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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 12 — Jun. 17, 2013
  • pp: 14262–14271
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Achievable capacity improvement by using multi-level modulation format in trench-assisted multi-core fiber system

J. H. Chang, H. G. Choi, and Y. C. Chung  »View Author Affiliations


Optics Express, Vol. 21, Issue 12, pp. 14262-14271 (2013)
http://dx.doi.org/10.1364/OE.21.014262


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Abstract

We evaluate the impacts of using multi-level modulation formats on the transmission capacity of the multi-core fiber (MCF) having trench-assisted index profile and hexagonal layout. For this evaluation, we utilize the spectral efficiency per unit area, defined as the spatial spectral efficiency (SSE). The results show that the SSE improvement achievable by using the higher-level modulation format can be reduced due to its lower tolerance to the inter-core crosstalk. We also evaluate the effects of using large effective area on the transmission capacity of the trench-assisted MCF. The results show that the use of large effective area can decrease this capacity due to the increased inter-core crosstalk and lengthened cable cutoff wavelength, although it can help increase the transmission distance. Thus, it is necessary to optimize the effective area of MCF by considering both the SSE and transmission distance. However, the results indicate that the effect of using different effective areas on the SSE-distance product is not significant, and it is not useful to increase the effective area of the trench-assisted MCF to be larger than ~110 μm2.

© 2013 OSA

1. Introduction

To overcome the imminent capacity limit of the conventional single-mode fiber (SMF), there have recently been many efforts to realize the space-division-multiplexing (SDM) technology [1

1. S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle Jr., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19(17), 16697–16707 (2011). [CrossRef] [PubMed]

4

4. J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Proc. Optical Fiber Commun. Conf. (OFC) (2011), paper PDP5C.1.

]. In particular, there have been many attempts to develop the multi-core fiber (MCF) in the hope of increasing the capacity of a single strand of fiber in proportion to the number of cores used in it [2

2. T. Morioka, “New generation optical infrastructure technologies:“EXAT initiative” towards 2020 and beyond,” in Proc. OptoElectron. Commun. Conf. (OECC) (2009), paper FT4.

4

4. J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Proc. Optical Fiber Commun. Conf. (OFC) (2011), paper PDP5C.1.

]. In order to maximize the capacity of MCF, it is necessary to increase the core density per unit area. However, as we reduce the inter-core distance, the inter-core crosstalk is increased. This increased crosstalk can hinder the use of the spectrally efficient high-level modulation format, which is also critical to maximize the capacity of MCF, since the higher-level modulation format is more sensitive to the crosstalk. Thus, the capacity of MCF may not be maximized simply by reducing the inter-core distance to increase the core density. In principle, this problem can be solved by using the multiple-input multiple-output (MIMO) signal processing technique [5

5. R. Ryf, R.-J. Essiambre, S. Randel, A. H. Gnauck, P. J. Winzer, T. Hayashi, T. Taru, and T. Sasaki, “MIMO-based crosstalk suppression in spatially multiplexed 3x56-Gb/s PDM-QPSK signals for strongly coupled three-core fiber,” IEEE Photon. Technol. Lett. 23(20), 1469–1471 (2011). [CrossRef]

]. However, this technique requires the use of heavy computational resources. In addition, in the all-optical networks implemented with a large number of optical add/drop multiplexers, it may be difficult to solve this inter-core crosstalk problem by using MIMO technique. This is because, in such a network, the received signals can be contaminated with different inter-core crosstalk components originating from different sections of the MCF link.

The performances of the high-speed optical signals in the MCF transmission system can also be affected by the fiber nonlinearities, as in the conventional SMF system. It is well known that the higher-level modulation format is more vulnerable to these nonlinearities. Thus, to facilitate the use of the high-level format in the MCF system, one may think that it is desirable to increase the effective area of each core. However, as we increase the effective area, the inter-core crosstalk can also be increased due to the increased mode-field diameter (MFD) [6

6. T. Hayashi, T. Sasaki, and E. Sasaoka, “Multi-core fibers for high capacity transmission,” in Proc. Optical Fiber Commun. Conf. (OFC) (2012), paper OTu1D4. [CrossRef]

]. As a result, the capacity of MCF may not be increased as expected by increasing the effective area of each core.

