. Failure probability after 20 years as a function of cladding diameterfor bending diameters of D = 30 mm and D = 60 mm [62].

is about 10−7. This failure probability of 10−7 would be em-ployed for a threshold also in MCFs, and the failure probabilityof MCFs should be smaller than 10−7 at bending diameter of60 mm, which is the bending diameter in a storage box. It can beseen from Fig. 13 that the cladding diameter of MCFs should besmaller than around 230 μm to satisfy the limit of failure prob-ability [62]. In addition, the cladding thickness (CT), which isa distance from a center of outer core to outer cladding edge,should be sufficiently large for reducing micro-/macro-bendinglosses in outer cores [63], [64]. Therefore, the number of coresas well as the core arrangement have to be determined by takingthe allowable crosstalk and the required CT into account underthe limitation of the CD.

Table I summarizes the recently reported weakly-coupledSM-MCFs [23], [26], [27], [29], [30], [46], [55], [62], [65]–[68]. In Table I, in order to compare the core density andcrosstalk level of these MCFs, SCC, Aeff , CD, CT, 100-kmworst crosstalk, and relative SE (RSE) are included. SCC isgiven by core count, N, in a fiber times mode count, M, in acore. In SM-MCFs, SCC corresponds to N. The SE of MCF,SEMCF , is defined as

SEMCF = SCC/(π

4CD2

)(18)

and RSE, which is SEMCF normalized by the SE of a standardSM-SCF, SESMF , with cladding diameter of 125 μm, is givenas

RSE = SEMCF/SESMF = SCC

(125CD

)2

. (19)

We can see that there is a trade-off relationship between highRSE and low crosstalk. Fig. 14 shows the SCC as functionsof the 100-km worst crosstalk and the CD for MCFs listed inTable I. For SM-MCFs, the reported maximum RSE and themaximum SCC are, respectively, 9 and 30 [55] with the worstcrosstalk of −42 dB/100 km so far. It should be noted that thecrosstalk of MCFs increases with increasing the wavelength andthe slope of crosstalk over wavelength regimes was measuredto be approximately 0.1 dB/nm [30], [66], [69], [70]. Therefore,the worst case crosstalk at the longer edge of L band is about10 dB larger than that at the shorter edge of C band.


TABLE ICHARACTERISTICS OF RECENTLY REPORTED WEAKLY-COUPLED SINGLE-MODE MULTICORE FIBERS

Reference SCC Aeff [μm2] at 1550 nm CD [μm] CT [μm] 100-km worst crosstalk [dB] at 1550 nm RSE

T. Hayashi et al. [65] 7 80 150 30 −64 4.86B. Zhu et al. [23] 7 ∼75 186.5 46.4 ∼−31 3.14S. Matsuo et al. [62] 10 116 204.4 43 −23 3.74H. Takara et al. [27] 7 110 195 48.5 −56 2.88S. Matsuo et al. [66] 12 80 225 39 −42 3.7H. Takahashi et al. [29] 7 99 200 55 −39.6 2.73J. Sakaguchi et al. [26] 19 72 200 30 −14.3 7.42T. Sakamoto et al. [46] 6 72.7 125 30.9 −32.5(at 1625 nm) 6A. Sano et al. [30] 12 105.8 230 35 −45 3.56J. Sakaguchi et al. [67] 19 85 220 34.8 −36.8 6.13Y. Amma et al. [55] 30 77.3 228 33.8 −42 9T. Hayashi et al. [68] 8 ∼55(at 1310 nm) 125 22 −42(at 1310 nm) 8

Fig. 14. SCC as functions of the 100-km worst crosstalk and the CD forSM-MCFs listed in Table I.

III. FEW-MODE MULTICORE FIBERS FOR HIGH SCC

Mode division multiplexing (MDM) over MMFs/FMFs isan attractive approach for SDM with high SE. Various FMFshave been reported for large-capacity MDM transmission withreduce differential mode group delay (DMD) [71]–[75]. How-ever, for long-distance transmission using MMFs/FMFs, com-plex MIMO DSP is required to separate coupled modes duringpropagation in most cases. The number of multiplexed modesmay be limited regarding the signal processing system com-plexity and controllability of mode dependent loss. In addition,scalability of SCC in MMFs is also limited in terms of the fabri-cation tolerance of the DMD characteristics [11], since it wouldbe very sensitive to structural parameter fluctuation during fab-rication with increasing the number of multiplexed modes.

