## Abstract

We propose and design a kind of heterogeneous rod-assisted and trench-assisted multi-core fiber (Hetero-RA-TA-MCF) with 32 cores arranged in square-lattice structure (SLS), and then we introduce the design method for Hetero-RA-TA-MCF. Simulation results show that the Hetero-RA-TA-32-Core-Fiber achieves average effective area (*A*_{eff}) of about 74 μm^{2}, low crosstalk (XT) of about −31 dB/100km, threshold value of bending radius (*R*_{pk}) of 7.0 cm, relative core multiplicity factor (RCMF) of 8.74, and cable cutoff wavelength (λ_{cc}) of less than 1.53 μm.

© 2017 Optical Society of America

## 1. Introduction

Nowadays, by employing time-, wavelength-, polarization-division multiplexing, as well as multi-level modulations, the current optical fiber transmission systems have achieved ultra-high transmission capacity of 100 Tb/s per fiber [1–3]. However, the transmission capacity of single mode single core fiber (SM-SCF) is rapidly approaching the fundamental limit owing to the limitation of amplifier bandwidth, nonlinear noise and fiber fuse phenomenon [4, 5], it is predicted that capacity crunch will happen in the near future. In order to overcome the capacity limit, space division multiplexing (SDM) techniques based on weakly-coupled multi-core fiber (MCF) is one of promising candidates to enlarge the capacity [4]. In MCFs, the suppression of crosstalk (XT) between neighboring cores becomes an issue if the number of cores increases in a limited cladding space. In order to decrease XT in MCFs, the coupling coefficient between cores has to be reduced. Therefore, the core design which has strong confinement of modes is important for the suppression of the mode coupling coefficient. Core structure with high-index and small-diameter is one of the options, but it degrades the effective area (*A*_{eff}) and increases the nonlinear noise [6, 7]. Recently, several research groups have investigated specially designed refractive index profiles to meet the requirement of low XT, such as trench-assisted (TA) profile [8–12], hole-assisted (HA) profile [13, 14], which are shown as Figs. 1(a) and 1(b). Besides, low index rod-assisted (RA) profile shown as Fig. 1(c) can also be used to suppress the inter-core XT. In this work, we adopt RA profile instead of TA profile and HA profile, since rod has smaller size than trench so that it can suppress XT as well as shorten the cable cutoff wavelength (λ_{cc}) of higher order mode in the core, especially in the central core. Furthermore, a type of optical fiber called heterogeneous MCF (Hetero-MCF) has been proposed to realize much lower XT, in which there are not only identical cores but also non-identical cores [8, 9, 15, 16]. Besides the core structure, we also need to analyze and carefully design the core arrangement for MCFs. Figures 2(a)-2(c) show three kinds of core arrangement for high core density MCFs, which are hexagonal closed-packed structure (HCPS) [17], ring-lattice structure (RLS) [9] and square-lattice structure (SLS) [16]. Here, the red, blue and green circles stand for non-identical cores. However, both HCPS and RLS needs three kinds of cores with RA profile to produce a heterogeneous relation for all the adjacent cores with similar *A*_{eff}, and each central core needs six low index rods to suppress XT, resulting in lengthening λ_{cc} of the inner cores. Furthermore, it is very difficult to pick out three heterogeneous RA cores with relative large effective index difference (Δ*n*_{eff}) and ensure similar *A*_{eff} simultaneously. On the other hand, SLS shown as Fig. 2(c) can arrange 32 cores with only two kinds of cores with RA profile.

Therefore, in this paper, we adopt SLS instead of HCPS and RLS for high core density MCFs with 32 cores arranged inside it, and investigate the characteristics such as *A*_{eff,} XT, threshold value of bending radius (*R*_{pk}), relative core multiplicity factor (RCMF) and λ_{cc} to prove the feasibility and advantages of square-lattice structured 32-core fiber. The discussion of *R*_{pk}, RCMF will be introduced later. In Section 2, we firstly propose Hetero-RA-32-Core fiber based on SLS. Then, we introduce the design method and analyze the rationality of the designed MCFs. In Section 3, we present an optimization scheme*−*Hetero-RA-TA-32-Core-Fiber, then introduce the design method and give the core parameter design. In Section 4, we investigate the characteristics including *A*_{eff}, XT, *R*_{pk} and RCMF of Hetero-RA-TA-32-Core-Fiber, and compare the proposed Hetero-RA-TA-32-Core-Fiber with other reported MCFs to point out the superiority of our design. In Section 5, we conclude our work.

