Abrupt focus and bright spot formation in fractional system with PT-symmetric nonlocal nonlinearity

Abstract We study the dynamics of Gaussian beams in fractional system with PT-symmetric nonlocal nonlinearity. It is found that the Gaussian beam with transverse displacement can abruptly focus to form bright spot in one sub-branch after experiencing a symmetric split, depending on the nonlinear intensity, initial launched amplitude, angle and chirp of the beam, and the initial chirp can shift the time of abrupt focus and bright spot formation. Furthermore, the Talbot-like effect and breather train are explored by setting the initial amplitude parameter of every component of an initial Gaussian beam train. Moreover, for longitudinally periodically modulated nonlinearity, the bright spots can be formed periodically and asymmetrically in two sub-branches for a single Gaussian beam, and Moiré-like lattices can be generated for a Gaussian beam train. Finally, the conical diffraction and crescent-like evolution in the two-dimensional system are investigated in detail. It is found that the direction of crescent-like evolution is determined by the initial launched angles, which may be an inspiration to design channel path through choosing suitable initial launched angles at will.