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This review describes recent theoretical and experimental advances in the area of multimode solitons, focusing primarily on multimode fibers. We begin by introducing the basic concepts such as the spatial modes supported by a multimode fiber and the coupled mode equations for describing the different group delays and nonlinear properties of these modes. We review several analytic approaches used to understand the formation of multimode solitons, including those based on the 3D+1 spatiotemporal nonlinear Schrödinger equation (NLSE) and its approximate 1D+1 representation that has been found to be highly efficient for studying the self-imaging phenomena in graded-index multimode fibers. An innovative Gaussian quadrature approach is used for faster numerical simulations of the 3D+1 NLSE. The impact of linear mode coupling is discussed in a separate section using a generalized Jones formalism because of its relevance to space-division multiplexed optical communication systems. The last section is devoted to the relevant experimental studies involving multimode solitons.
Sun et al. (Tue,) studied this question.
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