## 2. Design of Hetero-RA-32-Core-Fiber

#### 2.1 Profile of Hetero-RA-32-Core-Fiber

Figure 3 shows the schematic structure and core index profile of Hetero-RA-32-Core-Fiber with SLS. In Fig. 3(a), outer cladding thickness (*OCT*) is the distance from the center of outer core to the circumference of cladding, Λ is the core-to-core distance, *D*_{cl} is the cladding diameter. In Fig. 3(b), *r*_{1}, *r*_{h}, *d*_{cr}, Δ_{1}, Δ_{2}, and Λ correspond to core radius, rod radius, the distance between the center of core and the center of rod, the relative refractive index difference between core and cladding, the relative refractive index difference between cladding and rod, and the core-to-core distance, respectively.

#### 2.2 Design of low-index rod

In the simulation of this work, the operation wavelength is assumed to be 1550 nm. And in order to arrange more cores in a limited cladding space, we set Λ to 30 μm for making sure it is weakly-coupled MCF [18]. To simplify the fiber design scheme, *d*_{cr} is set to 15 μm which means that the rod is located at the center of two non-identical cores. Considering the design of Hetero-RA-32-Core-Fiber, we only need to focus on rod parameters and core parameters, since the core arrangement, Λ and *d*_{cr} are fixed.

Figure 4 shows the numerically calculated mean value of XT between two non-identical RA cores after 100-km propagation as function of rod radius when Δ_{2} = −0.7%, where the calculated XT values are obtained by coupled-power theory (CPT) [19]. In this work, the fiber is assumed to be twisted at twisting rate of 5 turns per 100 m [20] and all the XT values are calculated by using CPT with the correlation length *d* being set as 0.05 m, based on which the calculated average XT values agree well with the experimental results [17, 19, 21]. And we set core with (*r*_{11}, Δ_{11}) of (5.2 μm, 0.37%) as Core 1, core with (*r*_{21}, Δ_{21}) of (4.6 μm, 0.31%) as Core 2 for calculation. In Fig. 4, we can find that as *r*_{h} increases, XT level decreases. Therefore, we set *r*_{h} to 6.0 μm as a compromise value, since larger *r*_{h} can suppress XT but lengthen λ_{cc}.

Figure 5 illustrates the XT calculated by CPT [19] between Core 1 and Core 2 as function of bending radius (*R*) at various Δ_{2} when *r*_{h} = 6.0 μm. In Fig. 5, we can see that with the increase of *R*, the XT of Hetero-MCF firstly increases, however after *R* reaching a threshold value, which is called *R*_{pk}, the XT decreases immediately and then it converges to a certain value no matter how *R* increases [8]. There is a relationship between *R*_{pk}, *n*_{eff}, Δ*n*_{eff} and Λ, which is given by [11]

*n*

_{eff}, Δ

*n*

_{eff}, and Λ are the effective index of a core, the effective index difference between the non-identical cores and the core-to-core distance, respectively. According to Eq. (1), we can know that

*R*

_{pk}increases as Δ

*n*

_{eff}decreases when

*n*

_{eff}and Λ are fixed. Therefore, a large Δ

*n*

_{eff}will be required for pushing the value of

*R*

_{pk}to sufficiently small range, so that we can obtain a large non-phase-matching region,

*R>R*

_{pk}, in which the bending extent will not impact the crosstalk any more.

From Fig. 5, we can also obtain that when we fix *r*_{h} and shift Δ_{2}, the XT level decreases with the decrease of Δ_{2}. Thus, Δ_{2} is set to −0.7% for simulation, which is the structural parameter used in the fabricated index trench assisted MCFs [12].

