dispersive shock waves

We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a defocusing nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be described within a nondispersive approximation by means of Riemann's approach. We are also able to calculate the wave-breaking time, at which nonlinear nondispersive spreading leads to a gradient catastrophe. The theoretical results are in excellent agreement with numerical simulations. Experimental and theoretical studies have demonstrated the occurence of wave breaking even in absence of background. Our results exhibit this feature and the corresponding theoretical wave-breaking time agrees very well with simulations.

In a nonlinear medium, the phase and amplitude of a coherent beam are affected by nonlinearity. This modifies the laws of geometrical optics and may also lead to a gradient catastrophe resulting in complex optical patterns. I will discuss two such configurations resulting in the formation of a dispersive shock in a local nonlinear medium and of an Airy beam in a highly nonlocal one.