The combination of core multiplexing and mode multiplex-ing, which is FM-MCF, is also promising candidate for SDM,since it can directly increase the SCCs by increasing the core andmode multiplicity. For example, 19-core fiber supporting 2-LPmode (3 spatial modes) in each core can achieve SCC of 36, andin 12-core fiber with 4-LP mode (6 spatial modes), SCC becomes72. In FM-MCFs, required core-to-core distance becomes largecompared with that in SM-MCFs, since the crosstalk between

Fig. 15. Crosstalk between LP01 modes (XT01−01 ), LP11 modes (XT11−11 ),and LP02 modes (XT02−02 ) in single-mode core, 2-LP-mode core, and 4-LP-mode core, respectively, as a function of core-to-core distance at 1565 nmwavelength.

higher-order modes is larger than that between fundamentalmodes. Fig. 15 shows the numerically simulated crosstalk be-tween LP01 modes (XT01−01), LP11 modes (XT11−11), and LP02modes (XT02−02) in a single-mode core, a 2LP-mode core, anda 4LP-mode core, respectively, as a function of core-to-coredistance at 1565 nm wavelength, where each core has a trench-assisted index profile with r2 /r1 = 2.0, W/r1 = 1.0, and Δ2 =−0.70%. All the cores have the same Aeff of 80 μm2 for thefundamental mode, and r1 and Δ1 are assumed to be 4.7 μmand 0.38%, 5.4 μm and 0.56%, and 5.9 μm and 0.86%, respec-tively, for single-mode core, 2LP-mode core, and 4LP-modecore. XT11−11 between the 2LP-mode cores and XT02−02 be-tween the 4LP-mode cores are about 5-dB and 20-dB larger,respectively, compared with XT01−01 between the single-modecores. Therefore, larger core-to-core distance is required forincreasing the number of modes in FM-MCFs for achievingsimilar crosstalk compared with SM-MCFs.

Table II summarizes characteristics of weakly-coupled FM-MCFs reported so far [76]–[85], where C and M in Table IImean “core” and “mode”, respectively. DMD values are alsoshown in Table II, since the DMD suppression is a critical is-sue in MDM transmission. Figs. 16 and 17 show the SCC as afunction of the crosstalk and the relationship between SCC andthe maximum |DMD|, respectively, for the reported FM-MCFs.


TABLE IICHARACTERISTICS OF REPORTED WEAKLY-COUPLED FEW-MODE MULTICORE FIBERS

Reference SCC Aeff [μm2] of LP0 1 mode CD [μm] CT [μm] MaximunDMD [ps/km] 100-km worst crosstalk [dB] at 1550 nm RSE

D. Qian et al. [76] 18(12 C×1M+2C×3M) − 216 30 − −7 6C. Xia et al. [77] 21(7C×3M) ∼110 192 56 4600 −12.2 8.9K. Mukasa et al. [78] 21(7C×3M) 183 243 60 − −25.2 5.6K. Mukasa et al. [79] 57(19C×3M) 218 440 98.6 − −7.4 4.6Y. Sasaki et al. [80] 12(4C×3M) 114 176 51 3000 −39 6Y. Sasaki et al. [81] 21(7C×3M) 110 195.4 51.5 2729 −40.2 8.6T. Mizuno et al. [82] 36(12C×3M) 96 229.5 49.8 520 −55 10.7K. Shibahara et al. [83] 36(12C×3M) 110 230 47 63 −58 10.6J. Sakaguchi et al. [84] 108(36C×3M) 76 306 51 7400 −5 18K. Igarashi et al. [85] 114(19C×6M) − 318 35 1000 −19 17.6

Fig. 16. SCC for the reported FM-MCFs as a function of the crosstalk.

Fig. 17. Relationship between SCC and the maximum |DMD| for the reportedFM-MCFs.

In Fig. 16, filled circles correspond to the MCFs with CD ofsmaller than 230 μm, while open circles represent the MCFswith CD of larger than 230 μm. 7-core 2LP-mode homoge-neous MCF [81] having a step-index profile with trench showedlow worst crosstalk of−40.2 dB/100 km, however, its DMD wasa few thousand ps/km. 12-core 2LP-mode heterogeneous MCFshaving a multi-step index profile with trench and a graded indexprofile with trench achieved low crosstalk and low DMD, si-multaneously [82], [83]. Recently, SCC more than 100 has beenalso reported by using the 36-core 2LP-mode heterogeneousMCF [84] and the 19-core 4LP-mode homogeneous MCF [85],although their CDs were larger than 300 μm.

Fig. 18. Wavelength dependence of the DMD for the fabricated 12-core 2LP-mode MCFs with (a) a multi-step index profile [82] and (b) a graded indexprofile [83].

