Abstract

We analyze the coupled nonlinear equations which describe the polarization interaction of two intense counterpropagating beams in a randomly birefringent fiber. We use rotational and relativistic symmetry to find exact steady-state and travelling wave solutions of the system, formulated in terms of the Stokes vectors, and view the solutions as the vibrations of a vector harmonic oscillator on the Poincaré sphere. We show how to determine the frequencies of all possible vibrational modes, subject to the endpoint boundary conditions, and construct the explicit Stokes vectors for each such mode. We revisit stability properties to demonstrate that all steady-state and travelling wave solutions, even those of lowest frequency, are unstable for fiber lengths exceeding a critical value which depends on the speed of propagation, but are always stable for small fiber lengths. Polarization attraction can occur for signal and wave pumps of differing intensity, provided boundary conditions are imposed which induce a travelling wave of a specified speed.

© 2016 Optical Society of America

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