# Tailorable and Broadband On-Chip Optical Power Splitter
## 3 Results  
Power splitting behaviors in the TE-like mode are presented in Figure 2. The cross-sectional view of the electric field intensity profile of the fundamental TE-like mode at position A of Figure 2a is shown in Figure 2b. The cross-sectional views of the fundamental electric field intensity profiles at location B and C for various upper gap sizes (d\({}_{1}\) = [150 nm, 200 nm, 315 nm]) are seen in Figure 2c-e, respectively. Note that all the intensity profiles in Figure 2 are normalized with a constant to emphasize the optical power splitting results. The lower gap size is fixed at 150 nm. The top-down views of the power flux density for various d\({}_{1}\) gap sizes are seen in Figure 2f-h, and the extracted output power ratios are (**f**) 50:50, (**g**) 70:30, and (**h**) 90:10 at d\({}_{1}\) = [150 nm, 200 nm, 315 nm], respectively. From the boundary conditions of Maxwell's equations, the discontinuity of the electric fields at the boundaries of two adjacent waveguides amplifies the electric field in the gap, referred to as a slot waveguide mode [22]. Therefore, input light arriving at the coupling region slowly converges to double slot waveguide mode, as seen in the left-hand figures of Figure 2c-e. These show the fundamental modes of the electric field intensity profile at the cross section B in Figure 2a. At the end of the coupling section the electric field is strongly confined to the two output waveguides, splitting the optical power as a function of the gap size, \(\mathrm{d}_{1}\). The right-hand figures of Figure 2c-e show the intensity profile of the two output ports at section C of Figure 2a, proving that the optical power through the upper (lower) output port decreases (increases) as enlarging the upper gap size, \(\mathrm{d}_{1}\). In the coupling region, in order to avoid the excitation to higher modes, it is required to maintain a large difference between the effective index of fundamental and secondary modes. The width of input/output waveguides is optimized to 400 nm in order to keep the index difference with low propagation and bending loss [20]. However, in our scheme, the asymmetry structure by \(\mathrm{d}_{1}\
eq\mathrm{d}_{2}\) and the large gap size reduce the effective index difference between the fundamental mode and the higher modes, but the excitation to unwanted higher modes can be prevented by designing the coupling length [23]. To maintain the fundamental mode transition, the coupling length of 15 \(\upmu\)m is determined from the careful simulations. Figure 2: Simulation results showing the split mechanism of the proposed optical power splitter. (**a**) Pictorial top-down view of the splitter. Here, the upper gap size, \(\mathrm{d}_{1}\), varies to control the output power ratio. The lower gap size, \(\mathrm{d}_{2}\), is fixed at 150 nm. (**b**) Electric field intensity profile for fundamental transverse electric (TE)-like mode at the cross-section A on Figure 2a. (**c**)–(**e**) Electric field intensity profiles of the splitter for various gap sizes of \(\mathrm{d}_{1}\) as (**c**) 150 nm, (**d**) 200 nm, or (**e**) 315 nm. The fundamental modes at cross sections B, and the output electric field intensities at cross sections C are presented. (**f**)–(**h**) Top-down view of the power flux density for various gap sizes. The power ratios are (**f**) 50:50, (**g**) 70:30, and (**h**) 90:10. The white arrow and bar in (**f**) indicates the energy flow and 15 \(\upmu\)m.  
A beam splitter with a specific power ratio can be designed by controlling the upper gap size. In Figure 3a, the simulation results of the transmittance through the upper, lower, and the total output channels are shown for the upper gap size. As the upper gap size increases, the coupling with the upper (lower) output waveguide exponentially decreases (increases) at the same rate, respectively. The coupling ratio is defined as \(\mathrm{R}=\mathrm{P}_{\mathrm{up}}/\big{(}\mathrm{P}_{\mathrm{up}}+\mathrm{P}_ {\mathrm{down}}\big{)}\).