A simple, analytic method for describing the evolution of polarization along a single-mode optical fiber is presented. A system of linear differential equations for the change of the Stokes parameters, and hence for the change in polarization, along a fiber is derived from coupled-mode theory and the definition of the Stokes parameters. The polarization eigenstates—the polarization states not affected by the perturbations—are determined from these equations. The general solution of the system of equations is found. This solution is applied to several specific cases and is found to agree with results obtained from the geometric method of Ulrich and Simon [ Appl. Opt. 18, 2241 ( 1979)].
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