# Si Photonics for Practical LiDAR Solutions
## 4 Si Photonics Optical Phased Array
### Key Components
#### 4.2.2 Antenna Array  
With a proper antenna design in place, the next important thing is to arrange them for high quality beam forming. For 1D OPA, the arrangement is relatively straightforward with all antennae, which are often long linear gratings, lined up in parallel as the example shown in Figure 6a.  
As analyzed in Section 4.1.2, to achieve a wide steering angle, narrow spacing between antennae is preferred to increase aliasing angle. The spacing is ultimately constrained by unwanted optical coupling when two waveguides are placed very close to each other. The coupling becomes significantly when the spacing is below around 1.5 \(\upmu\)m at which 60\({}^{\circ}\) FOV can be achieved. Smaller spacing has been demonstrated [69] by reducing waveguide coupling with uneven waveguide width to disturb coupling symmetry. This approach produces a very good FOV but may be more sensitive to fabrication errors and temperature variations in practice.  
The use of narrow antenna spacing inevitably results in a large number of antennae, as well as corresponding phase shifters when the aperture size is required to be sufficiently large for narrow beamwidth. The mm size aperture easily demands hundreds of antennae and phase shifters that greatly complicates control electronics and interconnection.  
For a 2D OPA array, waveguide and metal routing becomes a critical issue with limited chip real estate. A tree-branch waveguide routing architecture is a straightforward choice with a group of first level waveguide branches split from an input bus waveguide via directional couplers or multimode interferometers (MMIs), and a group of second level waveguide branches split from each first level branch. A typical 2D antenna arrangement using directional couplers is shown in Figure 6b. Such arrangement demands a phase shifter in proximity to each antenna and forms a phase shifter and antenna unit cell. The unit cell usually takes a significant footprint, from nearly 10 \(\upmu\)m to over 30 \(\upmu\)m [54; 62] in each dimension, much larger than the pitch required for a large aliasing angle.  
In principle, an unequally spaced antenna array design may be used to reduce the number of antennae and allows larger antenna spacings while maintaining steering range [52; 78]. The principle behind this method is to avoid constructive interference among the higher order grating lobes. However, it actually redistributes the power originally in these grating lobes over many more angles with smaller average values rather than absorbs it in the desired main beam. Therefore, while it does help with  
Figure 6: A typical example of antennae arrangement of **(a)** a 1D OPA (adapted with permission from [65] © The Optical Society) and **(b)** a 2D OPA © 2019 IEEE. Reprinted, with permission, from [54]).  
effective steering angle, it wastes optical energy and increases noise floor. The applicability of this method depends on the system SNR design and applications.  
It is also possible to place all the phase shifters at a region away from the antenna array and use waveguide to arrange the antennae in 2D [49]. However, the density is ultimately limited by how closely two waveguides can be placed, and it quickly becomes comparable to that of the unit cell tree-branch architecture when more than 10 antennae is used in either dimension. There are other attempts, such as multi-layer waveguides, multi-antenna in a single waveguide [79], etc., to tackle this issue while their fabrication complexity and practicality may be up for debate.