## Heterogeneous trench-assisted few-mode multi-core fiber with low differential mode delay |

Optics Express, Vol. 22, Issue 4, pp. 4329-4341 (2014)

http://dx.doi.org/10.1364/OE.22.004329

Acrobat PDF (2148 KB)

### Abstract

We propose a kind of heterogeneous multi-core fiber (Hetero-MCF) with trench-assisted multi-step index few-mode core (TA-MSI-FMC) deployed inside. After analyzing the impact of each parameter on differential mode delay (DMD), we design a couple of TA-MSI-FMCs with *A*_{eff} of 110 μm^{2} for LP_{01} mode. DMD of each TA-MSI-FMC is smaller than |170| ps/km over C + L band and the total DMD can approach almost 0 ps/km over C + L band if we adopt DMD managed transmission line technique by using only one kind of Hetero-TA-FM-MCF. For such Hetero-TA-FM-MCF, crosstalk is about –30 dB/100km at wavelength of 1550 nm as bending radius becomes larger than 15 cm, core number can reach 12, a relative core multiplicity factor (*RCMF*) is 15.7, and the *RCMF* can even reach 26.1 if we treat LP_{11} mode as two special modes thanks to the multiple-input-multiple-output technology.

© 2014 Optical Society of America

## 1. Introduction

1. S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh, and M. Kosihba, “12-core fiber with one ring structure for extremely large capacity transmission,” Opt. Express **20**(27), 28398–28408 (2012). [CrossRef] [PubMed]

3. K. Takenaga, Y. Sasaki, N. Guan, M. Kasahara, K. Saitoh, and M. Koshiba, “Large effective-area few-mode multicore fiber,” IEEE Photon. Technol. Lett. **24**(21), 1941–1944 (2012). [CrossRef]

4. C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. May-Arrioja, A. Schulzgen, M. Richardson, J. Linares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Low-crosstalk few-mode multi-core fiber for high-mode-density space-division multiplexing,” in *European Conference and Exhibition on Optical Communication* (ECOC) (Optical Society of America, Washington, DC, 2012), paper Mo.1.F.5.

6. T. Sakamoto, T. Mori, T. Yamamoto, and S. Tomita, “Differential mode delay managed transmission line for wide-band WDM-MIMO system,” in *Optical Fiber Communication Conference*, OSA Technical Digest (CD) (Optical Society of America, 2012), paper OM2D.1. [CrossRef]

8. K. Sato, R. Maruyama, N. Kuwaki, S. Matsuo, and M. Ohashi, “Optimized graded index two-mode optical fiber with low DMD, large A_{eff} and low bending loss,” Opt. Express **21**(14), 16231–16238 (2013). [CrossRef] [PubMed]

8. K. Sato, R. Maruyama, N. Kuwaki, S. Matsuo, and M. Ohashi, “Optimized graded index two-mode optical fiber with low DMD, large A_{eff} and low bending loss,” Opt. Express **21**(14), 16231–16238 (2013). [CrossRef] [PubMed]

9. T. Mori, T. Sakamoto, M. Wada, T. Yamamoto, and F. Yamamoto, “Low DMD four LP mode transmission fiber for wide-band WDM-MIMO system,” in *Optical Fiber Communication Conference*, OSA Technical Digest (CD) (Optical Society of America, 2013), paper OTh3K.1. [CrossRef]

10. R. Maruyama, N. Kuwaki, S. Matsuo, K. Sato, and M. Ohashi, “DMD free transmission line composed of TMFs with large effective area for MIMO processing,” in *European Conference and Exhibition on Optical Communication* (ECOC) (Optical Society of America, Washington, DC, 2012), paper Tu.1.F.2. [CrossRef]

11. J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express **20**(14), 15157–15170 (2012). [CrossRef] [PubMed]

12. J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Optimized design method for bend-insensitive heterogeneous trench-assisted multi-core fiber with ultra-low crosstalk and high core density,” J. Lightwave Technol. **31**(15), 2590–2598 (2013). [CrossRef]

## 2. Design of trench-assisted multi-step index few-mode core (TA-MSI-FMC)

### 2.1 Profile of TA-MSI-FMC

_{01}mode and LP

_{11}mode. Besides the number of mode transmitting in the core, we should also take into account the inter-mode crosstalk and the differential mode delay (DMD) [13

13. T. Sakamoto, T. Mori, T. Yamamoto, and S. Tomita, “Differential mode delay managed transmission line for WDM-MIMO system using multi-step index fiber,” J. Lightwave Technol. **30**(17), 2783–2787 (2012). [CrossRef]

_{01}mode and LP

_{11}mode, since the DMD characteristics are sensitive to the change of the refractive index profile. In Fig. 1,

