Fig. 1. Illustration of the proposed scheme under circularly polarized basis vector. The cases (0, –1, π / 4), (1, 0, 0), and (1, 1, π / 4) are presented in panels (a)–(c) in turn. The first and second columns display the intensity and phase profiles of right-(R) and left-handed (L) circular polarization states, respectively. The synthetic polarization, normalized Stokes parameters along angular direction and polarization mapping tracks on Poincaré sphere are depicted in the third to the fifth columns, respectively. The red and blue ellipses represent right- and left-handed polarization states, respectively.

Fig. 2. Modulation effect of l and m on polarization gradient. The polarization structures, the polarization mapping tracks, and the evolution curves of longitude and latitude angles along angular direction are depicted in the first to the third rows, respectively.

Fig. 3. Hybrid vector beams under various base states. The red and blue ellipses represent right- and left-handed polarization states, respectively.

Fig. 4. Polarization structures (upper) and transverse Poynting vector patterns (lower) of hybrid vector beams with (a)–(d): (0, –1, 0), (0, –1, π / 3), (1, 1, π / 3), and (3, –1, 0) under X–Y base vectors, (e): (1, 1, π / 3) under R–L base vectors, and (f): (3, –1, 0) a pair of elliptical base vectors. The red and blue ellipses represent right- and left-handed polarization states, respectively.

Fig. 5. Experimental setup. BE: beam expansion module; HWP: half-wave plate; PBS: polarizing beam splitter; M1–M4: mirrors; RAPM: right-angle prism mirror; SLM: spatial light modulator; QWP: quarter-wave plate; L: lens; F: spatial filter; PMS: polarization measuring system; CCD: charge coupled device. Insets: (a) the computer-generated holograms and (b) the measured intensity patterns of x and y components for the case (1,0,0) on the base of X–Y basis vectors, i.e., radial vector beam.

Fig. 6. Experimental and theoretical results for (a) (1, –2, π/4) under X–Y basis vector, (b) (2, –3, 0) under R–L basis vector, and (c) (1, –1, 0) under elliptical basis vector E_p1 – E_p2. The longitude and latitude of E_p1 and E_p2 on Poincaré sphere are (–π / 3, π / 3) and (2 π / 3, –π / 3), respectively. The measured intensity patterns of orthogonal basis vectors are shown in panels (a1)–(c1). Theoretical (left) and experimental (right) results of Stokes parameters and produced polarization structures are depicted in panels (a2)–(c2) and (a3)–(c3) in turn. The red and blue ellipses represent right- and left-handed polarization states, respectively.