# Silicon Ribbon-Based Dual-Beam Optical Phased Array with Low Crosstalk and Large FoV
## 3 Results  
FDTD is used to calculate the FFP intensity of a 32-antenna-based bi-directional OPA, and the results in the center wavelength of 1550 nm for the traditional FBG are shown in Figure 7a. The steering angle of the chirped FBG with SR appears at 8.4 degrees and is shown in Figure 7b. Due to the linear radiation through the whole physical grating length, the 0.24 degrees of FWHM in the theta direction from the SR-based chirped FBG is better than 0.82 degrees via the conventional FBG, as shown in Figure 8.  
After the 0.167\(\pi\) phase difference of each of the 32 antennas is applied, the FFP main beam of the chirped FBG OPA with SR through FDTD demonstrates 30 degrees in the \(\Phi\) horizontal directions, and the grating lobe is \(-\)65 degrees. Therefore, an FoV with the SR inserted in the 0.6 \(\upmu\)m pacing FBG could reach 95 degrees in the \(\Phi\) direction, as shown in Figure 9. The side lobe adjacent to the main and grating lobes of the FBG in this study is reduced by about 10 dB. The reduced energy was concentrated on the main lobe and the grating lobe, resulting in a 6 dB increase in the total spot energy intensity. \begin{table}
\begin{tabular}{c c c c} \hline
**Type** & **FBG** & **Period (\(\Lambda\), \(\upmu\)m)** & **Period Number** \\ \hline
1 & 0.5–0.45 \(\upmu\)m & 0.68 & 200 \\ \hline
2 & 0.5–0.42 \(\upmu\)m & 0.69 & 200 \\ \hline
3 & 0.5–0.4 \(\upmu\)m & 0.70 & 70 \\ \hline
4 & 0.5–0.38 \(\upmu\)m & 0.71 & 60 \\ \hline
5 & 0.5–0.36 \(\upmu\)m & 0.72 & 50 \\ \hline \end{tabular}
\end{table} 
Table 1: The design parameters for the FBG built with the SR.  
Figure 7: The FFP intensity is calculated using FDTD for 32 antennas. (**a**) The OPA main beams of a conventional single-width combination without a SR grating. (**b**) The primary beam intensity of a chirped FBG built with SR in OPA steering. In this bi-directional OPA, the light will be injected into the phased array through two sets of the grating antennas by the equal path-length S-bend. The wavelength adjustment from 1510 nm to 1600 nm can move a spot from 15 degrees to \(-0.8\) degrees in the theta direction, and the total moving angle is about 15.8 degrees, as shown in Figure 10. The steering angle of the 1500 nm center wavelength is \(\pm 15\) degrees in the theta direction through two sets of inputs, as shown in Figure 11a, and the 1550 nm wavelength moves to \(\pm 8.4\) degrees, as shown in Figure 11b. A total shift of \(\mp 0.8\) degrees is observed at the 1600 nm wavelength. The beam steering for bi-directional grating antennas of the SR-based chirped FBG OPA demonstrates that the \(\theta\) horizontal directions have a FoV of 30 degrees. Figure 8: \(\theta\)-directional strength is compared between SR-based linear attenuation (red line) with the chirped FBG and conventional antennas (blue line). Figure 9: The strength of SR linearly attenuated antennas and conventional antennas are compared in the \(\Phi\) direction after \(\Delta\psi\) = 0.167\(\pi\). Table 2 shows the comparison between the 32-channel low-coupled dual-beam linear attenuator antenna designed in this study and recent OPA designs [14; 15; 16; 17]. The emitter number of each OPA is shown in the fourth column. The linear attenuator design in this study achieves a similar FWHM in the theta direction at a 400 \(\upmu\)m length compared with some OPAs using longer grating antennas. When the grating spacing is reduced to 600 nm, the last column shows that the steering angles in the vertical and horizontal direction can be demonstrated to be 95 and 30 degrees, respectively. The 30 degrees in the vertical beam steering is to modulate the 90 nm bandwidth from 1510 to 1600 nm wavelength in this kind of SR-grating-based bi-directional chirped FBG. Figure 11: The far-field distribution for the bi-directional OPA is simulated through FDTD at different input wavelengths. (**a**) The operating wavelength is 1510 nm, and the vertical scanning angle is turned to +15 degrees and \(-15\) degrees, respectively.