Fig. 18 (a) and (b) show the experimentally measured wave-length dependence of the DMD for the fabricated 12-core 2LP-mode MCFs with a multi-step index profile [82] and a gradedindex profile [83], respectively. The maximum |DMD| over C-band in the MCF with the multi-step index was 520 ps/km,whereas it was reduced to 63 ps/km by using the graded indexprofile. In both MCFs, a square lattice core arrangement was


adopted. This is because only two kinds of cores are required forthe heterogeneous core arrangement in the square lattice struc-ture. On the other hand, if we use an HCPS, at least three kindsof cores are needed for the heterogeneous core arrangement.The square lattice structure is also beneficial in terms of theworst case crosstalk, as the number of the nearest neighboringcores is four, resulting in ΔXT of 6 dB. The measured attenua-tion and Aeff for LP01 mode were 0.218 dB/km and 110 μm2,respectively, at 1550 nm wavelength. By using this FM-MCF,the 527-km 36-spatial-channels transmission was achieved [83].These results indicate the high potential of FM-MCFs for furtherincrement of SCC.

IV. CONCLUSION

In this paper, weakly-coupled MCF technology for the appli-cation of high-capacity SDM transmission has been described.Crosstalk estimation method was reviewed and three crosstalksuppression schemes, which are trench-assisted structure, het-erogeneous core arrangement, and PDI technique, were ex-plained. In addition, the relation between achievable crosstalk,SE, and SCC was presented. It was shown that the core-to-coredistance should be carefully determined by considering the al-lowable crosstalk based on the transmission distance and themodulation format to be used, while the number of cores aswell as the core arrangement have to be determined by takingthe ΔXT and the required CT under the limitation of the CDrelated to their mechanical reliability. It was also shown that thecombination of core multiplexing and mode multiplexing by us-ing FM-MCFs is a very promising approach to realize high SCCover 100. In FM-MCFs, not only crosstalk suppression for thehigher-order modes but also the control of DMD in each coreduring the fabrication are challenging issues as increasing thenumber of modes. Further researches on design optimization ofMCFs and development of related devices such as FI/FO andamplifier are highly expected.

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[56] S. Matsuo, K. Takenaga, K. Saitoh, K. Nakajima, Y. Miyamoto,T. Morioka, “High-spatial-multiplicity multi-core fibres for future densespace-division-multiplexing system,” presented at the Eur. Conf. Opt.Commun., Valencia, Spain, 2015, Paper Th.1.2.1.

[57] H. Ono, Y. Abe, K. Shikama, T. Takahashi, M. Yamada, K. Takenaga, andS. Matsuo, “Amplification method for crosstalk reduction in multi-corefibre amplifier,” Electron. Lett., vol. 49, no. 2, pp. 138–140, Jan. 2013.

[58] T. Ito, E. L. T. de Gabory, M. Arikawa, Y. Hashimoto, and K. Fukuchi,“Reduction of influence of inter-core cross-talk in MCF with bidirec-tional assignment between neighboring cores,” presented at the Opt. FiberCommun. Conf., Anaheim, CA, USA, 2013, Paper OTh3K.2.

[59] A. Sano, H. Takara, T. Kobayashi, and Y. Miyamoto, “Crosstalk-managedhigh capacity long haul multicore fiber transmission with propagation-direction interleaving,” J. Lightw. Technol., vol. 30, no. 16, pp. 2771–2779,Aug. 2014.


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[62] S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, K. Saitoh,and M. Koshiba, “Large-effective-area ten-core fiber with cladding diam-eter of about 200 μm,” Opt. Lett., vol. 36, no. 23, pp. 4626–4628, Dec.2011.

[63] K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh,and M. Koshiba, “A large effective area multi-core fiber with an optimizedcladding thickness,” presented at the Eur. Conf. Opt. Commun., Geneva,Switzerland, 2011, Paper Mo.1.LeCervin.2.

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[66] S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama,K Saitoh, and M. Kosihba, “12-core fiber with one ring structure forextremely large capacity Transmission,” Opt. Exp., vol. 20, no. 27,pp. 28398–28408, Dec. 2012.

[67] J. Sakaguchi, W. Klaus, B. J. Puttnam, J. M. D. Mendinueta, Y. Awaji,N. Wada, Y. Tsuchida, K. Maeda, M. Tadakuma, K. Imamura, R. Sugizaki,T. Kobayashi, Y. Tottori, M. Watanabe, and R. V. Jensen, “19-core MCFtransmission system using EDFA with shared core pumping coupled viafree-space optics,” Opt. Exp., vol. 22, no. 1, pp. 90–95, Jan. 2013.

[68] T. Hayashi, T. Nakanishi, K. Hirashima, O. Shimakawa, F. Sato,K. Koyama, A. Furuya, Y. Murakami, and T. Sasaki, “125-μm-cladding 8-core multi-core fiber realizing ultra-high-density cable suitable for O-bandshort-reach optical interconnects,” presented at the Opt. Fiber Commun.Conf., Los Angeles, CA, USA, 2015, Paper Th5C.6.

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[72] R. Maruyama, N. Kuwaki, S. Matsuo, K. Sato, and M. Ohashi, “Modedispersion compensating optical transmission line composed of two-modeoptical fibers,” presented at the Opt. Fiber Commun. Conf., Los Angeles,CA, USA, 2012, Paper JW2A.13.