*a*

_{1},

*r*

_{1},

*r*

_{2},

*W*, Δ

_{1}, Δ

_{2}and Δ

_{t}stand for inner core radius, outer core radius, the distance between the center of inner core and the inner edge of trench, the thickness of the trench layer, the relative refractive-index difference between inner core and cladding, the relative refractive-index difference between outer core and cladding, and the relative refractive-index difference between trench and cladding, respectively. In the following subsections, we analyze and discuss the relationship between these parameters and DMD and find out the appropriate set of

*a*

_{1}, Δ

_{1},

*r*

_{1}/

*a*

_{1}, Δ

_{d},

*r*

_{2}/

*r*

_{1},

*W/r*

_{1}, and Δ

_{t}to obtain a couple of TA-MSI-FMCs with low DMD, low DMD slope, small inter-core crosstalk, and large effective area (

*A*

_{eff}).

### 2.2 TA-MSI-FMC with low DMD and low DMD slope

_{LP01}) from that of the higher-order mode (τ

_{LP11}) and the expression of DMD is written as follows:where

*c*is the light velocity in a vacuum,

*n*

_{eff}is the effective index, and λ means free space wavelength. Since we should also ensure the low DMD over C + L bands transmission, we need to design two kinds of TA-MSI-FMCs with not only low DMD at a certain operating wavelength but also low DMD slope for the wavelength (λ).

*r*

_{2}/

*r*

_{1}at λ = 1550 nm. Here, we fixed the value for

*a*

_{1}, Δ

_{1},

*r*

_{1}/

*a*

_{1}, Δ

_{d},

*W/r*

_{1}, and Δ

_{t}, which are assumed as 3.6 µm, 0.5%, 2.0, −0.13%, 1.0, and −0.7%, respectively. From Fig. 2, we can know that the location of trench layer has a big impact on the DMD and DMD slope. Furthermore, we can also observe that as

*r*

_{2}/

*r*

_{1}increases, DMD and DMD slope are getting smaller and when

*r*

_{2}/

*r*

_{1}= 1.6, the absolute value of DMD slope for λ = 1550 nm is the smallest and approximates to 0 ns/km/nm.

*r*

_{1}/

*a*

_{1}and Δ

_{d}at λ = 1550 nm. Here, we assumed

*a*

_{1}, Δ

_{1},

*r*

_{2}

*/r*

_{1},

*W/r*

_{1}, and Δ

_{t}to be 3.6 µm, 0.5%, 1.6, 1.0, and −0.7%, respectively. In Fig. 3, we can see that when we fix Δ

_{d}and shift

*r*

_{1}/

*a*

_{1}, DMD does not change flexibly but DMD slope alters slowly. On the contrary, if we fix

*r*

_{1}/

*a*

_{1}and shift Δ

_{d}, DMD changes flexibly and DMD slope also alters slowly. The above-mentioned two approaches can both make DMD slope change, but only the second approach can help us control the DMD over the wide band. When

*r*

_{1}/

*a*

_{1}is fixed, we can compensate the increment and decrement of DMD and DMD slope caused by altering

*r*

_{2}

*/r*

_{1}via changing the value of Δ

_{d}. This phenomenon implies that we can keep a suitable value for

*r*

_{1}/

*a*

_{1}at first and then take advantage of both

*r*

_{2}/

*r*

_{1}and Δ

_{d}to find a reference point with relative low DMD and DMD slope. If we set

*r*

_{1}/

*a*

_{1}to be 2.0, the Δ

_{d}can be shifted from −0.17% to −0.11% so that the approximate range of DMD slope is −2 × 10

^{−4}~ + 2.7 × 10

^{−4}ns/km/nm and that of DMD is −1 ~ + 1 ns/km. It indicts that

*r*

_{1}/

*a*

_{1}of 2.0 is an appropriate design value, which make it possible for us to find suitable

*a*

_{1}, Δ

_{1}for inner core nearby the reference point —

*a*

_{1}of 3.6 µm and Δ

_{1}of 0.5% to obtain both low absolute DMD and DMD slope under the condition that

*r*

_{2}/

*r*

_{1}= 1.6 and Δ

_{d}= −0.13%. Here, we do not analyze the impact of

*W/r*

_{1}and Δ

_{t}on the DMD, which will be discussed in the following subsection.

