## 3 Component Design and Modeling
### Apodized Bidirectional Grating Coupler
The grating structure parameters (grating pitches (P\({}_{\rm i}\)), grating filling factors (FF\({}_{\rm i}\)) and filling factor of subwavelength gratings (FFs)) are carefully engineered for the optimal device performance with a series of numerical calculations by the Finite-difference-time-domain (FDTD) simulation method. The design procedure of the GCs is as follows. First, the grating directionality and coupling strength are calculated as a function of grating filling factor, respectively. According to the mode matching theory of grating coupling, the grating coupling strength profile for a quasi-Gaussian diffraction field can be calculated. Second, the grating parameters are initially settled based on the calculation results. In addition, the subwavelength gratings are introduced to replace the grating segments with small filling factors, according to the effective medium theory (EMT) [36]. Finally, the grating couplers are optimized using particle swarm algorithm with 2D FDTD method and then verified using 3D FDTD method. Figure 4a,b show the calculated optical field intensity profile of the bidirectional GC (ABG\({}_{1}\)) with the fiber incidence coupling and the waveguide incidence coupling, respectively. As can be seen, the coupler is highly efficient, and the parasitic reflections and substrate leakage power are greatly suppressed. Figure 5a shows the coupling efficiency and upward reflection spectra of ABG\({}_{1}\). The central coupling wavelength is designed to be 1557 nm and the peak coupling efficiency reaches 88.28% (\(-\)0.54 dB). The 1-dB bandwidth of ABG1 is about 37 nm. To obtain a channel nonuniformity below 1 dB, a WDM channel spacing of 5 nm is utilized for our transmitter design. As depicted in Figure 5a, eight wavelength channels are distributed in \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & & & & & & & & \\ \hline \multirow{3}{*}{ABG1} & P\({}_{\rm i}\)(nm) & 579 & 560 & 568 & 575 & 600 & 595 * & 589 * & 592 * & 595 * & 598 * \\ \cline{2-10}  & FF\({}_{\rm i}\) & 0.38 & 0.38 & 0.38 & 0.35 & 0.23 & 0.47 * & 0.51 * & 0.44 * & 0.37 * & 0.23 * \\ \cline{2-10}  & P\({}_{\rm i}\)(nm) & 579 & 560 & 568 & 627 & 600 & 595 * & 589 * & 592 * & 595 * & 598 * \\ \cline{2-10}  & FF\({}_{\rm i}\) & 0.38 & 0.38 & 0.38 & 0.30 & 0.23 & 0.47 * & 0.51 * & 0.44 * & 0.37 * & 0.23 * \\ \hline \hline \end{tabular}  
* The parameters of subwavelength grating structure: FF\({}_{\rm s}\) = 0.67, P\({}_{\rm s}\) = 400 nm.  
\end{table} 
Table 1: The specific parameters of grating period and duty cycle. Figure 4: Calculated optical field intensity profile of (**a**) in-plane coupling and (**b**) out of plane coupling with the ABG\({}_{1}\). the central wavelength range with high coupling efficiency and low upward reflection. For the optical transmitter, the upward reflection of the GCs should be suppressed to avoid strong F-P resonance. To compensate for the bandwidth limitation of the grating coupler, another grating coupler (ABG\({}_{2}\)) with a central wavelength of 1570 nm is designed for the optical modulators of the last three wavelength channels (\(\lambda_{6}\)-\(\lambda_{8}\)). Figure 5b shows the simulated coupling performance of ABG\({}_{2}\). The maximum coupling efficiency is 88.54% (\(-0.52\) dB), the 1-dB bandwidth is 38 nm. As can be seen, all the wavelength channels are located in the low-reflection wavelength region. Table 2 shows the comparison between our coupler design and other state-of-the art fiber-chip grating couplers [37; 38; 39; 40; 41; 42; 43], from which it can be seen that our coupler exhibits the advantages of high coupling efficiency, ease of fabrication and surface-normal optical coupling.