#### 2.3 Selection of RA core

We begin to design core parameters, such as core *r*_{1} and core Δ_{1}, since all the low index rod structural parameters are designed before. Figure 6 illustrates the *n*_{eff} and *A*_{eff} of LP_{01} mode at 1550-nm wavelength as function of core *r*_{1} and core Δ_{1} when *r*_{h} = 6.0 μm and Δ_{2} = −0.7%. And color map means the *n*_{eff} values. The black solid lines and the black dashed lines represent certain special values of *n*_{eff} and *A*_{eff} of LP_{01} mode at 1550-nm wavelength, which are simulated by full-vector finite element method (FEM) [22]. The upper and lower white bold solid lines in Fig. 6 correspond to the cutoff limit of LP_{11} mode and the bending loss (BL) limit of LP_{01} mode. On the one hand, according to the deployment configuration in IEC 60793-1-44 document, we think that LP_{11} mode has been mostly cut off if BL of LP_{11} mode is larger than 1 dB/m at *R* = 140 mm and λ = 1530 nm, which can make the total BL*>*20 dB/22 m; on the other hand, the BL of LP_{01} mode should be smaller than 0.5 dB/100 turns at *R* = 30 mm and λ = 1625 nm according to ITU-T recommendations G.655 and G.656, which can be thought that LP_{01} mode has been totally confined inside the core. The field which is surrounded by the upper and lower white bold solid lines is called single mode operation region (SMOR) [9, 23]. Thus, for single-mode operation from C-band to L-band, we should choose two non-identical RA cores in such field, noticing that the two non-identical RA cores should better have the same *A*_{eff}, because the different *A*_{eff} will cause splice loss [21]. In Fig. 6, we can also observe that if we enlarge the expected *A*_{eff}, the maximum Δ*n*_{eff} we can obtain between non-identical cores will decrease, which means there is a trade-off relationship between Δ*n*_{eff} and *A*_{eff}, and this kind of trade-off relationship also exists similarly between *R*_{pk} and *A*_{eff}. Therefore, if the required Δ*n*_{eff} is set to 0.001 and the target *A*_{eff} is 80 μm^{2}, we designate core with (*r*_{1}, Δ_{1}) of (4.65 μm, 0.375%) as Core 1, core with (*r*_{1}, Δ_{1}) of (4.19 μm, 0.328%) as Core 2, which are shown as the filled circles in Fig. 6.

#### 2.4 Analysis of requirement for OCT

Subsequently, we analyze the BL dependence of LP_{01} mode at *R* = 140 mm and λ = 1625 nm on *OCT* for Core 1 and Core 2 when *r*_{h} = 6.0 μm and Δ_{2} = −0.7% and the results are shown as Fig. 7. In Fig. 7, we can observe that for Core 1 and Core 2, *OCT* should be larger than 37.1 μm and 41.8 μm to ensure BL at λ = 1625 nm and *R* = 140 mm of smaller than 0.001 dB/km [24]. In addition, the relationship between *D*_{cl}, Λ, and *OCT* of SLS in Fig. 3 (a) is given by

It is known that *D*_{cl} of MCFs should be smaller than around 230 μm to satisfy the limit of failure probability [25]. However, according to the Eq. (2), the structural upper limit of *OCT* is 28 μm when *D*_{cl} is smaller than 230 μm and Λ is set to be 30 μm. Thus, we need to optimize core index profile and core parameters to meet the requirement of *OCT* of 28 μm.

## 3. Optimization scheme—-Hetero-RA-TA-32-Core-Fiber

#### 3.1 Profile of Hetero-RA-TA-32-Core-Fiber

As core with RA profile at outer layer cannot satisfy the lower limit of *OCT*, in order to make stronger confinement on mode for outer layer cores, we deployed TA profile instead of RA profile for the eight corner outer cores in SLS. Figure 8 shows a schematic structure and heterogeneous core types of the proposed Hetero-RA-TA-32-Core-Fiber. Core 1 and Core 2 are RA cores and Core 3 is TA core. This structure shares the same parameters*—r*_{1}, *d*_{cr}, *r*_{h} Δ_{1}, Δ_{1}, Λ, *OCT*, *D*_{cl} with Fig. 3(b), and for Core 3, it also shares the same parameters*—r*_{2}, *W* with Fig. 1(a), where *r*_{2}, *W* in TA profile stand for the distance between the center of core and inner edge of trench, the thickness of the trench layer, respectively. Figure 8(b) shows eight types of heterogeneous core combinations, in which four types are RA core combinations and four types are combinations of RA core and TA core. The eight types will be discussed later in the XT characteristics.

#### 3.2 Design of low-index trench and rod

According to the previous discussion, we should first determine the trench parameters and then decide the rod parameters, so that we can calculate the cutoff limit of LP_{11} mode and the BL limit of LP_{01} mode for TA core and RA core, and obtain the core selection region.