*a*

_{1}and Δ

_{1}when

*r*

_{2}/

*r*

_{1}= 1.6 and Δ

_{d}= −0.13%. Here, we fixed the value for

*r*

_{1}/

*a*

_{1},

*W/r*

_{1}, and Δ

_{t}, which are assumed as 2.0, 1.0, and −0.7%, respectively. Because different effective area (

*A*

_{eff}) in both cores will cause splice loss between different groups and different optical signal-to-noise ratio (OSNR) depending on the groups [14

14. Y. Sasaki, Y. Amma, K. Takenaga, S. Matsuo, K. Saitoh, and M. Koshiba, “Investigation of crosstalk dependencies on bending radius of heterogeneous multicore fiber,” in *Optical Fiber Communication Conference*, OSA Technical Digest (CD) (Optical Society of America, 2013), paper OTh3K.3. [CrossRef]

*A*

_{eff}of LP

_{01}mode and LP

_{11}mode to be the same in these two cores. Therefore in order to decrease such splice loss and OSNR as far as possible, we require the same

*A*

_{eff}of LP

_{01}mode in both cores. Hence, we define the target value of

*A*

_{eff}of LP

_{01}mode (

*A*

_{eff_LP01}) in both TA-MSI-FMCs to be 110 μm

^{2}. Through investigation we find that when Δ

_{d}is around −0.13% under the condition that

*r*

_{2}/

*r*

_{1}is 1.6, it is possible to find

*a*

_{1}and Δ

_{1}which can make us obtain

*A*

_{eff_LP01}of 110 μm

^{2}and achieve low absolute value of DMD as well. In the Fig. 4, the black solid line and black dashed line represent

*A*

_{eff_LP01}and effective index of LP

_{01}mode (

*n*

_{eff_LP01}), which are both simulated based on full-vector FEM [15

15. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. **38**(7), 927–933 (2002). [CrossRef]

_{21}mode and the limit of LP

_{11}mode at

*W*/

*r*

_{1}of 0.2, 0.8 and 1.0, respectively. It should be noticed that

*W*/

*r*

_{1}of 1.0 here is just an example value and the change of

*W*/

*r*

_{1}will not influence the value of

*n*

_{eff}and

*A*

_{eff}to a large extent, but the two-mode operation region will shift as

*W*/

*r*

_{1}alters. We set

*W*/

*r*

_{1}to be 0.8 and 0.2 in order to make it probable to choose two sorts of TA-MSI-FMCs with same

*A*

_{eff_LP01}of 110 μm

^{2}, low DMD and relative large difference between

*n*

_{eff_LP01}in two TA-MSI-FMCs (Δ

*n*

_{eff_LP01}). Here, to define the two-mode operation, the bending loss (

*BL*) of LP

_{21}-like HOM should be > 1 dB/m at

*R*= 140 mm, which is similar to the definition of

*BL*of LP

_{11}-like HOM in [16

16. T. Matsui, K. Nakajima, and C. Fukai, “Applicability of photonic crystal fiber with uniform air-hole structure to high-speed and wide-band transmission over conventional telecommunication bands,” J. Lightwave Technol. **27**(23), 5410–5416 (2009). [CrossRef]

*BL*of LP

_{11}-like HOM to be 0.5 dB/100 turns at

*R*= 30 mm, according to the description of

*BL*of fundamental mode in ITU-T recommendations G.655 and G.656. To ensure a relative small

*R*

_{pk}which is a critical value of bending radius [17

17. T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fiber due to fiber bend,” in *Proceedings of 36th European Conference and Exhibition on Optical Communication* (Institute of Electrical and Electronics Engineers, 2010), paper We.8.F.6. [CrossRef]

*n*

_{eff_LP01}to be about 0.0008. In this case, we can select two kinds of TA-MSI-FMCs with low DMD and DMD slope in the two-mode operation regions at

*W*/

*r*

_{1}of 0.2 and 0.8, which are shown as the filled circles in red and green in Fig. 4. For the filled circles in red which is designated as core 1,

*a*

_{1}= 3.81 μm, Δ

_{1}= 0.406%, DMD at λ of 1550 nm is –160.90 ps/km and DMD slope at λ of 1550 nm is 0.27 ps/km/nm; For the filled circles in green which is designated as core 2,

*a*

_{1}= 3.92 μm and Δ

_{1}= 0.458%, DMD at λ of 1550 nm is 168.30 ps/km and DMD slope at λ of 1550 nm is –0.27 ps/km/nm.

### 2.3 Impact of r_{2}/r_{1} and Δ_{d} on DMD and DMD slope

*r*

_{2}/

*r*

_{1}shifts, DMD will decrease or increase. So in order to compensate for the decreased or increased DMD, we can find the solution in Fig. 3 that to alter the absolute Δ

_{d}, which means that we can change

*r*

_{2}/

*r*

_{1}and Δ

_{d}to control the DMD. We analyzed and obtained the appropriate Δ

_{d}for different

*r*

_{2}/

*r*

_{1}that (a)

*r*

_{2}/

*r*

_{1}= 1.3, Δ

_{d}= −0.16%, (b)

*r*

_{2}/

*r*

_{1}= 1.4, Δ

_{d}= −0.15%, (c)

*r*

_{2}/

*r*

_{1}= 1.5, Δ

_{d}= −0.14%, (d)

*r*

_{2}/

*r*

_{1}= 1.6, Δ

_{d}= −0.13%, (e)

*r*

_{2}/

*r*

_{1}= 1.7, Δ

_{d}= −0.12%, (f)

*r*

_{2}/

*r*

_{1}= 1.8, Δ

_{d}= −0.11%.

