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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 9 — May. 6, 2013
  • pp: 10801–10809
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Impact of power allocation strategies in long-haul few-mode fiber transmission systems

Danish Rafique, Stylianos Sygletos, and Andrew D. Ellis  »View Author Affiliations


Optics Express, Vol. 21, Issue 9, pp. 10801-10809 (2013)
http://dx.doi.org/10.1364/OE.21.010801


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Abstract

We report for the first time on the limitations in the operational power range of few-mode fiber based transmission systems, employing 28Gbaud quadrature phase shift keying transponders, over 1,600km. It is demonstrated that if an additional mode is used on a preexisting few-mode transmission link, and allowed to optimize its performance, it will have a significant impact on the pre-existing mode. In particular, we show that for low mode coupling strengths (weak coupling regime), the newly added variable power mode does not considerably impact the fixed power existing mode, with performance penalties less than 2dB (in Q-factor). On the other hand, as mode coupling strength is increased (strong coupling regime), the individual launch power optimization significantly degrades the system performance, with penalties up to ~6dB. Our results further suggest that mutual power optimization, of both fixed power and variable power modes, reduces power allocation related penalties to less than 3dB, for any given coupling strength, for both high and low differential mode delays.

© 2013 OSA

1. Introduction

With the ever increasing demand for high information rates and current advances in bandwidth intense user-end applications (online gaming, ubiquitous video, etc.), the available transmission capacity for single mode optical fiber is exhausting at a very fast rate, and radical solutions are now sought in order to be able to keep up with rapidly growing traffic demand. One of the solutions to enable significant capacity scale-up is space division multiplexing, or spatial multiplexing [1

1. R. Essiambre and A. Mecozzi, “Capacity limits in single mode fiber and scaling for spatial multiplexing,” Optical Fiber Communication Conference, OFC ‘12, OW3D.1, (2012).

3

3. E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, S. Bickham, H. Tam, C. Lu, M. Li, S. Ten, A. P. T. Lau, V. Tse, G. Peng, C. Montero, X. Prieto, and G. Li, “88x3x112-Gb/s WDM transmission over 50-km of three-Mode fiber with inline multimode fiber amplifier,” European Conference on Optical Communication, ECOC’11, Th.13.C.2, (2011).

]. Spatial multiplexing increases transmission capacity by multiplexing several data signals in the cores of multicore fibers (MCFs) [4

4. T. Hayashi, T. Sasaki, and E. Sasaoka, “Multi-core fibers for high capacity transmission,” Optical Fiber Communication Conference, OFC ‘12, OTu1D.4, (2012).

] or in the modes of multimode fibers (MMFs), in which case, it is often called mode-division multiplexing (MDM) [5

5. S. Randel, R. Ryf, A. Gnauck, M. A. Mestre, C. Schmidt, R. Essiambre, P. 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,” Optical Fiber Communication Conference, OFC ‘12, PDP5C.5, (2012).

].

While MDM solutions enable high capacity growth, these systems present complex trade-offs to system designers. One such challenge is associated with linear and nonlinear mode coupling effects, which strongly connect the achieved capacity to the achievable transmission distance [6

6. A. Mecozzi, C. Antonelli, and M. Shtaif, “Nonlinear propagation in multi-mode fibers in the strong coupling regime,” Opt. Express 20(11), 11673–11678 (2012). [CrossRef] [PubMed]

8

8. N. MacSuibhne, R. Watts, S. Sygletos, F. C. G. Gunning, L. GrüNernielsen, and A. D. Ellis, “Nonlinear pulse distortion in few-mode fiber,” European Conference on Optical Communication, ECOC’12, Th.2.F.5, (2012).

]. Index perturbations in fibers, whether intended or not, can induce coupling between signals in different modes, and can cause propagating fields to evolve randomly. Mode coupling can significantly impact the transmission performance in several ways, i.e. crosstalk between spatially multiplexed signals, end-to-end group delay spread of signals, mode dependent loss/gain, etc [9

9. J. M. Kahn, K. Ho, and M. B. Shemirani, “Mode coupling effects in multi-mode fibers,” Optical Fiber Communication Conference, OFC ‘12, OW3D.3, (2012).

