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

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 114-Gb/s bit streams in the PDM-QPSK format 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. The extent of improvement depends on the fiber design and how many spatial modes are used for SDM transmission. We investigated both step-index and graded-index multimode fibers and considered up to three spatial modes in each case. In this paper, we also consider multicore fibers and show that the Manakov equations remain valid as long as the length scale of birefringence fluctuations is about 100 times shorter than that of linear coupling. 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 singlemodes fiber for large number of propagating spatial modes.

Birefringence effects in multi-core fiber: coupled local-mode theory

“…On the other hand, in [14][15][16][17] the Manakov equations have been extended to multi-mode fibers (MMFs) and multi-mode multi-core fibers (MM-MCFs) to analyze linear and nonlinear propagation in SDM systems modeling intra-and inter-core coupling effects. In addition, in [18,19] the mode coupling has also been theoretically investigated in MMFs and MM-MCFs considering both orthogonal polarizations and the longitudinal random perturbations of the fiber.…”

“…In [18] the bending and twisting of the media were modeled in the coupling matrix (composed by the coupling coefficients of the coupled-mode theory proposed in [20] for anisotropic optical waveguides), and in [19] the spatial random perturbations were included in the propagation matrix of the optical media. In all these previous works [8][9][10][11][12][13][14][15][16][17][18][19], the longitudinal perturbations of the fiber have been described assuming ideal modes but omitting the temporal fluctuations of the SDM fiber perturbations.…”

Polarization modulation instability in a Manakov fiber system

“…In particular, when considering the two coupled orthogonally polarized components of the optical field, the Manakov system admits trivial two-component stable solutions formed by two incoherent bright (self-focusing case) or dark (self-defocusing case) solitons. More generally, the Manakov system has attracted enormous attention as it is considered to be a promising model for the description of interactions between wavelengthdivision-multiplexed (WDM) channels of long optical fiber transmission systems [9], polarization-division-multiplexed systems (PDM) [10,11], or even space-division-multiplexed (SDM) systems using multimode or multicore fibers [12].…”

Theory of modal attraction in bimodal birefringent optical fibers

“…Recently there has been a resurgency of interest in this topic, given the potential of few-mode fibers to enhance the capacity of optical transmission systems via spatial multiplexing [3].…”