*a*

_{1}and Δ

_{1}under these six situations. Here, we still assume

*r*

_{1}/

*a*

_{1}to be 2.0 since in this case Δ

_{d}that shifts within −0.17% ~−0.11% can guarantee the low absolute DMD and DMD slope. Moreover, we fixed

*W/r*

_{1}to be 1.0 and Δ

_{t}to be −0.7% to simulate the DMD for the above-mentioned six situations. We also define the target

*A*

_{eff_LP01}and Δ

*n*

_{eff_LP01}to be 110 μm

^{2}and about 0.0008, and then we pick up six pairs of TA-MSI-FMCs with low DMD which are corresponding to the filled circles in Fig. 5.

*r*

_{2}/

*r*

_{1}increases, the DMD slope is getting smaller and when it equals 1.6, the DMD slope is almost 0 ns/km/nm. Furthermore, when

*r*

_{2}/

*r*

_{1}increases, the difference between the DMD in both cores becomes larger.

### 2.4 Impact of W/r_{1} and Δ_{t} on DMD and DMD slope

*a*

_{1}, Δ

_{1},

*r*

_{1}/

*a*

_{1}that are 3.6 µm, 0.5%, 2.0, respectively. Figures 7(a) and 7(b) show DMD and DMD slope dependence on

*W*/

*r*

_{1}. In Figs. 7(a) and 7(b), we can see that adjusting

*W*/

*r*

_{1}is another way to control DMD and DMD slope, but when

*W*/

*r*

_{1}becomes lager than ~0.5, it will not affect the DMD and DMD slope any more. Moreover, as

*r*

_{2}/

*r*

_{1}increase,

*W*/

*r*

_{1}has less impact on the DMD and DMD slope, which means that when the trench layer is deployed far away from the outer core, the thickness of trench will not influence the value of DMD and DMD slope. Figures 8(a) and 8(b) show DMD and DMD slope dependence on Δ

_{t}. In Fig. 8(a), we can also observe a similar phenomenon that when

*r*

_{2}/

*r*

_{1}is getting larger, the impact of Δ

_{t}on the DMD will become smaller. In Fig. 8(b), we can see that when Δ

_{t}increases, the DMD slope decreases no matter how we arrange the location of trench layer and design the refractive index of outer core.

*a*

_{1}, Δ

_{1},

*r*

_{1}/

*a*

_{1}, Δ

_{d}, and

*r*

_{2}/

*r*

_{1}can help us find the required TA-MSI-FMCs with low DMD, low DMD slope, and large

*A*

_{eff}. When these parameters are all set, we do not hope the both variables of trench structure —

*W*/

*r*

_{1}and Δ

_{t}affect the results too much. Instead,

*W*/

*r*

_{1}and Δ

_{t}can be used to control the bending loss of modes and the inter-core crosstalk. Therefore, we should deploy the trench layer far from the outer core, in other words, we need to increase

*r*

_{2}/

*r*

_{1}as much as possible so that the change of

*W*/

*r*

_{1}and Δ

_{t}will not influence the DMD and DMD slope a lot. However, we can conclude from Fig. 6 that if

*r*

_{2}/

*r*

_{1}becomes larger than 1.6, the maximum absolute DMD over C + L band will exceed |200| ps/km/nm, which is relative large value for DMD. Since MIMO system requires low DMD, we set |200| ps/km/nm to be the upper limit in this work. Hence,

*r*

_{2}/

*r*

_{1}of 1.6 can be regarded as a relative optimum value, which can make TA-MSI-FMCs achieve relative low DMD over wide band and meanwhile have large tolerance of

*W*/

*r*

_{1}and Δ

_{t}. More interestingly, when we set

*r*

_{2}/

*r*

_{1}to 1.6, we can obtain two TA-MSI-FMCs with positive and negative DMD (−160 and + 168 ps/km) whose absolute values are close to each other. This phenomenon implies that we can adopt DMD managed transmission line technique by using only one kind of Hetero-TA-FM-MCF and rotating one to splice different cores together to make the total DMD approach 0 ps/km over C + L band.