]. Recently, a few preliminary reports analyzing propagation impairments considering both linear [10

10. J. Vuong, P. Ramantanis, A. Seck, D. Bendimerad, and Y. Frignac, “Understanding discrete linear mode coupling in few-mode fiber transmission systems,” European Conference on Optical Communication, ECOC’11, Tu5B2, (2011).

] and nonlinear coupling [6

6. A. Mecozzi, C. Antonelli, and M. Shtaif, “Nonlinear propagation in multi-mode fibers in the strong coupling regime,” Opt. Express 20(11), 11673–11678 (2012). [CrossRef] [PubMed]

] have been reported, however the recent developments in spatially multiplexed systems demand not only a deeper and clearer understanding of coupling effects, but also their impact on system design choices.

2. Simulation model

The transmission system comprised of two 28Gbaud QPSK transponders, for each of the two emulated bi-modal fibers. For each fiber, independent de-correlated De Bruijin bit sequences (DBBS) of length 214, with different random number seeds were used. Each DBBS was coded into two two-level output symbol stream, optically modulated as an in-phase and a quadrature phase carrier using a continuous wave laser source (1550nm) and a nested Mach-Zehnder Modulator structure. After modulation the two modes were combined using an ideal mode multiplexer (inter mode crosstalk at the transmitter was neglected). The simulation conditions ensured 16 samples per symbol with 213 (8192) total simulated symbols per mode, corresponding to a total 32,768 bits (one detected error corresponding to a bit error rate of 3x10−5). As an initial condition the modes had the same average power level. For simplicity we also neglected polarization mode dispersion and laser line-width in this paper.

The mode division multiplexed signal was propagated over a few-mode fiber. The linear mode coupling effects in a few-mode fiber are well described by traditional coupled mode theory [13

13. D. Marcuse, Theory of Dielectric Optical Waveguides chapters 3&5, (New York: Academic, 1974).

, 15

15. G. Agrawal, Applications of nonlinear Fibre Optics chapter 2, (Academic Press, 2001).

], applied on a simplified model of the optical fiber that assumes step index waveguide geometry with a sinusoidal deformation of the radius at the core-cladding interface. Following the corresponding derivation process in [15

15. G. Agrawal, Applications of nonlinear Fibre Optics chapter 2, (Academic Press, 2001).

] and accounting for nonlinearity through the introduction of inter and intra mode effective areas, it is found that the slowly varying field envelopesAm(z,t), with m=1,2 of two co-polarized optical modes, defined with respect to a common rapidly varying part ofexp[i(ωtβz)], are governed in the time domain by the following set of coupled propagation equations:

A1ziδaA1+1vg1A1tiβ2122A1t2+α2=iκA2in2ωc(f11|A1|2+2f12|A2|2)A1
(1)
A2z+iδaA2+1vg2A2tiβ2222A2t2+α2=iκA1in2ωc(f22|A2|2+2f21|A1|2)A2
(2)

where the parameters ofβ=(β01+β02)/2and δa=(β01β02)/2have been introduced with β0m representing the propagation constant of the mth mode. Also,vgm=1/β1mrepresents the group velocity, β2m the group-velocity dispersion (GVD),α is the loss coefficient,n2the nonlinear refractive index and c the speed of light. The linear and nonlinear coupling mechanisms appear on the right-hand side of the above equations. The coupling coefficient κ introduces a periodic exchange of optical power between the two co-propagating modes. The maximum ratio of optical power that is transferred from the one to the other mode is defined by the coupling strength factorF=κ2/(κ2+δa2), and occurs within a coupling length ofLe=π/2κ2+δa2. On the other hand, the nonlinear interactions due to Kerr effect can occur either within the same mode or between different modes, and their relative magnitude is governed by the overlapping integralfpq:

fpq=|Fp(x,y)|2|Fq(x,y)|2dxdy|Fp(x,y)|2dxdy|Fq(x,y)|2dxdy
(3)

