# Si Photonics for Practical LiDAR Solutions
## 3 Si Photonics for LiDAR
### LiDAR System Design Considerations
#### 3.2.2 Waveguiding Material
The propagation loss and the bending radius data of Si and SiN waveguides in Table 3 are coarse ranges nevertheless they are good measures to evaluate the scalability of a design, i.e., how many optical elements can be packed on chip for a given size. Propagation loss is related to fabrication processes and can be moderately improved by using advanced lithography with better line edge roughness (LER). Thanks to a maturing ecosystem, these and many other data, provided by foundries' PDK [17; 20], become increasingly rich and statistically predictable. It allows a robust Si photonics product, e.g., a LiDAR chip, design which must consider tolerance and margins based on these data. The waveguides for LiDAR often transmit optical waves at very high power at which non-linear effects cannot be neglected. The Kerr effect, or quadratic electro-optic (QEO) effect, corresponding to the real part or the imaginary part of the nonzero third order nonlinear susceptibility, is responsible for many non-linear behaviors in waveguides such as self-phase modulation (SPM), cross-phase modulation (XPM), four-wave mixing (FWM) and two-photon absorption (TPA). Other nonlinear effects also exist such as stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) due to photon-phonon interactions and molecular vibrational or rotational transition respectively. TPA may be the first one come to mind when people worries the impact of non-linear effects on their Si photonics LiDAR chips. Si has a relatively large TPA coefficient i.e., \(\beta_{\text{TPA}}\) as listed in Table 3 and the corresponding propagation loss can be described as [32]  
\[10\log_{10}(e)\frac{\beta_{\text{TPA}}}{A_{eff}}, \tag{1}\]  
where \(A_{eff}\) is the effective mode size. Taking a \(220\times 500\) nm\({}^{2}\) Si waveguide at 1550 nm for example, the loss is about 2 dB/cm/W. Therefore, TPA introduces non-negligible optical loss when transmitting light above hundreds of mW and may limit the implementation of direct ToF requiring very high peak optical power. TPA may be greatly mitigated by sweeping the induced free carriers away from waveguide with electric field, e.g., generated by a p-i-n diode [38], therefore orders of magnitude higher optical power may be tolerated. TPA in SiN has so far not been observed. SPM introduces optical intensity dependent phase shift which may be an issue of OPA designs relying on specific phase relations among antennae. For pulsed light operation, the induced phase shift varies with time leads to chirping which may cause pulse broadening at the presence of dispersion in waveguides. The instability of such phase modulation also introduces noise to the detected signals. A semi-quantitative way to evaluate this effect is by examining a nonlinear coefficient representing the phase shift per unit propagation length per unit power [39]  
\[\gamma=\frac{2\pi}{\lambda}\frac{n_{2}}{A_{eff}}, \tag{2}\]  
where \(\lambda\) is wavelength and \(n_{2}\) is Kerr coefficient of refractive index listed in Table 3. Taking the same Si waveguide for example \(\gamma\) is on the order of 1 cm\({}^{-1}\)W\({}^{-1}\). Therefore, this phase shift is insignificant for a mm size chip with continuous wave operation which seldomly goes beyond 1 W but is possibly an issue for pulsed light with high peak power. The \(n_{2}\) of SiN is an order of magnitude smaller and SiN waveguides usually have larger mode size so the power constraint due to this effect may be relaxed by 10-100 times. SRS may also be taken into consideration in Si waveguides. The effect of SRS can be analyzed by the Raman pumping threshold, which, under Lorentzian gain spectrum assumption, is estimated to be [36]  
\[\frac{16A_{eff}}{g_{R}L_{eff}}\sim\frac{16\alpha A_{eff}}{g_{R}}, \tag{3}\]  
where \(g_{R}\) is the Raman gain coefficient and \(\alpha\) is propagation loss.