## 3. Layout of TA-MSI-FMCs in the fiber

*r*

_{2}/

*r*

_{1}of 1.6, Δ

_{d}of −0.13%, and

*r*

_{1}/

*a*

_{1}of 2.0 as a relative optimum design scheme. Based on the design of these parameters, two kinds of TA-MSI-FMCs can be found which are shown in Fig. 4. The values of

*a*

_{1}, Δ

_{1},

*W*/

*r*

_{1}, Δ

_{t}and the characteristics of effective index (

*n*

_{eff}), mode field diameter (MFD), effective area (

*A*

_{eff}), dispersion parameter, DMD and

*BL*of core 1 and core 2 are summarized in Table 1. The difference between effective index of inter-modes (Δ

*n*

_{eff}’) in core 1 and core 2 are 2.38 × 10

^{−3}and 2.39 × 10

^{−3}, which proves that mode-coupling phenomena in core 1 and core 2 can be limited because both Δ

*n*

_{eff}’ are larger than the critical value of 0.5 × 10

^{−3}[2]. On the other hand, the difference between effective index of LP

_{01}mode in core 1 and effective index of LP

_{01}mode in core 2 (Δ

*n*

_{eff_LP01}) is about 0.0008. The difference between effective index of LP

_{11}mode in core 1 and effective index of LP

_{11}mode in core 2 (Δ

*n*

_{eff_LP11}) is also about 0.0008.

### 3.1 The appropriate core pitch

11. J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express **20**(14), 15157–15170 (2012). [CrossRef] [PubMed]

12. J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Optimized design method for bend-insensitive heterogeneous trench-assisted multi-core fiber with ultra-low crosstalk and high core density,” J. Lightwave Technol. **31**(15), 2590–2598 (2013). [CrossRef]

18. K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by trench-assisted multi-core fiber,” in *Optical Fiber Communication Conference*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWJ4. [CrossRef]

19. B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “112-Tb/s Space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber,” Opt. Express **19**(17), 16665–16671 (2011). [CrossRef] [PubMed]

*R*

_{pk}. The crosstalk of Hetero-MCF decreases immediately after bending radius (

*R*) reaching a critical value

*R*

_{pk}and then it converges to a certain value no matter how

*R*increases [17

17. T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fiber due to fiber bend,” in *Proceedings of 36th European Conference and Exhibition on Optical Communication* (Institute of Electrical and Electronics Engineers, 2010), paper We.8.F.6. [CrossRef]

*R*

_{pk}can be an extremely small value so that we can obtain a large non-phase-matching region with

*R*>

*R*

_{pk}. In this non-phase-matching region, the bending extent doesn’t impact the crosstalk any more, which can make us design a kind of bend-insensitive Hetero-TA-FM-MCF.

_{01}-LP

_{01}crosstalk (

*XT*

_{01-01}), LP

_{01}-LP

_{11}crosstalk (

*XT*

_{01-11}), LP

_{11}-LP

_{01}crosstalk (

*XT*

_{11-01}), and LP

_{11}-LP

_{11}crosstalk (

*XT*

_{11-11}) at λ = 1550 nm,

*R*= 500 mm, and propagation length (

*L*) = 100 km as function of core pitch. The reason why we set the

*R*to be 500 mm is that this bending radius is much larger than the

*R*

_{pk}, which means that the crosstalk at

*R*of 500-mm is the one in the bend-insensitive situation. In Fig. 9, we can find that

*XT*

_{11-11}is the largest crosstalk of the three kinds of inter-core crosstalk. The

*XT*

_{11-11}of less than −30 dB is realized when the core pitch becomes larger than about 37 µm. Figure 10 illustrates bending radius dependence of

*XT*

_{11-11}at λ = 1550 nm after 100-km propagation when Λ = 37 µm. As shown in Fig. 10, in the case that Λ = 37 µm, when

*R*becomes larger than about 15 cm, the bend-insensitive characteristics of the Hetero-TA-FM-MCF in the practical applications can be guaranteed.

### 3.2 The appropriate core number

*CD*) can be determined by using the formula expressed as follows:where

*N*

_{core}is the number of core and the outer cladding thickness (

*OCT*) is the radial distance between the center of the outer core and the cladding edge. In order to reduce the micro-bending loss, the

*OCT*has different required minimum value corresponding to the different

*A*

_{eff}. Here, we set the

*OCT*to be at least 40 µm [3

3. K. Takenaga, Y. Sasaki, N. Guan, M. Kasahara, K. Saitoh, and M. Koshiba, “Large effective-area few-mode multicore fiber,” IEEE Photon. Technol. Lett. **24**(21), 1941–1944 (2012). [CrossRef]

20. K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fiber with an optimized cladding thickness,” Opt. Express **19**(26), B543–B550 (2011). [CrossRef] [PubMed]

*CD*should not be larger than 225 µm [21

21. S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Taniagwa, K. Saitoh, and M. Koshiba, “Large-effective-area ten-core fiber with cladding diameter of about 200 μm,” Opt. Lett. **36**(23), 4626–4628 (2011). [CrossRef] [PubMed]

*N*

_{core}of 12 is the upper limit and in this case

*CD*is about 223 µm.

