# Si Photonics for Practical LiDAR Solutions
## 4 Si Photonics Optical Phased Array
### Key Components
#### 4.2.1 Antenna
Without the help of a stopping layer, it's challenging to achieve a few nm etch accuracy with in-wafer or wafer-to-wafer consistency. For a side modulated grating, the small width difference, e.g., 10 nm, brings challenges in accuracy control, if not violates design rules, for most commercial Si photonics processes. In addition, it may be difficult to obtain good upward diffraction efficiency compared with its top side etched counterparts. Another approach is to over clad a Si waveguide with a SiN grating which has shown sub 0.1\({}^{\circ}\) results [76]. Such a process may not be readily available in a commercial Si photonics process and it may present  
Figure 4: An example of (**a**) a deep-etched focusing grating antenna for 2D OPA (c) 2019 IEEE. Reprinted, with permission, from [54]) and (**b**) a weak coupling strength linear grating antenna for 1D OPA (adapted with permission from [68] © The Optical Society). some challenges with respect to strain control and planarization. Nevertheless, in the authors' opinion it may be a more promising approach. An important metric of a grating antenna for wavelength steering is steering efficiency which can be analyzed from grating coupler phase matching relation [77]  
\[\mathrm{n}_{eff}=\mathrm{n}_{cl}\sin\theta_{c}+N\frac{\lambda}{\Lambda}N=\dots,- 1,0,1,2,\dots, \tag{6}\]  
where \(\mathrm{n}_{eff}\) is the effective index of a waveguide, \(\mathrm{n}_{cl}\) is the index of a cladding material, \(\theta_{c}\) is out-coupling diffraction angle, \(\Lambda\) is grating pitch. Therefore,  
\[\frac{d\theta_{c}}{d\lambda}=-\frac{1}{\mathrm{n}_{cl}\cos\theta_{c}}\left( \frac{N}{\Lambda}-\frac{d\mathrm{n}_{eff}}{d\lambda}\right). \tag{7}\]  
Most people use a detuned second order grating (\(N=1\)) for better upward out-of-plane diffraction efficiency and less back reflection thus the choice of grating pitch does not differ very much for common diffraction angles centered in the range of 5-15\({}^{\circ}\) (in SiO\({}_{2}\) cladding). Therefore, the efficiency of wavelength steering is roughly the same (\(\sim\)0.15 deg/nm) for most results listed in Table 5. The results from [63; 64] are slightly better and those from [68] are about two times higher. In those works, a narrow side modulated waveguide grating is used as an antenna, and the higher steering efficiency may result from higher wavelength-dependent effective index change for narrower waveguides, as shown in Figure 5b, according to Equation (6). With the benefit of low loss and wavelength dependence, a waveguide edge coupler may be used as an antenna for 1D array cases [52]. Although an edge coupler may be considered less complex to implement, it also presents some challenges. Commonly used waveguide edge couplers, e.g., an inverse taper-based spot size convertor (SSC), are usually engineered to have a large mode size for efficient coupling to a fiber or another waveguide. However, such end couplers result in small divergence angle. i.e., far field envelope, which narrows steering range. An end coupler can be designed for large divergence, but it then may face the issue of high reflectance from its facet due to large refractive index change between a waveguide end and its adjacent medium. A simple anti-reflection (AR) coating may not be the solution. Si cannot be cleaved in straight line for die singulation, therefore deep etch is used in most Si photonics processes to make edge facet exposed. The process design rules often require leaving a short (few \(\upmu\)m) gap between the waveguide end and the etched sidewall. This gap made of SiO\({}_{2}\) is unfortunately inaccurate due to the MEMS type deep etch process and disturbs the performance of any AR coating in an uncontrollable fashion. This issue is not as important as in the  
Figure 5: (**a**) The effective refractive index change and its relative error at 5 nm etch error as a function of grating etch depth for a 500 \(\times\) 220 nm\({}^{2}\) Si waveguide.