Anomalous transverse transformation of astigmatic four-petal Gaussian beams in isotropic nonlocal nonlinear media

In this paper, the evolution dynamics of astigmatic four- petal Gaussian beams in isotropic nonlocal nonlinear media is investigated. A series of analytical expressions are derived to describe the beam evolution, the beam width, and the critical power. The anomalous transverse transformation is presented, i.e., an astigmatic four-petal Gaussian beam is compressed in one transverse direction and it is broadened in the other transverse direction. These evolution characteristics of astigmatic four- petal Gaussian beams are illustrated through some numerical simulations.