*CMF*) for FM-MCF [3

3. K. Takenaga, Y. Sasaki, N. Guan, M. Kasahara, K. Saitoh, and M. Koshiba, “Large effective-area few-mode multicore fiber,” IEEE Photon. Technol. Lett. **24**(21), 1941–1944 (2012). [CrossRef]

*CMF*for Hetero-FM-MCF can be proposed as follows:where

*A*

_{eff-}

*is effective area of*

_{p-m}*m*-th mode in core

*p*,

*A*

_{eff-}

*is effective area of*

_{q-m}*m*-th mode in core

*q*,

*l*is the number of mode,

*CD*

_{FM-MCF}is the cladding diameter of FM-MCF.

*RCMF*is a ratio between

*CMF*of a FM-MCF and a standard single core single mode fiber with

*A*

_{eff}= 80 µm

^{2}at 1550 nm and

*CD*= 125 µm, which is shown asThe

*RCMF*of the two-LP mode Hetero-TA-12-core fiber (whose

*A*

_{eff-1}of LP

_{01}mode and LP

_{11}mode are ~110 µm

^{2}and ~225 µm

^{2};

*A*

_{eff-2}of LP

_{01}mode and LP

_{11}mode are ~110 µm

^{2}and ~219 µm

^{2}) is 15.7. If we use the degenerated LP

_{11}mode as two different special modes thinks to MIMO technology [22

22. S. Randel, R. Ryf, A. H. Gnauck, M. A. Mestre, C. Schmidt, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6×20-GBd QPSK transmission over 1200-km DGD-compensated few-mode fiber,” in *Optical Fiber Communication Conference*, OSA Technical Digest (CD) (Optical Society of America, 2012), paper PDP5C.5. [CrossRef]

*RCMF*can be further enhanced to be 26.1 which exceeds the record value of 14.8 for a two-LP mode seven-core fiber [3

**24**(21), 1941–1944 (2012). [CrossRef]

*N*

_{core}of 12, Λ of 37 µm,

*OCT*of 40 µm,

*CD*of 223 µm,

*RCMF*of 15.7 for 24 special paths, and

*RCMF*of 26.1 for 36 special paths.

*XT*) and

*RCMF*for the reported single-mode MCFs (SM-MCFs) [11

11. J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express **20**(14), 15157–15170 (2012). [CrossRef] [PubMed]

12. J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Optimized design method for bend-insensitive heterogeneous trench-assisted multi-core fiber with ultra-low crosstalk and high core density,” J. Lightwave Technol. **31**(15), 2590–2598 (2013). [CrossRef]

20. K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fiber with an optimized cladding thickness,” Opt. Express **19**(26), B543–B550 (2011). [CrossRef] [PubMed]

21. S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Taniagwa, K. Saitoh, and M. Koshiba, “Large-effective-area ten-core fiber with cladding diameter of about 200 μm,” Opt. Lett. **36**(23), 4626–4628 (2011). [CrossRef] [PubMed]

**24**(21), 1941–1944 (2012). [CrossRef]

_{01}mode, the blue triangles mean the FM-MCFs with LP

_{01}mode and LP

_{11}mode, and the blue squares stand for the FM-MCFs with LP

_{01}mode, LP

_{11a}mode and LP

_{11b}mode. It is obvious that the Hetero-TA-FM-12-core fiber presented in this work has the largest

*RCMF*.

## 4. Conclusion

*a*

_{1}, Δ

_{1},

*r*

_{1}/

*a*

_{1}, Δ

_{d},

*r*

_{2}/

*r*

_{1},

*W/r*

_{1}, and Δ

_{t}. After analyzing how the

*r*

_{2}/

*r*

_{1}and Δ

_{d}affect the DMD and DMD slope for wavelength, we found that as

*r*

_{2}/

*r*

_{1}changes, DMD and DMD slope will alter correspondingly and we can shift the absolute value of Δ

_{d}to compensate the increment or decrement of the DMD and DMD slope. Furthermore, as

*r*

_{2}/

*r*

_{1}increases, the maximum absolute DMD in two TA-MSI-FMCs over C + L band is getting larger but the impact of

*W/r*

_{1}and Δ

_{t}on the DMD will become smaller. As a result,

*r*

_{2}/

*r*

_{1}of 1.6 is regarded as a relative optimum design value since we should make sure not only the low DMD over wide band but also large tolerance of

*W*/

*r*

_{1}and Δ

_{t}.

*R*

_{pk}and decreasing

*A*

_{eff}. In the second strategy, we only use one kind of Hetero-FM-MCF and rotate one to splice different cores together to form DMD-managed transmission line so that the total DMD of almost 0 ps/km can be achieved over C-L band.