In this paper, we evaluate the impacts of using the high-level modulation formats on the capacity of MCF. In this evaluation, we assume that a weakly coupled MCF fabricated with a trench-assisted index profile is used as a transmission fiber. We then evaluate the effects of the inter-core crosstalk on the performances of the SDM signals modulated in various types of multi-level formats such as the quadrature phase-shift keying (QPSK), 16 quadrature amplitude modulation (16QAM), and 64QAM. As expected, it is necessary to increase the inter-core distance (and sacrifice the spatial efficiency) for the utilization of the higher-level format due to its lower tolerance to the inter-core crosstalk. Thus, we evaluate the spectral efficiency (SE) per unit area, defined as the spatial spectral efficiency (SSE), achievable by using each modulation format. The results show that the SSE of the 100-km long MCF transmission system can be increased by a factor of only ~2.3 by using the 64QAM format instead of the QPSK format, while it is 3 in the conventional SMF system. This improvement is further reduced as the transmission distance is increased. We also estimate the impacts of increasing the effective area of each core on the SSE of MCF. For this purpose, we assume the use of MCFs having various effective areas in the range of 75 ~130 μm2, and estimate the SSE improvement achievable by using the high-level formats. The results show that the use of the large effective area in the MCF is not as efficacious as in the conventional SMF for increasing the fiber capacity, since it increases the cable cutoff wavelength as well as the inter-core crosstalk.

2. Minimum core pitch of MCF required for the transmission of multi-level signals

The most important sources of the performance degradation in the MCF transmission system are the inter-core crosstalk and fiber nonlinearities. Thus, the MCF should be designed to avoid these problems. Recently, it has been reported that the MCF with trench-assisted index profile is quite effective in satisfying these requirements compared to the one with step-index profile [4

4. J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Proc. Optical Fiber Commun. Conf. (OFC) (2011), paper PDP5C.1.

], [6

6. T. Hayashi, T. Sasaki, and E. Sasaoka, “Multi-core fibers for high capacity transmission,” in Proc. Optical Fiber Commun. Conf. (OFC) (2012), paper OTu1D4. [CrossRef]

10

10. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-loss and large-Aeff multi-core fiber for SNR enhancement,” in Proc. European Conf. on Opt. Commun. (ECOC) (2012), paper Mo.1.F.3.

]. Thus, we first focused our evaluation on such a MCF described in [7

7. K. Takenaga, T. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by trench-assisted multi-core fiber,” in Proc. Optical Fiber Commun. Conf. (OFC) (2011), paper OWJ4. [CrossRef]

]. Figure 1
Fig. 1 Refractive-index profile of the trench-assisted MCF.
shows the index profile of the trench-assisted MCF. The geometrical parameters of this MCF, d1, d2, d3, Δ1, and Δ2 were 8.2 µm, 18.3 µm, 26.5 µm, 0.38%, and −0.65%, respectively. Accordingly, we assumed that the effective area, chromatic dispersion, and dispersion slope of each core in the MCF were 75 µm2, 18 ps/nm/km, and 0.09 ps/nm2/km, respectively, at the wavelength of 1550 nm.

To estimate the inter-core crosstalk level, we initially evaluated the coupling coefficient between two cores in the MCF as a function of the core pitch by using the full-vector beam propagation method (BPM). We then calculated the crosstalk level under the bending condition [9

9. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express 19(17), 16576–16592 (2011). [CrossRef] [PubMed]

], [11

11. M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” IEEE Photon. J. 4(5), 1987–1995 (2012). [CrossRef]

,12

12. T. Hayashi, T. Sasaki, E. Sasaoka, K. Saitoh, and M. Koshiba, “Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend,” Opt. Express 21(5), 5401–5412 (2013). [CrossRef] [PubMed]

]. In this calculation, we assumed that the bending radius was 100 mm and the signal’s wavelength was either 1550 nm or 1625 nm. Figure 2
Fig. 2 Inter-core crosstalk level estimated as a function of the core pitch in the MCF with trench-assisted index profile [7]. The operating wavelength was assumed to be either 1550 nm or 1625 nm.
shows the crosstalk level at the core surrounded by six other cores (i.e., the worst case) calculated as a function of the core pitch for a homogeneous MCF with hexagonal layout. In this figure, the inter-core crosstalk in the y-axis represents the sum of the mean crosstalk from six neighboring cores. It should be noted that, when the MCF was designed to have multiple cores in the hexagonal layout, the crosstalk from other than these six cores in the most proximate layer could be neglected. The results also show that the inter-core crosstalk becomes larger by ~10 dB at 1625 nm than the value at 1550 nm due to the larger MFD at the longer wavelength. We confirmed that these values were similar to those reported in [7

7. K. Takenaga, T. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by trench-assisted multi-core fiber,” in Proc. Optical Fiber Commun. Conf. (OFC) (2011), paper OWJ4. [CrossRef]

].