3. Results and discussions

Figure 2 illustrates the performance in Q-factor after a total transmission distance of 1,600km for high DMD fiber, where the power of one mode was first optimized in single mode transmission (approximately 1dBm in both cases), and then the power of the second mode was swept (a case of both individual and mutual power optimization). It can be seen that as the launch power of the second mode is varied, the transmission performance is initially limited by optical signal-to-noise ratio (OSNR), and reaches an optimum power (also known as nonlinear threshold – NLT), beyond which performance is degraded due to nonlinear fiber impairments. Two key conclusions can be drawn from Fig. 2, 1) as the launch power of second channel is varied; the performance of first channel is virtually unaffected. 2) The optimal performance of the second channel is similar to that of the first channel, even after –worst case (see Table 1)- individual launch power optimization (i.e. mutual power optimization does not play any role). Both of these conclusions can be attributed to the absence of linear mode coupling. Note that the penalties may increase in a WDM system, where strongly phase matched spectral regions will exist [12

12. G. Rademacher, S. Warm, and K. Petermann, “Analytical description of cross-modal nonlinear interaction in mode multiplexed multmode fibers,” IEEE Photon. Technol. Lett. 24(21), 1929–1932 (2012). [CrossRef]

].

As we would expect, given the low difference in the effective area of the modes, the relative launch power in the two modes has negligible impact in the absence of linear mode coupling. In the rest of the paper we systematically investigate the impact of linear mode coupling strength on the transmission performance for various power allocation strategies, both for high DMD and low DMD fibers. Figure 3(a)
Fig. 3 a) Q-factor [dB] as a function of launch power per mode [dBm], for QPSK transmission over 1,600km with 5% mode coupling strength, for high DMD fiber (blue squares) showing slow (open) and fast (solid) modes and low DMD fiber (red circles) for slow (solid) and fast (open) modes. b&c) Constellation plots, at optimum launch power of 1dBm, for b) fast mode transmitted over high DMD fiber, and c) slow mode transmitted over low DMD fiber. (This figure represents a case of homogenous power optimization).
plots the Q-factor as a function of launch power per mode, for MDM few-mode transmission, for the case of equal launch powers for the two modes (homogenous optimization) at a mode coupling strength of 5%. It can be seen that with finite linear mode coupling, the transmission performance for low DMD fiber is worse than that of high DMD mode pair fiber. This performance is consistent with the fundamental behavior of increased mode coupling efficiency with reduced DMD, essentially worsening the transmission performance (more details to follow). Figure 3(b) and Fig. 3(c) qualitatively show the performance for high and low DMD transmission, for the fast and slow modes, respectively, consistent with uncorrelated noise sources and a high Q factor. Note that, with 5% linear mode coupling, the transmission performance is degraded by ~3dB for the high DMD fiber and 4dB for the low DMD fiber, compared to the case with no linear coupling (as shown in Fig. 2). This behavior can be attributed to increase in crosstalk with increasing mode coupling strength.

The impact of linear mode coupling strength on the transmission performance is shown in Fig. 4
Fig. 4 a) Q-factor as a function of mode coupling strength [%], for QPSK transmission over 1,600km, for high (square) and low (circle) DMD fiber. b) Nonlinear Q-factor penalty difference (Q factor at optimum launch power and Q factor without nonlinearity at the same lauch power) as a function of mode coupling strength [%], for high (square) and low (circle) DMD fiber. (This figure represents a case of homogenous power optimization).
, where we plot the system performance as a function of mode coupling strength employing homogeneous power optimization (equal powers in both modes), and each point taken at the optimal power from a plot similar to Fig. 3(a). As seen in Fig. 4(a), with increasing mode coupling strength, the transmission performance monotonically decreases for both fibers. Moreover, it can be seen that the degradation of the high DMD fiber is slower than for the low DMD fiber as expected from the increased impact of linear mode coupling with lower DMD. However, whilst the overall behavior is consistent with our understanding of linear mode coupling effects, in Fig. 4(b) we plot the contribution of nonlinearity to the Q-factor penalty as a function of mode coupling strength. The penalty is calculated by subtracting the results of Fig. 4(a) from purely linear transmission at similar optimal launch power per mode. The value of ~1.4dB at 0% mode coupling strength corresponds to the typical nonlinearity penalty observed at the optimum launch power for conventional single mode transmission systems. As the mode coupling strength is increased, the net nonlinear penalty reduces, more rapidly for the low DMD fiber, confirming that mode coupling reduces the impact of nonlinearity as recently observed in [19