*R*

_{pk}, cladding diameter, and

*RCMF*, we can design a kind of two-LP mode Hetero-TA-12-core fiber with

*XT*of about –30 dB/100km at λ of 1550 nm as

*R*becomes larger than 15 cm,

*RCMF*of 15.7 for 24 special paths, and

*RCMF*of 26.1 for 36 special paths. Actually, when the wavelength becomes larger, we can also obtain the low

*XT*by scarifying

*R*

_{pk}and

*RCMF*respectively.

## Acknowledgments

## References and links

1. | S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh, and M. Kosihba, “12-core fiber with one ring structure for extremely large capacity transmission,” Opt. Express |

2. | M. Bigot-Astruc, D. Boivin, and P. Sillard, “Design and fabrication of weakly-coupled few-modes fibers,” in |

3. | K. Takenaga, Y. Sasaki, N. Guan, M. Kasahara, K. Saitoh, and M. Koshiba, “Large effective-area few-mode multicore fiber,” IEEE Photon. Technol. Lett. |

4. | C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. May-Arrioja, A. Schulzgen, M. Richardson, J. Linares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Low-crosstalk few-mode multi-core fiber for high-mode-density space-division multiplexing,” in |

5. | R. Maruyama, N. Kuwaki, S. Matuo, K. Sato, and M. Ohashi, “Mode dispersion compensating optical transmission line composed of two-mode optical fibers,” in |

6. | T. Sakamoto, T. Mori, T. Yamamoto, and S. Tomita, “Differential mode delay managed transmission line for wide-band WDM-MIMO system,” in |

7. | M. Li, E. Ip, and Y. Huang, “Large effective area FMF with low DMGD,” in |

8. | K. Sato, R. Maruyama, N. Kuwaki, S. Matsuo, and M. Ohashi, “Optimized graded index two-mode optical fiber with low DMD, large A |

9. | T. Mori, T. Sakamoto, M. Wada, T. Yamamoto, and F. Yamamoto, “Low DMD four LP mode transmission fiber for wide-band WDM-MIMO system,” in |

10. | R. Maruyama, N. Kuwaki, S. Matsuo, K. Sato, and M. Ohashi, “DMD free transmission line composed of TMFs with large effective area for MIMO processing,” in |

11. | J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express |

12. | J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Optimized design method for bend-insensitive heterogeneous trench-assisted multi-core fiber with ultra-low crosstalk and high core density,” J. Lightwave Technol. |

13. | T. Sakamoto, T. Mori, T. Yamamoto, and S. Tomita, “Differential mode delay managed transmission line for WDM-MIMO system using multi-step index fiber,” J. Lightwave Technol. |

14. | Y. Sasaki, Y. Amma, K. Takenaga, S. Matsuo, K. Saitoh, and M. Koshiba, “Investigation of crosstalk dependencies on bending radius of heterogeneous multicore fiber,” in |

15. | K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. |

16. | T. Matsui, K. Nakajima, and C. Fukai, “Applicability of photonic crystal fiber with uniform air-hole structure to high-speed and wide-band transmission over conventional telecommunication bands,” J. Lightwave Technol. |

17. | T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fiber due to fiber bend,” in |

18. | K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by trench-assisted multi-core fiber,” in |

19. | B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “112-Tb/s Space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber,” Opt. Express |

20. | K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, and M. Koshiba, “A large effective area multi-core fiber with an optimized cladding thickness,” Opt. Express |

21. | S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Taniagwa, K. Saitoh, and M. Koshiba, “Large-effective-area ten-core fiber with cladding diameter of about 200 μm,” Opt. Lett. |

22. | S. Randel, R. Ryf, A. H. Gnauck, M. A. Mestre, C. Schmidt, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6×20-GBd QPSK transmission over 1200-km DGD-compensated few-mode fiber,” in |

**OCIS Codes**

(060.2270) Fiber optics and optical communications : Fiber characterization

(060.2280) Fiber optics and optical communications : Fiber design and fabrication

**ToC Category:**

Fiber Optics

**History**

Original Manuscript: December 20, 2013

Revised Manuscript: February 5, 2014

Manuscript Accepted: February 6, 2014

Published: February 18, 2014

**Citation**

Jiajing Tu, Kunimasa Saitoh, Katsuhiro Takenaga, and Shoichiro Matsuo, "Heterogeneous trench-assisted few-mode multi-core fiber with low differential mode delay," Opt. Express **22**, 4329-4341 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-4329

