Fig. 1. Reconstructed results of the ellipse beams with different topological charges [l1=2 for (a) and (b), l2=4 for (c) and (d)]. (a) and (c) are the intensity distributions. (b) and (d) are the phase distributions with differently marked topological charges.

Fig. 2. Intensity distributions at the filtering (Fourier) plane from the phase-only CGH calculated by (a) the grating encoding method and (b) the proposed F-DCGS method. (c) Flow chart of the proposed F-DCGS algorithm.

Fig. 3. Schematic representation of the experiment setup for generating an EPVB. P, polarizer; BE, beam expander; SLM, spatial light modulator; L, convex lenses (f1=400  mm, f2=300  mm, and f3=100  mm); QWP, quarter-wave plate; R, Ronchi grating; CCD, charge-coupled device.

Fig. 4. Generated intensity of the EPVB from the phase-only CGH calculated (a), (b) by the grating encoding method and (c), (d) by the F-DCGS method. The arrow marks in (b) and (d) indicate the polarization direction of an analyzer before the CCD.

Fig. 5. Experimental results of generating EPVBs under different ellipse modes and topological charges. The scaling factors are (a) a=1, b=0.5; (b) a=1, b=0.75; (c) a=1, b=1; (d) a=0.75, b=1; (e) a=0.5, b=1.

Fig. 6. Experimental intensity profiles of generating hybrid EPVBs after two analyzer directions.

Fig. 7. Experimental intensity patterns of the generated RPVBs. (a)–(d): RPVBs under different scaling modes of (a=1, b=0.5), (a=1, b=0.75), (a=0.75, b=1), and (a=0.5, b=1). (e) and (f) show hybrid RPVBs after two analyzer directions.

Fig. 8. Beam propagation in the xz and yz planes are displayed for the case of two beam shaping techniques. (a) Ellipse Bessel function method [3032" target="_self" style="display: inline;">–32]. (b) Our method. The beam intensity profiles before (z=−1  cm) and at (z=0) the focal plane are also shown in each case. (c) The one-dimensional beam intensity profile of the two methods at z=0 (red and blue color lines, respectively).

Fig. 9. Experimental results of the generated hybrid EPVBs in two different types of three-dimensional layouts under different analyzer directions.