Nonlinear dynamics of partially incoherent optical waves based on the Wigner transform method

A novel statistical approach based on theWigner transform method is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. TheWigner^Moyal equation is derived for theWigner distribution of the optical wave ¢eld governed by the nonlinear Schr˛dinger equation with an arbitrary nonlinearity. An application to incoherent light propagation in dispersive Kerr media shows that random phase £uctuations of a plane wave solution lead to a linear Landau-like damping e¡ect, which can stabilize the nonlinear modulational instability. A similar e¡ect 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.