Firstly, we analyze *r*_{2}/*r*_{1} and *W*/*r*_{1} of the trench layer for TA cores when we set core *r*_{1} and core Δ_{1} to 4.90 μm and 0.40%. Figures 9(a)-9(c) show BL, *A*_{eff} and *n*_{eff} of LP_{01} mode as function of *W*/*r*_{1} at various *r*_{2}/*r*_{1}, respectively. We can find that with the increase of *r*_{2}/*r*_{1}, BL decreases, but *A*_{eff} and *n*_{eff} stay almost unchanged. With the increase of *r*_{2}/*r*_{1}, BL decreases, but both *A*_{eff} and *n*_{eff} increase. Figure 9(a) can also help us know that to ensure BL of smaller than 0.001 dB/km, *r*_{2}/*r*_{1} and *W*/*r*_{1} should be larger than or equal to 1.5 and 1.2, respectively.

Figure 10 show cutoff limit and *OCT* lower limit of 28 μm as function of *r*_{1} and Δ_{1} when (a) *r*_{2}/*r*_{1} = 1.5, (b) *r*_{2}/*r*_{1} = 1.6 and (c) *r*_{2}/*r*_{1} = 1.7 at various *W*/*r*_{1} respectively. In Figs. 10(a)-10(c), the black dashed lines and bold black solid lines represent values of *n*_{eff} and *A*_{eff} of LP_{01} mode at 1550 nm wavelength, which are also simulated by using full-vector FEM [22], where (a) *r*_{2}/*r*_{1} = 1.5, (b) *r*_{2}/*r*_{1} = 1.6 and (c) *r*_{2}/*r*_{1} = 1.7. The group of blue, red and green solid lines and the group of blue, red and green dashed lines correspond to the cutoff limits of LP_{11} mode at *W*/*r*_{1} = 1.1, 1.2 and 1.3 when *R* = 140 mm and λ = 1530 nm and the *OCT* lower limits of LP_{01} mode at *W*/*r*_{1} = 1.1, 1.2 and 1.3 when *R* = 140 mm and λ = 1625 nm, respectively, where (a) *r*_{2}/*r*_{1} = 1.5, (b) *r*_{2}/*r*_{1} = 1.6 and (c) *r*_{2}/*r*_{1} = 1.7. According to Fig. 10, we need to know that we should select TA core above the *OCT* lower limit lines and under the cutoff limit lines simultaneously to meet the requirements of *OCT* of smaller than 28 μm and cable cutoff wavelength of smaller than 1530 nm. In order to show the intersections of the *OCT* lower limit lines, cutoff limit lines and *A*_{eff} lines more clearly, we enlarge the line intersections region in Fig. 10, which are shown in Fig. 11. Based on Fig. 11, when the target value of *A*_{eff} is 74 μm^{2}, and at the same time to keep the obtained *n*_{eff} value as large as possible, here maximum *n*_{eff} = 1.4533, the choices of (*r*_{2}/*r*_{1}, *W*/*r*_{1}) can be (1.5, 1.2) and (1.6, 1.2), which correspond to TA Core 1 in Fig. 11(a) and TA Core 2 in Fig. 11(b). Comparing Fig. 11(a) with Fig. 11(b), we can know that with *r*_{2}/*r*_{1} increased from 1.5 to 1.6, we can obtain TA core with the same *A*_{eff} and *n*_{eff} but higher refractive index Δ_{1} and smaller core radius *r*_{1} at the same time, which is effective in suppressing inter-core XT. Thus, we will choose (*r*_{2}/*r*_{1}, *W*/*r*_{1}) of (1.6, 1.2) for *A*_{eff} = 74 μm^{2}. When the target value of *A*_{eff} is 78 μm^{2}, the choice of (*r*_{2}/*r*_{1}, *W*/*r*_{1}) will be (1.5, 1.3), which correspond to TA Core 3 in Fig. 11(a). Thus, we present two options for TA core: (1) *r*_{2}/*r*_{1} = 1.6, *W*/*r*_{1} = 1.2, (2) *r*_{2}/*r*_{1} = 1.5, *W*/*r*_{1} = 1.3.

