Nonlinear Propagation in Multimode and Multicore Fibers: Generalization of the Manakov Equations (1207.6645v1)

Abstract: This paper starts by an investigation of nonlinear transmission in space-division multiplexed (SDM) systems using multimode fibers exhibiting a rapidly varying birefringence. A primary objective is to generalize the Manakov equations, well known in the case of single-mode fibers. We first investigate a reference case where linear coupling among the spatial modes of the fiber is weak and after averaging over birefringence fluctuations, we obtain new Manakov equations for multimode fibers. Such an averaging reduces the number of intermodal nonlinear terms drastically since all four-wave-mixing terms average out. Cross-phase modulation terms still affect multimode transmission but their effectiveness is reduced. We then verify the accuracy of our new Manakov equations by transmitting multiple PDM-QPSK signals over different modes of a multimode fiber and comparing the numerical results with those obtained by solving the full stochastic equation. The agreement is excellent in all cases studied. A great benefit of the new equations is to reduce the computation time by a factor of 10 or more. Another important feature observed is that birefringence fluctuations improve system performance by reducing the impact of fiber nonlinearities. Finally multimode fibers with strong random coupling among all spatial modes are considered. Linear coupling is modeled using the random matrix theory approach. We derive new Manakov equations for multimode fibers in that regime and show that such fibers can perform better than single-modes fiber for large number of propagating spatial modes.

• The paper extends the Manakov equations to multimode fibers by averaging fast birefringence fluctuations, effectively minimizing intermodal nonlinear terms.
• The methodology relies on numerical tests with 114-Gb/s PDM-QPSK streams, verifying strong agreement with full stochastic models.
• The study demonstrates that managing birefringence can boost SDM performance and cut computation time by over 10 times in multicore systems.

Nonlinear Propagation in Multimode and Multicore Fibers: Generalization of the Manakov Equations

The paper proposes an advancement in understanding the nonlinear propagation of signals in space-division multiplexed (SDM) systems utilizing multimode and multicore fibers. The authors aim to generalize the Manakov equations, which are typically applied to single-mode fibers, to accommodate fibers exhibiting rapidly varying birefringence in a multimode context.

Key Contributions and Methods

1. Generalization of Manakov Equations: The core of the paper involves extending the Manakov equations, originally developed for single-mode fibers, to multimode fibers. This is achieved through averaging over birefringence fluctuations. The new set of equations minimizes the number of intermodal nonlinear terms, as four-wave-mixing terms average out, leaving only cross-phase modulation terms significantly reduced in their impact.
2. Verification and Numerical Results: The validity of the newly derived Manakov equations is tested numerically by transmitting multiple 114-Gb/s bit streams using the PDM-QPSK format across different modes of a multimode fiber. The numerical agreement between the results obtained by using the new Manakov equations and the full stochastic equations corroborates the accuracy of the model.
3. Significance of Birefringence Fluctuations: Birefringence fluctuations enhance the performance of multimode transmission by diminishing fiber nonlinearities. The extent of improvement is a function of fiber design and the number of spatial modes employed for SDM transmission.
4. Multicore Fiber Analysis: The paper further ventures into the domain of multicore fibers, demonstrating that the generalized Manakov equations remain applicable when the scale of birefringence fluctuations is substantially shorter than the scale of linear mode coupling. A notable outcome is the reduction of computation time by a factor of 10 or more, providing a significant efficiency gain.
5. Strong Random Coupling Regime: Extending the analysis to multimode fibers with strong random coupling, the paper employs a random matrix theory approach to derive an adapted form of the Manakov equations. This regime shows potential performance benefits over single-mode fibers, especially as the number of propagating spatial modes increases.

Implications and Future Directions

This research implies a potential shift in how multimode and multicore fibers are utilized in SDM systems, showcasing the benefits of managing nonlinearities via rapidly varying birefringence. Practically, these insights can lead to more efficient fiber optic systems with higher capacity and performance. Theoretical advances, such as the adaptation of the Manakov equations to new contexts, provide a robust framework for future studies and developments within fiber optics.

The paper suggests several avenues for further research, including the exploration of more complex fiber designs to capitalize on the reduced nonlinear impairments via birefringence tuning. Additionally, further investigations into the impact of strong mode coupling and its practical implementation within compounded multicore/multimode fiber systems could yield substantial improvements in communication system design.

In conclusion, this paper lays a critical foundation for the continued evolution of optical fiber technologies, paving the way for intricate systems that leverage multimode dynamics efficiently, thereby supporting the ever-growing demand for data transmission capacity.