Fig. 1. Schematic illustration of generating a curvilinear light beam in the focal region, z ∈ [−d, d], of the Fourier lens.

Fig. 2. (a),(b) Different amplitude gradient [controlled by α(t)] and phase gradient [controlled by ϕ(t) or m] along a 2D Archimedean curve in the focal plane. (c),(d) Intensity distribution of a 3D Archimedean curve in the focal plane. (e),(f) Reconstructed intensity of the beam at −25, −15, −5, 0, and 15 mm from the focal plane, respectively.

Fig. 3. Schematic of the optical setup for generating CPVB, based on the superposition of two orthogonally polarized component beams. SLM, spatial light modulator; QWP, quarter-wave plate.

Fig. 4. Simulation and experimental results of a ring-shaped CPVB in the focal plane. (a) Ring-shaped trajectory of the beam having SoPs belonging to the equator of the PS. (b) The complex amplitude of right-circular polarization component needed for producing this CPVB. (c) The recorded intensity in three successive planes of the focal space. (d1)–(d4) The Stokes parameters (S₀, S₁, S₂, S₃) calculated by simulation. (e1)–(e4) Measured Stokes parameters (S₀, S₁, S₂, S₃) of the experimentally generated beam.

Fig. 5. Simulation and experimental results of the 3D CPVB with a tilt ring-shaped trajectory in the focal space. (a) SoPs belong to the PS’ great circle inclined at 45 deg around the S₁ axis. (b) The complex amplitude of right-circular polarization component needed for producing this CPVB. (c) The recorded intensity in three successive planes of the focal space. (d1)–(d4) The Stokes parameters (S₀, S₁, S₂, S₃) calculated by simulation. (e1)–(e4) Measured Stokes parameters (S₀, S₁, S₂, S₃) of the experimentally generated beam.

Fig. 6. Simulation and experimental results of the 3D CPVB with double tilt-ring-shaped trajectory in the focal space. (a) SoPs belong to the PS’ great circle inclined at ±45 deg around the S₁ axis. (b) The complex amplitude of right-circular polarization component needed for producing this CPVB. (c) The recorded intensity in three successive planes of the focal space. (d1)–(d4) The Stokes parameters (S₀, S₁, S₂, S₃) calculated by simulation. (e1)–(e4) Measured Stokes parameters (S₀, S₁, S₂, S₃) of the experimentally generated beam.