19. S. Mumtaz, R. 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]

], although the reduction in nonlinear penalty suggests that the reduction is due to a complex interaction of effects including cross mode nonlinearity, linear mode coupling and DSP convergence.. The net effect is thus dominated by linear mode coupling, and whilst this may, in principle, be compensated with an ideal receiver, it is un-compensable using practical blind DSP [10

10. J. Vuong, P. Ramantanis, A. Seck, D. Bendimerad, and Y. Frignac, “Understanding discrete linear mode coupling in few-mode fiber transmission systems,” European Conference on Optical Communication, ECOC’11, Tu5B2, (2011).

] as used in this paper.

Having established that linear crosstalk dominates the performance for homogenous power allocation (equal power in each mode), in Fig. 5
Fig. 5 Q-factor [dB] as a function of launch power [dBm], for QPSK transmission over 1,600km, employing a) High DGD fiber (square: fast mode, circle: slow mode) and b) Low DMD fiber (square: slow mode, circle: fast mode), where solid symbols represent the channel with fixed power (1dBm) and open symbols the channel with variable power. (This figure represents a case of individual/mutual power optimization)
, we report the impact of individual and mutual launch power strategies, and show the performance, in Q-factor, of both modes, as a function of launch power of one of them, after a total transmission distance of 1,600km using both fiber types. Note that the launch power of one is fixed at the previously established optimal launch power of 1dBm. It can be seen that as the launch power of either of the modes is increased towards its optimal value, the transmission performance of the fixed power mode degrades significantly. This behavior can be attributed to increased coherent crosstalk arising from a higher power being linearly coupled to the fixed mode when the launch power is increased [20

20. X. Chen, J. E. Hurley, M.-J. Li, and R. S. Vodhanel, “Effects of multipath interference (MPI) on the performance of transmission systems using Fabry-Perot lasers and short bend insensitive jumper fibers,” Optical Fiber Communication Conference, OFC ‘09, NWC5, (2009).

]. Note that, contrary to homogenous power optimization, the optimum launch power of the mode with variable power is different to its value in isolation (1dBm). This may be explained by considering the intra mode nonlinear penalty and the inter mode linear crosstalk penalty simultaneously. At this level of mode coupling, the linear crosstalk penalty is around 3dB, with an additional 1dB from intra mode nonlinearity. However, to first order if the signal power is increased the ratio of the signal power within the channel to the linear crosstalk arising from the fixed power channel reduces, reducing the linear crosstalk penalty more rapidly than the nonlinear penalty increases. Eventually the nonlinear penalty begins to dominate the performance, and the new optimum launch power is achieved, At this new optimum power level, as shown in Fig. 5, the performance of fixed power mode is reduced by a further ~3dB and ~4dB for high and low DMD fibers, respectively whilst the optimum performance of the variable power channel is only increased by 1dB at most, where almost identical performance is observed irrespective of the effective area of the mode carrying the variable power channel.

The aforementioned penalties in transmission performance, given the potential to vary the power in each mode, give rise to a critical question as to how the launch power should be optimized. In this regard, Fig. 5 suggests that each if all channels have the same launch power (according to mutual power optimization), rather than individually optimized powers, then minimum penalties are observed. Also, the mutually optimized launch power is actually very close to the homogenous optimal launch power of 1dBm, since individual modes had similar optimum power corresponding to similar effective areas (found in Fig. 3 for mode coupling strength of 5%, and data for other mode coupling strengths, not shown here for the sake of conciseness.

