Coupled nonlinear Schrödinger equations arising in the study of monomode step-index optical fibers

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Abstract
In this paper it is shown that nonlinear propagation in a step‐index, ‘‘monomode’’ optical fiber is not generally governed by the nonlinear Schrödinger equation, even when the fiber is axially symmetric. It is governed by a coupled pair of nonlinear partial differential equations that includes the nonlinear Schrödinger equations only as a special case. Three simple types of solution to the coupled system are analyzed and the corresponding field patterns are interpreted. One case shows that, for uniform wavetrains, nonlinearity not only alters the phase speed but also causes the field pattern in an ‘‘elliptically polarized’’ mode to rotate gradually about the fiber axis. The other two cases each allow the system to be reduced to a single nonlinear Schrödinger equation, so showing two distinct situations in which solutions have soliton properties.