Phase Space Vortices Using Structured Coherence

Abstract

In this thesis, we explore the nonlinear optics of spatially incoherent light with a non-standard statistical distribution. First, we construct a classical light state with non-local correlations and uniform intensity by structuring the coherence properties. We show that this state has a highly patterned phase space, including a nested hyperbola structure and Wigner function negativity. Second, we perform numerical simulations using coherent density theory to study the dynamics in self-focusing nonlinear media. We find that at both low and high nonlinearity, the initial evolution is characterized by the formation of a phase space vortex. At low nonlinearity, further evolution results in the emergence of internal phase space structures enclosed by the vortex. At high nonlinearity, further evolution results in the breakup of the vortex into separate phase space structures. These results demonstrate that tailoring the full phase space distribution – and not just its cross section – can lead to rich nonlinear dynamics.