In Fig. 6
Fig. 6 Q-factor penalty [dB] as a function of mode coupling strength [%], for QPSK transmission over 1,600km. a) High DMD fiber (fast mode is with variable power). Squares: Q1_HighDMD = Q [SlowMode(at individual Poptimal.) - SlowMode(at individual Poptimal of FastMode)], Circles: Q2_HighDMD = Q [SlowMode(at individual Poptimal) - SlowMode(at mutual Poptimal)], Up-triangle: Q3_HighDMD = Q [FastMode(at individual Poptimal) - FastMode(at mutual Poptimal)]. b) Low DMD fiber (slow mode is with variable power). Squares: Q1_LowDMD = Q [FastMode(at individual Poptimal) - FastMode(at individual Poptimal of SlowMode)], Circles: Q2_LowDMD = Q [FastMode(at individual Poptimal) - FastMode(at mutual Poptimal)], Up-triangle: Q3_LowDMD = Q [SlowMode(at individual Poptimal) - SlowMode(at mutual Poptimal)].
we plot various delta Q-factors as a function of mode coupling strength. Due to the similarity in performance of both channels, we consider only variable signal power in fast mode (high DMD fiber) and slow mode (low DMD fiber), respectively, and plot the performance penalties with reference to the individual optimal powers of both fixed and variable power modes (best performance). Note that in order to get each data point on Fig. 6, simulations similar to Fig. 3 and Fig. 5 were carried out for each mode coupling strength, for both low and high DMD fibers. In Fig. 6(a), Q-penalties are plotted for the high DMD fiber, where penalties represent: 1) Q1_HighDMD, representing performance penalty for fixed power mode (or slow mode) in case of individual launch power optimization for variable power mode (or fast mode). It is calculated by subtracting Q-factor (slow mode) at individual Poptimal of slow mode and Q-factor (slow mode) at individual Poptimal of fast mode, 2) Q2_HighDMD, representing performance penalty for fixed power mode (or slow mode) in case of mutual launch power optimization for fixed power mode and variable power mode (or fast mode). It is calculated by subtracting Q-factor (slow mode) at individual Poptimal of slow mode and Q-factor (slow mode) at mutual Poptimal of slow and fast modes, 3) Q3_HighDMD, representing performance penalty for variable power mode (or fast mode) in case of mutual launch power optimization for fixed power mode (or slow mode) and variable power mode. It is calculated by subtracting Q-factor (fast mode) at individual Poptimal of fast mode and Q-factor (fast mode) at mutual Poptimal of fast and slow modes. Similar approach is taken in Fig. 6(b) for low DMD fiber (corresponding penalties are Q1_LowDMD, Q2_LowDMD and Q3_LowDMD). As shown in Fig. 5, the penalties reported are predominantly influenced by intra mode nonlinearity and linear crosstalk, however, intra mode nonlinear effects have a non-negligible impact (Fig. 4(b)). It can be observed that, as the mode coupling strength is increased, the Q-penalties monotonically increase, in particular for the fixed power mode, irrespective of the DMD (Fig. 6(a) and Fig. 6(b)) or approach to power control. Interestingly, the performance of the variable power mode is not degraded significantly, with penalties below 1.5dB for any given scenario. At this transmission reach, the performance of a fixed power channel is severely degraded for coupling strength beyond few percentiles. This behavior can be attributed to increasing inter mode coupling with mode coupling strength, owing to the increasing power of the variable power mode. Figure 6(a) shows that at 10% mode coupling efficiency Q-penalties of ~5.5 dB (Q1_HighDMD), ~3.5 dB (Q2_HighDMD), and ~1.5 dB (Q3_HighDMD) are observed. These results clearly show that even though the impact of launch power allocation strategy is not extreme for low mode coupling values (<~2dB up to mode coupling strength of 2.5%), it significantly degrades the transmission performance with increasing mode coupling strength. with the mutual power optimization strategy offering lower overall penalties.

4. Conclusions

We have reported on the dynamics of power allocation strategies in few-mode fiber based long-haul transmission systems. It is shown that in the absence of linear coupling, the transmission performance is independent of power allocation approach, however in the weakly coupled regime, individual power allocation approach may induce penalties up to ~2dB. In contrast, when mode coupling strength is increased, transmission performance is significantly degraded, if modes are allowed to individually optimize their corresponding launch powers, with penalties up to ~5.5dB. Whilst optimum power differences of up to 0.5 dB may have been expected due to differences in effective area, we found no evidence favoring individual power optimization and that homogenous (or mutual in this case) power allocation should be used.

