Tight Focusing, Spin Textures, and Optical Forces of Amplitude–Phase-Asymmetric Hyperbolic-Chirped Double-Ring Airy–Gaussian Vortex Beams

We propose an amplitude–phase-asymmetric hyperbolic-chirped double-ring Airy–Gaussian vortex beam (AHC-DRAGVB). Oppositely signed radial chirps are imposed on the inner and outer rings, respectively, while a hyperbolic-cosine amplitude modulation is applied only to the outer ring. A vectorial tight-focusing model based on Richards–Wolf diffraction is used to examine the effects of the scale factor G, vortex displacement, optical distribution factor b, hyperbolic modulation coefficient κ, and radial-chirp coefficients. The scale factor jointly controls the focal position, depth of focus, and longitudinal peak-intensity ratio. Off-axis vortex displacement modifies the focal distribution and reshapes the focal-plane spin density and polarization ellipses. Increasing b changes the relative Gouy phase and the associated local phase slopes and thereby reconstructs the axial spin texture. Increasing κ enhances longitudinal peak weighting, accompanied by changes in focal widths and competing transverse peaks. Radial chirp further shifts the focal region and modifies the local field, although excessive chirp degrades the intensity balance between foci. Rayleigh-force calculations are complemented by three-dimensional force directions and coordinate cuts to examine the local restoring response for b = 0.3.