[73] L. Gruner-Nielsen, Y. Sum, J. W. Nicholson, D. Jakobsen, R. Lingle, andB. Palsdottir, “Few mode transmission fiber with low DGD, low modecoupling and low loss,” presented at the Opt. Fiber Commun. Conf., LosAngeles, CA, USA, 2012, Paper PDP5A.1.

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[77] C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. M. Arrioja,A. Schulzgen, M. Richardson, J. Linares, C. Montero, E. Mateo, X. Zhou,and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photon. Technol. Lett., vol. 24, no. 21,pp. 1914–1917, Nov. 2012.

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[81] Y. Sasaki, Y. Amma, K. Takenaga, S. Matsuo, K. Saitoh, and M. Koshiba,“Trench-assisted low-crosstalk few-mode multicore fiber,” presented atthe Eur. Conf. Opt. Commun., London, U.K., 2013, Paper Mo.3.A.5.

[82] T. Mizuno, T. Kobayashi, H. Takara, A. Sano, H. Kawakami, T. Nakagawa,Y. Miyamoto, Y. Abe, T. Goh, M. Oguma, T. Sakamoto, Y. Sasaki, I. Ishida,K. Takenaga, S. Matsuo, K. Saitoh, and T. Morioka, “12-core × 3-modedense space division multiplexed transmission over 40 km employingmulti-carrier signals with parallel MIMO equalization,” presented at theOpt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, Paper Th5B.2.

[83] K. Shibahara, T. Mizuno, H. Takara, A. Sano, H. Kawakami, D. Lee,Y. Miyamoto, H. Ono, M. Oguma, Y. Abe, T. Kobayashi, T. Matsui,R. Fukumoto, Y. Amma, T. Hosokawa, S. Matsuo, K. Saito, H. Nasu, andT. Morioka, “Dense SDM (12-core × 3-mode) transmission over 527 kmwith 33.2-ns mode-dispersion employing low-complexity parallel MIMOfrequency-domain equalization,” presented at the Opt. Fiber Commun.Conf., Los Angeles, CA, USA, 2015, Paper Th5C.3.

[84] J. Sakaguchi, W. Klaus, J.-M. D. Mendinueta, B. J. Puttnam1, R. S. Luis,Y. Awaji1, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun,T. Takahata, and T. Kobayashi, “Realizing a 36-core, 3-mode fiber with108 spatial channels,” presented at the Opt. Fiber Commun. Conf., LosAngeles, CA, USA, 2015, Paper Th5C.2.

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Kunimasa Saitoh (S’00–M’01) received the B.S., M.S., and Ph.D. degreesin electronic engineering from Hokkaido University, Sapporo, Japan, in 1997,1999, and 2001, respectively.

From 1999 to 2001, he was a Research Fellow of the Japan Society for thePromotion of Science. From 2001 to 2005, he was a Research Associate with theGraduate School of Engineering, Hokkaido University. From 2005 to 2013, hewas an Associate Professor at the Graduate School of Information Science andTechnology, Hokkaido University, where he became a Professor in 2013. Hehas been involved in research on fiber optics, nanophotonics, integrated opticaldevices, and computer-aided design and modeling of guided-wave devices. Heis the author of more than 160 research papers in refereed international journalsand 200 refereed conference presentations.

Dr. Saitoh is a member of the Optical Society of America and the Institute ofElectronics, Information and Communication Engineers (IEICE). He receivedthe Excellent Paper Award and the Young Scientist Award from the IEICE, in1999 and 2002, respectively, the Young Scientists’ Prize of the Commendationfor Science and Technology from the Ministry of Education, Culture, Sports,Science, and Technology, Government of Japan, in 2008. From 2009 to 2010,he served as a Secretary/Treasurer of the IEEE Sapporo Section.

Shoichiro Matsuo (M’11) received the B.E. and M.E. degrees in electrical en-gineering from Kyushu University, Fukuoka, Japan, in 1988 and 1990, and thePh.D. degree in production and information science from Utsunomiya Univer-sity, Tochigi, Japan, in 2008.

Since 1990, he has been with Fujikura Ltd., Chiba, Japan, where he is cur-rently a General Manager of the Advanced Technology Laboratory. He has beenworking on research and development of transmission fibers for long-haul net-work and FTTH network and rare-earth-doped fibers, photonic bandgap fibers,and manufacturing technology of these optical fibers. He is an author or coau-thor of more than 100 journals and conference papers and is an inventor ofmore than 90 granted patents over the world. He is a member of the OpticalSociety of America, the Japanese Society of Applied Physics, and the Instituteof Electronics, Information and Communication Engineers.

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Multicore Fiber Technology