Fig. 1. The initial intensities and angular spectra of the cPeG beams with different initial polarization states for n=1, 2 and 4. (a), (d): α=π/4, δ=π/8; (b), (e): α=0, δ=0; (c), (f): α=π/4, δ=−3π/4. The phase distribution and polarization states are described in the top form left to right in Figs.1 (a)−(c). Blue: left-handed elliptical polarization; Red: right-handed elliptical polarization; Black: linear polarization. The parameters are x₀=y₀=100 μm and Ω=1.4

Fig. 2. The theoretical design scheme of the cPeG beams with uniform polarization. BS: Beam Splitter; SLM: Spatial Light Modulator

Fig. 3. Normalized longitudinal Poynting vector (backgrounds) and transversal Poynting vector (arrows) of cPeG beams for different uniform polarizations (α, δ) at z=50z₀. (a), (d), (g): TE term; (b), (e), (h): TM term; (c), (f), (i): whole beam. The parameters are n=2 and Ω=1.4. The red point symbolizes topological charge l=+1, and the white point denotesl=−1

Fig. 4. Normalized longitudinal Poynting vector (backgrounds) and transverse Poynting vector (arrows) of cPeG beams for different n and Ω at z=50z₀, where the uniform polarization is (α, δ)=(π/4,π/8)

Fig. 5. Normalized longitudinal SAM (3D and 2D) and transverse SAM (arrows) of cPeG beams at z=50z₀. (a)−(c): α=π/4, δ=π/8; (d)−(f): α=π/4, δ=−3π/4. The other parameters are the same as those in Fig. 3

Fig. 6. Normalized longitudinal (3D and 2D) SAM and transverse SAM (arrows) of cPeG beams (n=1, 4) at z=50z₀. (a)−(c): n=1, Ω=3; (d)−(f): n=4, Ω=1. The other parameters are the same as those in Figs. 5 (α=π/4, δ=π/8)

Fig. 7. Normalized longitudinal OAM (3D and 2D) and transverse OAM (arrows) of cPeG beams (Ω=1.4) at z=50z₀. (a)−(c): α=π/4, δ=π/8; (d)-(f): α= 0, δ= 0; (g)−(i): α=π/4, δ=−3π/4; The other parameters are the same as those in Fig. 3. (n=2)

Fig. 8. Normalized longitudinal and transverse (arrows) OAM of cPeG beams (n=1, 4). (a)−(c):n=1, Ω=3; (d)−(f):n=4, Ω=1 at z=50z₀. The other parameters are the same as those in Fig. 4