Using this model, we estimated the required OSNR to achieve the BER better than the forward-error correction (FEC) limit (i.e., BER = 3.8x10−3) as a function of the inter-core crosstalk level in the 100-km and 1000-km long MCF links. Figure 4
Fig. 4 Required OSNRs to achieve the BER better than the FEC limit (i.e., BER = 3.8x10−3) as a function of the inter-core crosstalk for various modulation formats such as PDM-QPSK, PDM-16QAM and PDM-64QAM. The transmission distance was either 100 km or 1000 km.
shows the results. As we increased the crosstalk level, the required OSNR was also increased regardless of the modulation format. However, after the inter-core crosstalk reached a certain level, it was no longer possible to achieve the BER below the FEC limit even if we further increased the signal’s power (i.e., OSNR) due to the effects of fiber nonlinearities. From this result, we obtained the maximum allowable crosstalk level for each modulation format (shown by the vertical dotted lines in Fig. 4). This crosstalk level was used to compare the effects of using various multi-level formats on the achievable capacity of MCF. As expected, the higher-level modulation format had worse tolerance to the crosstalk. Using the results in Figs. 2 and 4, we estimated the minimum core pitches required to achieve the BER better than the FEC limit using various modulation formats. However, it should be noted that the larger core pitch is required to accommodate the signals operating at the longer wavelengths. Thus, it is necessary to design the core pitch to be large enough to support the longest wavelength used in the MCF. In this estimation, we assumed that the longest wavelength was 1625 nm (i.e., the upper limit of the L-band). The results showed that, when the transmission distance was 100 km, the required core pitches were 34.0, 35.8, and 38.7 µm for the QPSK, 16QAM and 64QAM signals, respectively. However, when we extended the transmission distance to 1000 km, these values were increased to 37.3 and 40.2 µm for the QPSK and 16QAM signals, respectively. It was not possible to transmit the 64QAM signal over 1000 km even in the absence of the inter-core crosstalk due to its high OSNR requirement.

3. Achievable spatial spectral efficiency of MCF transmission system

We also investigated the dependency of the achievable SSE on the transmission distance in the MCF link. For this purpose, we evaluated the SSE as a function of the number of spans. In this evaluation, every data was calculated by using its optimum launch power. For example, when the transmission distance was 1000 km, the optimum launch powers for the QPSK and 16QAM signals were 0 dBm and −2 dBm, respectively. Figure 5(b) shows the results. In this figure, we included the SSEs of the conventional SMF (i.e., cladding diameter: 125 μm) as references. As we increased the transmission distance of the MCF link, the inter-core crosstalk was accumulated as well as the amplified spontaneous emission (ASE) noises. Thus, to achieve the BER better than the FEC limit even after the long-distance transmission, it was necessary to utilize a large core pitch (which would inevitably reduce the spatial efficiency). As a result, the SSE was gradually deteriorated with the transmission distance. However, we noted that the SSE of the higher-level signal was deteriorated more rapidly than that of the lower-level signal. For example, in the case of using the QPSK signals, the core pitch should be increased from 34.0 μm to 37.3 μm to achieve the BER performance better than the FEC limit even after increasing the transmission distance from 100 km to 1000 km. However, in the case of using the 16QAM signals, the core pitch should be increased from 35.8 μm to 40.2 μm for the same purpose. These results indicated that the SSE improvement achievable by using the higher-level format deteriorated more rapidly with the increased transmission distance. For example, in the case of the 100-km long MCF link, the SSE could be improved by ~80% by using the 16QAM signals instead of the QPSK signals, regardless of the number of cores. However, this SSE improvement was reduced to ~53% when the transmission distance was increased to 1400 km.

4. Impact of increased effective area on the SSE of trench-assisted MCF

In the conventional SMF transmission system, the limitations imposed by fiber nonlinearities can be mitigated by increasing the fiber’s effective area. However, when the MCF is used, the inter-core crosstalk can also be increased as we increase the effective area of each core. Thus, the capacity of MCF may not be increased as expected by increasing its effective area. To resolve this problem and evaluate the effects of the increased effective area on the SSE of the MCF, we considered three types of MCFs having the trench-assisted index profile. Table 1

Table 1. Parameters of various trench-assisted MCFs

table-icon
View This Table
shows the parameters of these MCFs as well as their resulting effective areas. We designated the MCFs having the effective areas of 75 µm2, 110 µm2, and 130 µm2 as MCF A, MCF B, and MCF C, respectively. MCF A and MCF B were identical to the MCFs reported in [7

7. K. Takenaga, T. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by trench-assisted multi-core fiber,” in Proc. Optical Fiber Commun. Conf. (OFC) (2011), paper OWJ4. [CrossRef]

,8

8. 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]

], and MCF C was similar to the MCF reported in [10

10. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-loss and large-Aeff multi-core fiber for SNR enhancement,” in Proc. European Conf. on Opt. Commun. (ECOC) (2012), paper Mo.1.F.3.

