On stochastization of monochromatic wave propagation in an optical single-mode fiber

Abstract

The inhomogeneities in an optical fiber is one of the most significant problems of wavelength multiplexing in optical communications. We investigate the effect of such inhomogeneities giving rise to stochastization of the transmitted signal in a canonical formulation. We consider the nonlinear stage of modulational instability of a pump wave in a three-wave approximation. By employing equations for wave dynamics in the Hamiltonian form we show analytically that a “stochastic layer”, i.e. the region in which the phase trajectories behave chaotically, is formed in the phase space of a dynamical system even at rather weak inhomogeneity of the fiber. The estimates obtained indicate that the considered phenomenon is very likely to be observed in experiments.