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We show that light propagation in a group of degenerate modes of a multi-mode optical fiber in the presence of random mode coupling is described by a multi-component Manakov equation, thereby making multi-mode fibers the first reported physical system that admits true multi-component soliton solutions. The nonlinearity coefficient appearing in the equation is expressed rigorously in terms of the multi-mode fiber parameters.

Modal dispersion (MD) in a multimode fiber may be considered as a generalized form of polarization mode dispersion (PMD) in single mode fibers. Using this analogy, we extend the formalism developed for PMD to characterize MD in fibers with multiple spatial modes. We introduce a MD vector defined in a D-dimensional extended Stokes space whose square length is the sum of the square group delays of the generalized principal states. For strong mode coupling, the MD vector undertakes a D-dimensional isotropic random walk, so that the distribution of its length is a chi distribution with D degrees of freedom. We also characterize the largest differential group delay, that is the difference between the delays of the fastest and the slowest principal states, and show that it too is very well approximated by a chi distribution, although in general with a smaller number of degrees of freedom. Finally, we study the spectral properties of MD in terms of the frequency autocorrelation functions of the MD vector, of the square modulus of the MD vector, and of the largest differential group delay. The analytical results are supported by extensive numerical simulations.

We derive the fundamental equations describing nonlinear propagation in multi-mode fibers in the presence of random mode coupling within quasi-degenerate groups of modes. Our result generalizes the Manakov equation describing mode coupling between polarizations in single-mode fibers. Nonlinear compensation of the modal dispersion is predicted and tested via computer simulations.

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