]. Figure 6(a)
Fig. 6 (a) Inter-core crosstalk level estimated as a function of the core pitch for three types of 7-core MCFs. The operating wavelength and transmission distance were assumed to be 1625 nm and 100 km, respectively. (b) Cable cutoff wavelength as a function of the core pitch for three types of 7-core MCFs.
shows the inter-core crosstalk levels calculated as a function of the core pitch for these MCFs. In this calculation, the signal’s wavelength was assumed to be 1625 nm. The results showed that, if we utilized MCF B and MCF C instead of MCF A, the core pitch should be increased by ~1 µm and ~7 µm, respectively, to maintain the crosstalk to be <-20 dB.

It would be highly desirable if we could optimize the design of the trench-assisted MCF to have the large effective area, low inter-core crosstalk, and acceptable cable cutoff wavelength simultaneously. However, it appears to be a difficult task. In order to suppress the inter-core crosstalk in the trench-assisted MCF, it was necessary to increase the index difference of the trench. However, this increased index difference of the trench could also increase the effective index difference between the core and cladding and, as a result, reduce the effective area. We could of course suppress the inter-core crosstalk without this problem by increasing the width of the trench or the spacing between the core and trench layer. However, in this case, the cable cutoff wavelengths of the neighboring cores could be increased. Thus, there was a trade-off between the inter-core crosstalk and the cable cutoff wavelength for the design of the MCF having large effective area. In other words, the spatial efficiency improvement achievable by designing the MCF to have low inter-core crosstalk (i.e., by increasing the width of the trench) could be negated by the increased core pitch required to support the shortest wavelength used in the system. Thus, we concluded that the optimum effective area for maximizing the SSE-distance product was ~110 μm2 for the trench-assisted MCF.

5. Summary

Acknowledgment

This work was supported by the IT R&D program of MKE/KEIT (10043383, Research of mode-division-multiplexing optical transmission technology over 10 km multi-mode fiber).

References and links

1.

S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle Jr., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19(17), 16697–16707 (2011). [CrossRef] [PubMed]

2.

T. Morioka, “New generation optical infrastructure technologies:“EXAT initiative” towards 2020 and beyond,” in Proc. OptoElectron. Commun. Conf. (OECC) (2009), paper FT4.

3.

T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. Mag. 50(2), S31–S42 (2012). [CrossRef]

4.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Proc. Optical Fiber Commun. Conf. (OFC) (2011), paper PDP5C.1.

5.

R. Ryf, R.-J. Essiambre, S. Randel, A. H. Gnauck, P. J. Winzer, T. Hayashi, T. Taru, and T. Sasaki, “MIMO-based crosstalk suppression in spatially multiplexed 3x56-Gb/s PDM-QPSK signals for strongly coupled three-core fiber,” IEEE Photon. Technol. Lett. 23(20), 1469–1471 (2011). [CrossRef]

6.

T. Hayashi, T. Sasaki, and E. Sasaoka, “Multi-core fibers for high capacity transmission,” in Proc. Optical Fiber Commun. Conf. (OFC) (2012), paper OTu1D4. [CrossRef]

7.

K. Takenaga, T. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by trench-assisted multi-core fiber,” in Proc. Optical Fiber Commun. Conf. (OFC) (2011), paper OWJ4. [CrossRef]

8.

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]

9.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express 19(17), 16576–16592 (2011). [CrossRef] [PubMed]

10.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-loss and large-Aeff multi-core fiber for SNR enhancement,” in Proc. European Conf. on Opt. Commun. (ECOC) (2012), paper Mo.1.F.3.

11.

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” IEEE Photon. J. 4(5), 1987–1995 (2012). [CrossRef]

12.

T. Hayashi, T. Sasaki, E. Sasaoka, K. Saitoh, and M. Koshiba, “Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend,” Opt. Express 21(5), 5401–5412 (2013). [CrossRef] [PubMed]

13.

P. J. Winzer, A. H. Gnauck, A. Konczykowska, F. Jorge, and J.-Y. Dupuy, “Penalties from in-band crosstalk for advanced optical modulation formats,” in Proc. European Conf. on Opt. Commun. (ECOC) (2011), paper Tu.5.B.7. [CrossRef]

14.