Secondly, we need to figure out the suitable value of rod radius. Figure 12 illustrates BL of LP_{11} mode at λ = 1530 nm and *R* = 140 mm and BL of LP_{01} mode at λ = 1625 nm and *R* = 30 mm as function of *r*_{1} and Δ_{1} for RA core when (a) *r*_{h} = 7.0 μm, (b) *r*_{h} = 7.5 μm, and (c) *r*_{h} = 8.0 μm, and also describes the SMOR dependence on rod radius *r*_{h}. The black solid lines and the black dashed lines represent certain values of *n*_{eff} and *A*_{eff} of the LP_{01} mode at 1550 nm wavelength, which are simulated by full-vector FEM [22]. Here, all the *A*_{eff} values of RA cores are calculated by using core type 1 with four surrounding rods in Fig. 8(b). In Fig. 12, we can observe that as *r*_{h} increases, the SMOR becomes narrow, then the Max Δ*n*_{eff} we can obtain becomes small. When determining the suitable *r*_{h}, there are two things to be considered: the first one is *r*_{h} should be as large as possible to suppress XT between two adjacent Hetero-RA-cores which can be found in Fig. 5, the second one is that Δ*n*_{eff} between each pair of Hetero-RA-cores should be as large as possible to decrease *R*_{pk}. Thus, we choose *r*_{h} = 7.5 μm to compromise this tradeoff relationship.

#### 3.3 Selection of TA core and RA core

In the following discussion, we will introduce the core parameters selection in two parts, one is *r*_{2}/*r*_{1} = 1.6, *W*/*r*_{1} = 1.2, *r*_{h} = 7.5 μm, *A*_{eff} = 74 μm^{2}, and the other one is *r*_{2}/*r*_{1} = 1.5, *W*/*r*_{1} = 1.3, *r*_{h} = 7.5 μm, *A*_{eff} = 78 μm^{2}.

Figure 13 shows BL of LP_{11} mode at λ = 1530 nm and *R* = 140 mm and BL of LP_{01} mode at λ = 1625 nm and *R* = 30 mm as function of *r*_{1} and Δ_{1} with target *A*_{eff} is 74 μm^{2} when (a) TA core, *r*_{2}/*r*_{1} = 1.6, *W*/*r*_{1} = 1.2, *r*_{h} = 7.5 μm and (b) RA core, *r*_{2}/*r*_{1} = 1.6, *W*/*r*_{1} = 1.2, *r*_{h} = 7.5 μm. According to the principle of TA core-selecting described before, we designate core with (*r*_{1}, Δ_{1}) of (4.79 μm, 0.408%) as Core 3 when *r*_{2}/*r*_{1} = 1.6, *W*/*r*_{1} = 1.2, *r*_{h} = 7.5 μm, which is shown as the red filled circles in Fig. 13(a). For RA core-selecting, we should make sure that *A*_{eff} of RA cores is 74 μm^{2}, and at the same time, selecting RA cores which can ensure sufficiently large Δ*n*_{eff} between each set of non-identical cores so that fiber becomes bend-insensitive with small *R*_{pk}. Thus, we designate core with (*r*_{1}, Δ_{1}) of (4.39 μm, 0.371%) as Core 1 and core with (*r*_{1}, Δ_{1}) of (4.05 μm, 0.330%) as Core 2 when *r*_{2}/*r*_{1} = 1.6, *W*/*r*_{1} = 1.2, *r*_{h} = 7.5 μm, which is shown as the green and blue filled circles in Fig. 13(b). In this case, the designed fiber is called Fiber A.

Figure 14 shows BL of LP_{11} mode at λ = 1530 nm and *R* = 140 mm and BL of LP_{01} mode at λ = 1625 nm and *R* = 30 mm as function of *r*_{1} and Δ_{1} with target *A*_{eff} is 78 μm^{2} when (a) TA core, *r*_{2}/*r*_{1} = 1.5, *W*/*r*_{1} = 1.3, *r*_{h} = 7.5 μm and (b) RA core, *r*_{2}/*r*_{1} = 1.5, *W*/*r*_{1} = 1.3, *r*_{h} = 7.5 μm. Following the same principles of core-selecting as *A*_{eff} = 74 μm^{2}, when *A*_{eff} = 78 μm^{2}, we designate core with (*r*_{1}, Δ_{1}) of (4.98 μm, 0.378%) as Core 3 when *r*_{2}/*r*_{1} = 1.5, *W*/*r*_{1} = 1.3, *r*_{h} = 7.5 μm, which is shown as the red filled circles in Fig. 14(a). We designate core with (*r*_{1}, Δ_{1}) of (4.47 μm, 0.341%) as Core 1 and core with (*r*_{1}, Δ_{1}) of (3.94 μm, 0.301%) as Core 2 when *r*_{2}/*r*_{1} = 1.5, *W*/*r*_{1} = 1.3, *r*_{h} = 7.5 μm, which is shown as the green and blue filled circles in Fig. 14(b). At this time, the designed fiber is called Fiber B.