Acknowledgments

This work was partially supported by EU FP7-ICT project, MODE-GAP.

References and links

1.

R. Essiambre and A. Mecozzi, “Capacity limits in single mode fiber and scaling for spatial multiplexing,” Optical Fiber Communication Conference, OFC ‘12, OW3D.1, (2012).

2.

P. J. Winzer, “Energy-efficient optical transport capacity scaling through spatial multiplexing,” IEEE Photon. Technol. Lett. 23(13), 851–853 (2011). [CrossRef]

3.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, S. Bickham, H. Tam, C. Lu, M. Li, S. Ten, A. P. T. Lau, V. Tse, G. Peng, C. Montero, X. Prieto, and G. Li, “88x3x112-Gb/s WDM transmission over 50-km of three-Mode fiber with inline multimode fiber amplifier,” European Conference on Optical Communication, ECOC’11, Th.13.C.2, (2011).

4.

T. Hayashi, T. Sasaki, and E. Sasaoka, “Multi-core fibers for high capacity transmission,” Optical Fiber Communication Conference, OFC ‘12, OTu1D.4, (2012).

5.

S. Randel, R. Ryf, A. Gnauck, M. A. Mestre, C. Schmidt, R. Essiambre, P. 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,” Optical Fiber Communication Conference, OFC ‘12, PDP5C.5, (2012).

6.

A. Mecozzi, C. Antonelli, and M. Shtaif, “Nonlinear propagation in multi-mode fibers in the strong coupling regime,” Opt. Express 20(11), 11673–11678 (2012). [CrossRef] [PubMed]

7.

M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in mode-division-multiplexed transmission over few-mode optical fiber,” IEEE Photon. Technol. Lett. 23(18), 1316–1318 (2011). [CrossRef]

8.

N. MacSuibhne, R. Watts, S. Sygletos, F. C. G. Gunning, L. GrüNernielsen, and A. D. Ellis, “Nonlinear pulse distortion in few-mode fiber,” European Conference on Optical Communication, ECOC’12, Th.2.F.5, (2012).

9.

J. M. Kahn, K. Ho, and M. B. Shemirani, “Mode coupling effects in multi-mode fibers,” Optical Fiber Communication Conference, OFC ‘12, OW3D.3, (2012).

10.

J. Vuong, P. Ramantanis, A. Seck, D. Bendimerad, and Y. Frignac, “Understanding discrete linear mode coupling in few-mode fiber transmission systems,” European Conference on Optical Communication, ECOC’11, Tu5B2, (2011).

11.

P. Sillard, M. Bigot-Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” European Conference on Optical Communication, ECOC’11, Tu5C7, (2011).

12.

G. Rademacher, S. Warm, and K. Petermann, “Analytical description of cross-modal nonlinear interaction in mode multiplexed multmode fibers,” IEEE Photon. Technol. Lett. 24(21), 1929–1932 (2012). [CrossRef]

13.

D. Marcuse, Theory of Dielectric Optical Waveguides chapters 3&5, (New York: Academic, 1974).

14.

F. Ferreira, S. Jansen, P. Monteiro, and H. Silva, “Nonlinear semi-analytical model for simulation of few-mode fiber transmission,” IEEE Photon. Technol. Lett. 24(4), 240–242 (2012). [CrossRef]

15.

G. Agrawal, Applications of nonlinear Fibre Optics chapter 2, (Academic Press, 2001).

16.

F. Gardner, “A BPSK/QPSK timing-error detector for sampled receivers,” IEEE Commun. Mag. 34, 423–429 (1986).

17.

S. Savory, “Digital signal processing for coherent systems,” Optical Fiber Communication Conference, OFC ‘12, OTh3C.7, (2012).

18.

D. v. d Borne, C. R. S. Fludger, T. Duthel, T. Wuth, E. D. Schmidt, C. Schulien, E. Gottwald, G. D. Khoe, and H. de Waardt, “Carrier phase estimation for coherent equalization of 43-Gb/s POLMUXNRZ-DQPSK transmission with 10.7-Gb/s NRZ neighbours,” European Conference on Optical Communication, ECOC’107, 7.2.3, (2007).

