Fig. 1 CR intensity distribution for a circularly polarized input beam and under conditions of ρ₀ ≡ R₀/w₀ ≫ 1. (a) Intensity along the propagation direction z, which possesses cylindrical symmetry. (b) Transverse intensity pattern at z = 0 (focal plane) showing the two bright rings split by the dark Poggendorff one. Blue double arrows indicate the linear plane of polarization. w₀ is the beam waist and z_R the Rayleigh length.

Fig. 2 Transverse pattern of the Stokes parameters S₀, S₁, S₂, S₃ obtained from numerical simulations (box (a)) and experimentally (box (b)) for the CR beam transverse profile with a RHCP and a LP (Φ = 45°) Gaussian input beam. First and second rows correspond to the focal plane (Z = 0) while third and fourth rows to the Raman spot plane (Z = 10.92). The plane of optic axes of the crystal lies horizontally (φ_c = 0). Media 1 and Media 2 show in detail the evolution of the numerically calculated Stokes parameters along the axial direction both for RHCP and LP (Φ = 45°) Gaussian input beams.

Fig. 3 Experimental set-up. A diode laser coupled to a monomode fiber generates a Gaussian beam at 640nm with a beam waist radius w₀ = 1.26mm. Then the beam is focused by means of a focusing lens (FL) along one of the optic axes of a KGd(WO₄)₂ biaxial crystal (BC). Experiments from Fig. 2(b) were carried out using a FL with 100mm focal length and a biaxial crystal 10.5mm long, while FLs with focal lengths of 150mm, 200mm and 400mm and a biaxial crystal 2.3mm long were used for the experiments from Fig. 6. Linear and circular polarizers are used as polarization state generators (PSG) and polarization state detectors (PSD) to generate and measure the SOP of the input and output beam, respectively. The transverse patterns are recorded by means of an imaging lens (IL) that projects the image into a CCD camera.

Fig. 4 Intensity variation (a) along the radial direction ρ at the focal plane Z = 0 and (b) along the axial direction Z at the beam center (ρ = 0) for CR vector beams obtained using ρ₀ = 1.50 (blue-solid line), ρ₀ = 0.92 (red-dashed line) and ρ₀ = 0.45 (black-dotted line). The corresponding intensity distribution in the (Z, ρ) plane are shown in figures (c)–(e)

Fig. 5 Numerically calculated Stokes parameters for ρ₀ = 1.50 (a), ρ₀ = 0.92 (b), and ρ₀ = 0.45 (c). See Media 3, Media 4, Media 5, Media 6, Media 7, Media 8 for additional simulations on the evolution of Stokes parameters along the axial direction. The plane of optic axes of the crystal lies horizontally (φ_c = 0).

Fig. 6 Measured Stokes parameters for: (a) ρ₀ = 1.48, (b) ρ₀ = 0.95, and (c) ρ₀ = 0.44.

Fig. 7 Numerically simulated transverse intensity patterns and SOP (blue lines) at Z = 0 of vector beams obtained for a RHCP (first row) and a LP (Φ = 45°) input Gaussian beam for ρ₀ = 10.0 (first column), ρ₀ = 1.50 (second column), ρ₀ = 0.92 (third column) and ρ₀ = 0.45 (fourth column).