Controllable trajectory Hermite-Gaussian vortex beams in nonlinear fractional Schrödinger systems

We investigate the dynamics of off-axis chirped Hermite-Gaussian vortex beams (HGVBs) governed by the nonlinear fractional Schrödinger equation (FSE) with variable coefficients and potentials. Under cosine modulations, the beam exhibits periodic inversion and a serpentine trajectory, tunable via the chirp parameter. For power function modulations, the beam stabilizes after several rotations, maintaining a fixed position transmission at the shift limit. In a parabolic potential, self-focusing and defocusing behaviors emerge, accompanied by counter-clockwise rotation. Fractional diffraction leads to diminishing oscillation amplitudes and gradual movement towards the origin. When the Lévy index equals 2, the beam trajectory transitions from linear oscillations to circular or elliptical spirals, depending on the chirp parameter. Applying linear potentials, diverse diffraction conditions induce unique trajectories, including cross helices and triangular spirals. These findings provide fresh insights into vortex beam transport in nonlinear FSE, with potential applications in optical communication, switching, and particle manipulation.