19.

S. Mumtaz, R. 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]

20.

X. Chen, J. E. Hurley, M.-J. Li, and R. S. Vodhanel, “Effects of multipath interference (MPI) on the performance of transmission systems using Fabry-Perot lasers and short bend insensitive jumper fibers,” Optical Fiber Communication Conference, OFC ‘09, NWC5, (2009).

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(060.4256) Fiber optics and optical communications : Networks, network optimization

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: October 3, 2012
Revised Manuscript: December 3, 2012
Manuscript Accepted: December 22, 2012
Published: April 25, 2013

Citation
Danish Rafique, Stylianos Sygletos, and Andrew D. Ellis, "Impact of power allocation strategies in long-haul few-mode fiber transmission systems," Opt. Express 21, 10801-10809 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-10801


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References

  1. R. Essiambre and A. Mecozzi, “Capacity limits in single mode fiber and scaling for spatial multiplexing,” Optical Fiber Communication Conference, OFC ‘12, OW3D.1, (2012).
  2. P. J. Winzer, “Energy-efficient optical transport capacity scaling through spatial multiplexing,” IEEE Photon. Technol. Lett.23(13), 851–853 (2011). [CrossRef]
  3. E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, S. Bickham, H. Tam, C. Lu, M. Li, S. Ten, A. P. T. Lau, V. Tse, G. Peng, C. Montero, X. Prieto, and G. Li, “88x3x112-Gb/s WDM transmission over 50-km of three-Mode fiber with inline multimode fiber amplifier,” European Conference on Optical Communication, ECOC’11, Th.13.C.2, (2011).
  4. T. Hayashi, T. Sasaki, and E. Sasaoka, “Multi-core fibers for high capacity transmission,” Optical Fiber Communication Conference, OFC ‘12, OTu1D.4, (2012).
  5. S. Randel, R. Ryf, A. Gnauck, M. A. Mestre, C. Schmidt, R. Essiambre, P. 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,” Optical Fiber Communication Conference, OFC ‘12, PDP5C.5, (2012).
  6. A. Mecozzi, C. Antonelli, and M. Shtaif, “Nonlinear propagation in multi-mode fibers in the strong coupling regime,” Opt. Express20(11), 11673–11678 (2012). [CrossRef] [PubMed]
  7. M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in mode-division-multiplexed transmission over few-mode optical fiber,” IEEE Photon. Technol. Lett.23(18), 1316–1318 (2011). [CrossRef]
  8. N. MacSuibhne, R. Watts, S. Sygletos, F. C. G. Gunning, L. GrüNernielsen, and A. D. Ellis, “Nonlinear pulse distortion in few-mode fiber,” European Conference on Optical Communication, ECOC’12, Th.2.F.5, (2012).
  9. J. M. Kahn, K. Ho, and M. B. Shemirani, “Mode coupling effects in multi-mode fibers,” Optical Fiber Communication Conference, OFC ‘12, OW3D.3, (2012).
  10. J. Vuong, P. Ramantanis, A. Seck, D. Bendimerad, and Y. Frignac, “Understanding discrete linear mode coupling in few-mode fiber transmission systems,” European Conference on Optical Communication, ECOC’11, Tu5B2, (2011).
  11. P. Sillard, M. Bigot-Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” European Conference on Optical Communication, ECOC’11, Tu5C7, (2011).
  12. G. Rademacher, S. Warm, and K. Petermann, “Analytical description of cross-modal nonlinear interaction in mode multiplexed multmode fibers,” IEEE Photon. Technol. Lett.24(21), 1929–1932 (2012). [CrossRef]
  13. D. Marcuse, Theory of Dielectric Optical Waveguides chapters 3&5, (New York: Academic, 1974).
  14. F. Ferreira, S. Jansen, P. Monteiro, and H. Silva, “Nonlinear semi-analytical model for simulation of few-mode fiber transmission,” IEEE Photon. Technol. Lett.24(4), 240–242 (2012). [CrossRef]
  15. G. Agrawal, Applications of nonlinear Fibre Optics chapter 2, (Academic Press, 2001).
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