Fig. 1. The simulation of far-field beamforming. (a) Far-field patterns of beams pointing at different angles (each beam intensity is represented by a unique color), whose peak intensity follows an envelope function. (b) Two single beam points at −10° (red) or 30° (green), respectively; and (c) the dual-beam points at both angles (blue). (d) Two single beam points at −20° (red) or 20° (green), respectively; and (e) the dual-beam points at both angles (blue). (f) Schematic diagram of a uniform dividing scheme for generating independent dual beams.

Fig. 2. (a) Schematic of the OPA structure. (GC, grating coupler; MMIs, multi-mode interference couplers; PS, phase shifter; WEA, waveguide emitter array). Not drawn to exact scale or to exact number of elements. (b) An optical microscope image of the OPA chip after wire-bonding and wires are protected by black resin. (c) Schematic of the experimental setup used to characterize the OPA. (TL, tunable laser; FPC, fiber polarization controller; SMF, single-mode fiber; DUT, device under test; PD, photodetector; MVS, multi-channel voltage source, PC, personal computer.)

Fig. 3. Experimental far-field patterns of dual beams through uniform division. The dual-beam points at the same side: (a) −40° & −10°, (b) 10° & 30°, and (c) −40° & −20° simultaneously; at different sides: (d) −10° & 20°, (e) −20° & 30°, (f) −30° & −30°, and (g) −50° & −50°. Beam patterns are normalized to their peak intensities.

Fig. 4. Simulated and experimental intensity distributions of the dual-beam pointing at (a) −30° & 10° through uniform division, (b) −30° & 10° through non-uniform division, (c) −50° & −10° through uniform division, and (d) −50° & −10° through the non-uniform division scheme. Experimental intensity distributions of the dual-beam pointing at −50° & 50° through the non-uniform division scheme; the intensity ratios of the two beams are (e) 1.0, (f) 0.5, and (g) 0.3. All beam patterns are normalized to their peak intensities.

Fig. 5. (a) Experimental far-field pattern of a dual beam pointing at −3° & 2° through uniform division. (b) The corresponding infrared image (a) when the camera is facing the chip. Simulated average similarity between the far fields with and without residual phase error, for the case of (c) single beam, (d) symmetric dual beams, and (e) asymmetric dual beams. The phase error added to the ideal value randomly varies within the range of [−Δϕ, Δϕ], and the maximum phase error Δϕ is represented as the horizontal axis. (Uni, uniform division; Non, non-uniform division.)

Fig. 6. The variation range of OPAs’ far-field distribution with phase error and the corresponding ideal far-field distribution, for the case of (a) single beam pointing at 0° and (b) dual beams pointing at −30° and 30°. (c) Far-field samples with phase error influence (maximum phase error is 0.15π) are shown in the case of dual beams pointing at −30° and 30°. The legends show the maximum range of phase error variation, and the intensity value is normalized to the peak value of the ideal beam. The stability of the far-field distribution of the OPA under residual phase error with different total numbers of elements N, for the case of (d) single beam pointing at 0° and (e) dual beams pointing at −30° and 30°.