Table 1 and Table 2 summarize the structural parameters of Fiber A and Fiber B. Those structural parameters ensure that 32-core MCFs realize *A*_{eff} of around 74 μm^{2} and 78 μm^{2} at λ = 1.55 μm, respectively, λ* _{cc}* of smaller than 1.53 μm, and BL of smaller than 0.5 dB/100 turns at λ = 1.625 μm with

*R*= 30 mm.

## 4. Characteristics of Hetero-RA-TA-32-Core-Fiber

Figure 15 shows the numerically calculated mean value of inter-core XT results of Fiber A and Fiber B at 1.55 μm with eight types of heterogeneous core combinations after 100-km propagation as a function of bending radius *R*, where the calculated results are obtained by coupled-power theory (CPT) [19].

From Figs. 15(a) and 15(b), we can see that the 100-km worst XT of Fiber A is the XT_{type5} which is still lower than −30 dB, while the 100-km worst XT of Fiber B is the XT_{type2} and XT_{type3} which are −28 dB. It is interesting to notice that the XT_{type1} is very close to XT_{type4} in both Fiber A and Fiber B, which separate from the XT_{type2} and XT_{type3}. Thus, we can conclude that the XT between RA core and RA core is sensitive to the surrounding low index structures. On the other hand, the XT_{type5} is very close to XT_{type7}, and XT_{type6} is very close to XT_{type8} in both Fiber A and Fiber B. Then we can know that the XT between RA core and TA core is irrelevant to the surrounding low index structures. According to Eq. (1), the calculated *R*_{pk} of Fiber A and Fiber B are 7.0 cm and 6.5 cm, respectively. Thus, in order to ensure low crosstalk transmissions with high-order modulation format [18], Fiber A is our final design choice for Hetero-RA-TA-32-Core-Fiber. And RCMF of Fiber A is estimated to be 8.74. According to the definition of core multiplicity factor (CMF) for MCF [24], the CMF is given by

*N*

_{core}and

*D*

_{cl}represent the number of cores and cladding diameter, respectively. RCMF is a ratio between CMF of a MCF and a standard single core single mode fiber with

*A*

_{eff}= 80 μm

^{2}at 1550 nm and

*D*

_{cl}= 125μm, which is given by [24]

Figure 16 shows comparison of spatial multiplicity and inter-core XT at λ of 1550 nm between the reported high-density MCFs [17, 26–29] and the proposed Hetero-RA-TA-32-Core-Fiber in this work. Figure 16(a) and Fig. 16(b) show RCMF and core count, respectively. In Figs. 16(a) and 16(b), circle, diamond and square mean RLS, HCPS and SLS, respectively. It can be found that both 32-core fiber with SLS and 30-core fiber with HCPS [17] can make RCMF reach above 8 and 100-km XT of smaller than −31 dB/100 km which implies that 64-QAM can be used in 100 km transmission [18]. However, the λ_{cc} of 30-core fiber with HCPS is less than 1570 nm [30], which is larger than 1530 nm, while the λ_{cc} of the proposed Hetero-RA-TA-32-Core-Fiber with SLS is smaller than 1530 nm, which can ensure single-mode transmission over the C + L band from 1530 nm to 1625 nm.

## 5. Conclusion

In this paper, we first introduced a heterogeneous rod-assisted MCF with 32 cores arranged in SLS. After investigation, we found that the rod-assisted structure was unable to satisfy the requirement of OCT in the limited cladding space. Thus, we presented an optimized scheme for this SLS-MCF, which is a heterogeneous rod-assisted as well as trench-assisted 32-core multi-core fiber (Hetero-RA-TA-32-Core-MCF). For the optimized Hetero-RA-TA-32-Core-MCF, we introduced the design method for core parameters in detail. Simulation results showed that Hetero-RA-TA-32-Core-Fiber achieved average *A*_{eff} of about 74 μm^{2}, low XT of about −31 dB/100 km, *R*_{pk} of 7.0 cm, RCMF of 8.74, and λ_{cc} of less than 1.53 μm. In summary, Hetero-RA-TA-32-Core-Fiber with SLS can realize high-density transmission with improved performance.

## Funding

National Natural Science Foundation of China (NSFC) (Grant No. 61501027, 61370191, 61671053); Fundamental Research Funds for the Central Universities (Grant No. FRF-TP-15-031A1); Hong Kong Scholars Program (XJ2016029); Foundation of Beijing Engineering and Technology Center for Convergence Networks and Ubiquitous Services.

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