Fig. 1. Element phase distribution with (a) ϕ0=5π and (b) ϕ0=10π, respectively.

Fig. 2. Simulated near-field distribution above the array for (a) a Gaussian beam with n=0, ϕ0=0 and P0=1, (b) n=1 with a=1, ϕ0=5π, and P0=1, (c) n=2 with a=0.1, ϕ0=5π, and P0=1, and (d) n=3 with a=0.05, ϕ0=5π, and P0=1, where the dotted rectangle shows a hollow-core central cavity. (e), (f), (g), and (h) are the corresponding simulated curves of the transverse light field at Z=4  mm when n=0, 1, 2, and 3, respectively.

Fig. 3. Simulated near-field distribution above the array for the cubic phase change combination with (a) ϕ0=5π and P0=1, (b) ϕ0=10π and P0=1, (c) ϕ0=20π and P0=1, and (d) ϕ0=10π and P0=1/2.

Fig. 4. Simulated steering results for a quasi-Bessel beam with a cubic phase change combination and varying r of (a) −0.2, (b) 0.03, (c) 0.1, and (d) 0.2, respectively.

Fig. 5. (a) Schematic diagram of silicon OPA with (b) and (c) for the microscope image of the packaged device and OPA chip, respectively. (d) SEM image of the grating waveguide antenna.

Fig. 6. Schematic illustration of the experimental setup for the characterization of beam shaping and steering.

Fig. 7. (a) Measured cross-sectional intensity distribution of OPA along the exit Z direction in the free space for Gaussian beam with n=0. (b) Cross-sectional profile of the recorded light spot, with (c) and (d) for the steering result of simulation and experiment with a deflection angle of about ±70°, respectively.

Fig. 8. (a) Measured cross-sectional intensity above the chip for a quasi-Bessel beam generation (n=1, ϕ0=5π and P0=1), with top-down intensity (b) within the quasi-Bessel region of the emitted beam (Z=4.5  mm), (c) at the edge of the quasi-Bessel region (Z=9.5  mm), and (d) after breakdown of the quasi-Bessel region (Z=17.7  mm).

Fig. 9. (a) Measured cross-sectional intensity above the chip for a high-order quasi-Bessel beam generation (n=3, ϕ0=10π, and P0=1), with top-down intensity (b) near the converged region (Z=2.9  mm), (c) at the hollow-core region (Z=3.5  mm), and (d) at the split hollow core region (Z=4.5  mm). (e)–(g) are the simulated light field distributions at the corresponding region.

Fig. 10. Normalized intensity distribution of the simulated high-order quasi-Bessel beam above the chip at Z position of (a) 3.5 mm and (c) 4.5 mm, with (b) and (d) for the corresponding measured results, respectively.