## 2 Device Design  
As the proposed power splitter is based on the adiabatic coupling of tapered waveguides, the coupling strength of the waveguides is a key parameter to achieve a compact device design. The strong coupling can readily be obtained by reducing the gap spacing between the waveguides. However, small gap spacing beyond the lithography limit prohibits a wide spread of applications of the device. An alternative way to achieve strong coupling is to utilize shallow-etched rib waveguides for enhanced mode overlap. Figure 1 shows the coupling strength of two identical waveguides for different waveguide types: (1) Silicon strip waveguides and (2) silicon rib waveguides. The thickness and width of the waveguides were chosen to be 220 nm and 500 nm, which well supported the single TE\({}_{0}\) mode for both types of waveguides. The partial etch depth of the rib waveguide was 60 nm. The result clearly shows that the rib waveguides had stronger couplings than the strip waveguides. The gap spacing dimension can be relaxed for the rib coupled-waveguide. Therefore, we chose rib waveguides for our power splitter design to achieve DUV lithography-compatible CDs. Shallow-etched waveguides also provided low propagation loss, owing to the small mode overlap with the sidewall roughness.  
Figure 2 shows the schematic of the proposed 3-dB power splitter, consisting of one input waveguide and two output waveguides. A 2-\(\upmu\)m-thick buried oxide (BOX) layer (n = 1.444 at 1550 nm) is in grey. The silicon rib waveguides (n = 3.476 at 1550 nm), with a thickness of 220 nm and a partial etch depth of 60 nm, are in red. The input waveguide and the two output waveguides had identical dimensions. Using eigenmode expansion (EME) solver, the device design was optimized.  
Figure 1: Coupling strength versus gap of two types of waveguide structure. Structures in red and grey are silicon (Si) and buried oxide (BOX), respectively.  
The waveguides were linearly tapered from the tip width (w\({}_{1}\)) of 200 nm to the waveguide width (w\({}_{2}\)) of 700 nm. The gap spacing between waveguides was designed to be 300 nm. In order to design the taper length, we investigated the transmission with the taper length sweep, as shown in Figure 3a. The taper length was chosen to be 40 \(\upmu\)m, at which the transmission converged to \(-\)3.03 dB. Although our current design employed the linear taper, the taper length can be significantly reduced by utilizing the optimal curvature of the taper [31]. The spectral responses of the designed device were also simulated using the FDTD (Finite-Difference Time-Domain) solver. Thanks to the adiabatically tapered waveguides, the broad operation bandwidth over the 200-nm wavelength range was confirmed, as shown in Figure 3b. The normalized E-field intensity profile of the device is presented in Figure 4, which confirms symmetric 3-dB power splitting characteristic.  
Figure 4: The E-field intensity profile of 3-dB optical power splitter. The field values in the legend are normalized values.  
Figure 3: Simulated transmission result. (**a**) Taper length span; (**b**) wavelength sweep over 200-nm bandwidth.  
Figure 2: Schematic of 3-dB tapered rib waveguide optical power splitter. Structures in red and grey are silicon (Si) and buried oxide (BOX), respectively.