Using the two-dimensional nonlinear Schrödinger equation, the collapse dynamics of vortex beams in a Kerr medium with refractive index modulation and parity–time (PT) symmetric lattices are explored. The critical power for the collapse of vortex beams in a Kerr medium with real optical lattices (i.e., refractive index modulation lattices) was obtained and discussed. Numerical calculations showed that the number of self-focusing points, the locations of the collapse, and the propagation distances for collapse are sensitively dependent on the modulation factors, topological charge numbers, and initial powers. When the vortex optical field propagates in a Kerr medium with real optical lattices, the optical field will collapse into a symmetrical shape. However, the shape of the vortex beam will be chaotically distorted and collapse in asymmetric patterns during propagation in a Kerr medium with PT-symmetric lattices because of the presence of the complex refraction index. Introducing PT-symmetric lattices into nonlinear Kerr materials may offer a new approach to controlling the collapse of vortex beams.

Based on the two-dimensional (2D) nonlinear Schrödinger equation, we investigate the collapse dynamics of a vector vortex optical field (VVOF) in nonlinear Kerr media with parity–time (PT)-symmetric modulation. The critical power for the collapse of a VVOF in a Kerr-ROLP medium (Kerr medium with a real optical lattice potential) is derived. Numerical simulations indicate that the number, position, propagation distance, and collapse profile of the collapse of a VVOF in sine and cosine parity–time-symmetric potential (SCPT) Kerr media are closely related to the modulation depth, initial powers, and the topological charge number of a VVOF. The VVOF collapses into symmetric shapes during propagation in a Kerr-ROLP medium, and collapse shapes are sensitively related to the density of the PT-symmetric optical lattice potential. In addition, due to gain–loss, the VVOF will be distorted during propagation in the Kerr-SCPT medium, forming an asymmetric shape of collapse. The power evolution of the VVOF in a Kerr-SCPT medium as a function of the transmission distance with different modulating parameters and topological numbers is analyzed in detail. The introduction of PT-symmetric optical lattice potentials into nonlinear Kerr materials may provide a new approach to manipulate the collapse of the VVOF.