Controllable dynamics of circular Airy modulation vortex beams in fractional nonlinear optical systems with two vortex phase modulation structural models

The transmission dynamics of circular Airy modulation vortex beams (CAMVBs) with two distinct vortex phase modulation modes are investigated within a fractional-order Schrödinger optical system using a stepwise Fourier method. In the linear regime, the orbital angular momentum (OAM) determines the rotational direction of CAMVBs without altering their shape or transmission properties, with higher OAM splitting the beam into multiple spots ( L = l vortex modulation mode). For the second vortex modulation mode ( L = r l ), CAMVBs exhibit an Archimedean helix-like pattern influenced by OAM. By tuning the topological charge, phase folding number, modulation coefficient, initial phase, and Lévy index, tailored spot distributions can be achieved, offering potential in optical splitting and control. In nonlinear Kerr media, vortex solitons emerge, with their number matching the phase folding number. The solitons’ configuration depends on phase modulation and nonlinear strength, enabling information encoding through beam parameters. These findings hold promise for secure communication and advanced optical systems.