Fig. 1. Schematics of two DOPA variations implemented with an unbalanced splitter tree architecture: (a) a 16-element continuous DOPA; (b) a 16-element pixelated DOPA, where the distribution network is subdivided into four 4-element continuous DOPA blocks; and (c) schematic of the weak sidebox grating-based antenna.

Fig. 2. Microscope image of the fabricated devices in SiN, where other non-relevant devices are blurred out: (a) full microscope image showing the circuit of the continuous DOPA and the distribution network of the pixelated DOPA; (b) distribution network of the continuous DOPA; (c) distribution network of the pixelated DOPA; (d) close-up on one of the meander-shaped delay lines; and (e) delay-maintaining fan-in routing used to match the output pitch of the distribution network and the antenna array, while not adding extra delay between the antennas.

Fig. 3. Measurement results of the fabricated continuous DOPA: (a) far-field image at 1552 nm, showing the main lobe and a grating lobe separation of ≈15°; (b) scan rates along the x and y directions of ≈3.66 and ≈0.072 deg/nm, respectively; and (c) histogram of the FWHM measurements along the x direction with a median of 0.92°, and the y direction with a median of 0.36°.

Fig. 4. 2D beam steering results of the continuous DOPA. (a) Composite image of the far-field images of wavelength scan from 1500 to 1600 nm with a step of 0.1 nm (see Visualization 2), where the FOV is 15°×7.2°. For each image forming the composite, only the pixels with value higher than a certain threshold are shown to visually differentiate the scan lines. (b) A single scan line with the same wavelength step as (a), i.e., 0.1 nm. However, a lower threshold than in (a) is used and a visually continuous scan line can be observed, since the wavelength step here is less than the step required to move from one fully resolvable point to the next, i.e., 0.24 nm. (c) A single scan line with the same threshold as in (b) and a wavelength step of 0.3 nm.

Fig. 5. Side lobe suppression ratio (SLSR) and crosstalk suppression measurement results of the DOPA devices. (a) Histogram of the SLSR and crosstalk suppression of the continuous DOPA corresponding to a wavelength range of 1500 to 1600 nm, with median SLSR value of 3.6 dB and median crosstalk suppression value of 9.5 dB. (b), (c) SLSR and crosstalk suppression, respectively, of the continuous DOPA versus the wavelengths. (d) Histogram of the SLSR and crosstalk level of the pixelated DOPA at the constructive interference wavelengths, with a median SLSR value of 7.6 dB and a median crosstalk suppression value of 11 dB. (e), (f) SLSR and crosstalk suppression, respectively, of the pixelated DOPA versus the wavelengths, showing the local maxima of the SLSR corresponding to the constructive interference wavelengths.

Fig. 6. 2D beam steering results of the pixelated DOPA. (a) Composite of the far-field images of the wavelength scan from 1500 to 1600 nm at the constructive interference wavelengths (see Visualization 3). For each image forming the composite, only the pixels with value higher than a certain threshold are shown to visually differentiate the scan lines. (b) A single scan line showing four pixels per scan line. However, a lower threshold than in (a) is used to show the spot clearly.

Fig. 7. Measurement results of the fabricated pixelated DOPA: (a) far-field image at 1552.86 nm, showing the main lobe and a grating lobe separation of ≈15°; (b) scan rates along the x and y directions of ≈3.66 and ≈0.072 deg/nm, respectively; and (c) histogram of the FWHM measurements along the x direction with a median of 0.97°, and the y direction with a median of 0.36°.

Fig. 8. Different DOPA architectures. (a) The AWG which consists of a parallel bundle of waveguides with incremental increase in the waveguide length by ΔL. (b) The unbalanced splitter tree which is presented in this work. The delay is added to one arm of each splitter. In each stage m, the delay added to the splitter arm is 2mΔL. (c) The snake using the implementation of Ref. [14], where the delay is introduced by the grating antennas and the “flyback” waveguides. (d) An alternative implementation of the snake, presented in Ref. [22], where light is distributed via a bus waveguide. The light is tapped off to the grating antennas at fixed distances ΔL.

Fig. 9. Angular resolution considerations. (a) The angular resolution along the y axis δθy is defined by the differential delay length. The number of resolvable points is then Ny=Δθyδθy, provided that the spot size along y is smaller than or equal to δθy. (b) FWHMy>δθy, and hence, the number of resolvable points along y is limited by the spot size. In this case, ΔL is larger than necessary and only contributing to extra phase errors. (c) The angular resolution in the x direction δθx of the continuous DOPA is considered equivalent to the angular separation between two fully resolvable points along the x direction, i.e., the beam divergence. (d) The angular resolution along the x direction δθx of the pixelated DOPA depends on the number of antennas per block and is independent of the beam divergence.

Fig. 10. Crosstalk extraction. (a)–(c) The far-field image at different input laser power levels, showing the main lobe, the grating lobes, and the background. (d) The main lobe pixel level and the 90^th percentile pixel level versus the laser power, where the crosstalk level is extracted as the difference in the laser power level at which the 90^th percentile has the same level as the main lobe.