Nonlinear Dynamics of Partially Incoherent Optical Waves Based on the Wigner Transform Method

Abstract

A novel statistical approach based on the Wigner transform method is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. The Wigner–Moyal equation is derived for the Wigner distribution of the optical wave field governed by the nonlinear Schrödinger equation with an arbitrary nonlinearity. An application to incoherent light propagation in dispersive Kerr media shows that random phase fluctuations of a plane wave solution lead to a linear Landau-like damping effect, which can stabilize the nonlinear modulational instability. A similar effect is shown to occur in the case of the two-stream instability of two partially incoherent optical waves interacting with each other through cross-phase modulation initiated by the nonlinearity. In the limit of the geometrical optics approximation, it is shown that 1D and 2D self-trapped, stationary and incoherent wave pulse structures may exist for a wide class of nonlinear media. Furthermore, time-dependent self-similar 1D and 2D structures have been found in the case of the Kerr nonlinearity.