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### References

- S. Matsuo, Y. Sasaki, T. Akamatsu, I. Ishida, K. Takenaga, K. Okuyama, K. Saitoh, M. Kosihba, “12-core fiber with one ring structure for extremely large capacity transmission,” Opt. Express 20(27), 28398–28408 (2012). [CrossRef] [PubMed]
- M. Bigot-Astruc, D. Boivin, and P. Sillard, “Design and fabrication of weakly-coupled few-modes fibers,” in IEEE Photonics Society Summer Topical Meetings (2012), paper TuC1.1.
- K. Takenaga, Y. Sasaki, N. Guan, M. Kasahara, K. Saitoh, M. Koshiba, “Large effective-area few-mode multicore fiber,” IEEE Photon. Technol. Lett. 24(21), 1941–1944 (2012). [CrossRef]
- C. Xia, R. Amezcua-Correa, N. Bai, E. Antonio-Lopez, D. May-Arrioja, A. Schulzgen, M. Richardson, J. Linares, C. Montero, E. Mateo, X. Zhou, and G. Li, “Low-crosstalk few-mode multi-core fiber for high-mode-density space-division multiplexing,” in European Conference and Exhibition on Optical Communication (ECOC) (Optical Society of America, Washington, DC, 2012), paper Mo.1.F.5.
- R. Maruyama, N. Kuwaki, S. Matuo, K. Sato, and M. Ohashi, “Mode dispersion compensating optical transmission line composed of two-mode optical fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper JW2A.13.
- T. Sakamoto, T. Mori, T. Yamamoto, and S. Tomita, “Differential mode delay managed transmission line for wide-band WDM-MIMO system,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper OM2D.1. [CrossRef]
- M. Li, E. Ip, and Y. Huang, “Large effective area FMF with low DMGD,” in IEEE Photonics Society Summer Topical Meetings (2013), paper MC3.4.
- K. Sato, R. Maruyama, N. Kuwaki, S. Matsuo, M. Ohashi, “Optimized graded index two-mode optical fiber with low DMD, large Aeff and low bending loss,” Opt. Express 21(14), 16231–16238 (2013). [CrossRef] [PubMed]
- T. Mori, T. Sakamoto, M. Wada, T. Yamamoto, and F. Yamamoto, “Low DMD four LP mode transmission fiber for wide-band WDM-MIMO system,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2013), paper OTh3K.1. [CrossRef]
- R. Maruyama, N. Kuwaki, S. Matsuo, K. Sato, and M. Ohashi, “DMD free transmission line composed of TMFs with large effective area for MIMO processing,” in European Conference and Exhibition on Optical Communication (ECOC) (Optical Society of America, Washington, DC, 2012), paper Tu.1.F.2. [CrossRef]
- J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express 20(14), 15157–15170 (2012). [CrossRef] [PubMed]
- J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, S. Matsuo, “Optimized design method for bend-insensitive heterogeneous trench-assisted multi-core fiber with ultra-low crosstalk and high core density,” J. Lightwave Technol. 31(15), 2590–2598 (2013). [CrossRef]
- T. Sakamoto, T. Mori, T. Yamamoto, S. Tomita, “Differential mode delay managed transmission line for WDM-MIMO system using multi-step index fiber,” J. Lightwave Technol. 30(17), 2783–2787 (2012). [CrossRef]
- Y. Sasaki, Y. Amma, K. Takenaga, S. Matsuo, K. Saitoh, and M. Koshiba, “Investigation of crosstalk dependencies on bending radius of heterogeneous multicore fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2013), paper OTh3K.3. [CrossRef]
- K. Saitoh, M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. 38(7), 927–933 (2002). [CrossRef]
- T. Matsui, K. Nakajima, C. Fukai, “Applicability of photonic crystal fiber with uniform air-hole structure to high-speed and wide-band transmission over conventional telecommunication bands,” J. Lightwave Technol. 27(23), 5410–5416 (2009). [CrossRef]
- T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fiber due to fiber bend,” in Proceedings of 36th European Conference and Exhibition on Optical Communication (Institute of Electrical and Electronics Engineers, 2010), paper We.8.F.6. [CrossRef]
- K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by trench-assisted multi-core fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWJ4. [CrossRef]
- B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, F. V. Dimarcello, “112-Tb/s Space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber,” Opt. Express 19(17), 16665–16671 (2011). [CrossRef] [PubMed]
- K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh, M. Koshiba, “A large effective area multi-core fiber with an optimized cladding thickness,” Opt. Express 19(26), B543–B550 (2011). [CrossRef] [PubMed]
- S. Matsuo, K. Takenaga, Y. Arakawa, Y. Sasaki, S. Taniagwa, K. Saitoh, M. Koshiba, “Large-effective-area ten-core fiber with cladding diameter of about 200 μm,” Opt. Lett. 36(23), 4626–4628 (2011). [CrossRef] [PubMed]
- S. Randel, R. Ryf, A. H. Gnauck, M. A. Mestre, C. Schmidt, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6×20-GBd QPSK transmission over 1200-km DGD-compensated few-mode fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper PDP5C.5. [CrossRef]

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