Background-enhanced collapse instability of optical speckle beams in nonlocal nonlinear media

Abstract

We study the focusing dynamics of incoherent wave-packets (speckle beams) in the presence of a nonlocal nonlinear response in the framework of the nonlocal nonlinear Schrödinger (NLS) equation. In the highly nonlocal regime, we show that the speckle beam develops a collective incoherent collapse instability — at variance with a conventional collapse that is inherently a coherent object, here it is the incoherent beam as a whole that develops a collapse. More specifically, we study the impact of a homogeneous incoherent background on the development of the incoherent collapse instability. Despite the fact that the homogeneous background is modulationally stable, we show that it significantly strengthens the formation of the incoherent collapse instability. Our theoretical analysis is based on a wave turbulence formulation of the Vlasov equation, which allows us to introduce an effective hydrodynamic model that is subsequently solved by the method of characteristics. A quantitative agreement is obtained between the simulations of the NLS equation, the Vlasov equation and the hydrodynamic model, without using adjustable parameters. The interaction between the background and the collapsing structure is described by means of a coupled system for the singular and smooth components of the solution of the Vlasov equation. The theory reveals that the mechanism underlying the background-induced collapse enhancement is due to a transfer of momentum from the background to the collapsing structure, while there is no ‘mass’ exchange among them. Furthermore, we show that a strong background level significantly boosts the collapse dynamics. Our work should stimulate the development of nonlinear experiments aimed at observing the incoherent collapse phenomenon in nonlinear thermal media. From a broader perspective, these investigations pave the way for the study of novel forms of global incoherent collective behaviors in wave turbulence, such as the formation of incoherent rogue waves.