K.-P. Ho, “Effects of homodyne crosstalk on dual-polarization QPSK signals,” IEEE J. Lightw. Technol. 29(1), 124–131 (2011). [CrossRef]

15.

S. Mumtaz, R.-J. Essiambre, and G. P. Agrawal, “Reduction of nonlinear penalties due to linear coupling in multicore optical fibers,” IEEE Photon. Technol. Lett. 24(18), 1574–1576 (2012). [CrossRef]

16.

P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” IEEE J. Lightw. Technol. 28(4), 547–556 (2010). [CrossRef]

17.

B. Zhu, J. M. Fini, M. F. Yan, X. Liu, S. Chandrasekhar, T. F. Taunay, M. Fishteyn, E. M. Monberg, and F. V. Dimarcello, “High-capacity space-division-multiplexed DWDM transmissions using multicore fiber,” J. Lightwave Technol. 30(4), 486–492 (2012). [CrossRef]

18.

S. Chandrasekhar, A. H. Gnauck, X. Liu, P. J. Winzer, Y. Pan, E. C. Burrows, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “WDM/SDM transmission of 10 x 128-Gb/s PDM-QPSK over 2688-km 7-core fiber with a per-fiber net aggregate spectral-efficiency distance product of 40,320 km·b/s/Hz,” Opt. Express 20(2), 706–711 (2012). [CrossRef] [PubMed]

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4080) Fiber optics and optical communications : Modulation

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: March 18, 2013
Revised Manuscript: May 4, 2013
Manuscript Accepted: May 27, 2013
Published: June 7, 2013

Citation
J. H. Chang, H. G. Choi, and Y. C. Chung, "Achievable capacity improvement by using multi-level modulation format in trench-assisted multi-core fiber system," Opt. Express 21, 14262-14271 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-14262


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References

  1. S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express19(17), 16697–16707 (2011). [CrossRef] [PubMed]
  2. T. Morioka, “New generation optical infrastructure technologies:“EXAT initiative” towards 2020 and beyond,” in Proc. OptoElectron. Commun. Conf. (OECC) (2009), paper FT4.
  3. T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. Mag.50(2), S31–S42 (2012). [CrossRef]
  4. J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Proc. Optical Fiber Commun. Conf. (OFC) (2011), paper PDP5C.1.
  5. R. Ryf, R.-J. Essiambre, S. Randel, A. H. Gnauck, P. J. Winzer, T. Hayashi, T. Taru, and T. Sasaki, “MIMO-based crosstalk suppression in spatially multiplexed 3x56-Gb/s PDM-QPSK signals for strongly coupled three-core fiber,” IEEE Photon. Technol. Lett.23(20), 1469–1471 (2011). [CrossRef]
  6. T. Hayashi, T. Sasaki, and E. Sasaoka, “Multi-core fibers for high capacity transmission,” in Proc. Optical Fiber Commun. Conf. (OFC) (2012), paper OTu1D4. [CrossRef]
  7. K. Takenaga, T. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by trench-assisted multi-core fiber,” in Proc. Optical Fiber Commun. Conf. (OFC) (2011), paper OWJ4. [CrossRef]
  8. 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. Express19(26), B543–B550 (2011). [CrossRef] [PubMed]
  9. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express19(17), 16576–16592 (2011). [CrossRef] [PubMed]
  10. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Low-loss and large-Aeff multi-core fiber for SNR enhancement,” in Proc. European Conf. on Opt. Commun. (ECOC) (2012), paper Mo.1.F.3.
  11. M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” IEEE Photon. J.4(5), 1987–1995 (2012). [CrossRef]
  12. T. Hayashi, T. Sasaki, E. Sasaoka, K. Saitoh, and M. Koshiba, “Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend,” Opt. Express21(5), 5401–5412 (2013). [CrossRef] [PubMed]
  13. P. J. Winzer, A. H. Gnauck, A. Konczykowska, F. Jorge, and J.-Y. Dupuy, “Penalties from in-band crosstalk for advanced optical modulation formats,” in Proc. European Conf. on Opt. Commun. (ECOC) (2011), paper Tu.5.B.7. [CrossRef]
  14. K.-P. Ho, “Effects of homodyne crosstalk on dual-polarization QPSK signals,” IEEE J. Lightw. Technol.29(1), 124–131 (2011). [CrossRef]
  15. S. Mumtaz, R.-J. Essiambre, and G. P. Agrawal, “Reduction of nonlinear penalties due to linear coupling in multicore optical fibers,” IEEE Photon. Technol. Lett.24(18), 1574–1576 (2012). [CrossRef]
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