# Tailorable and Broadband On-Chip Optical Power Splitter
## 4 Discussion  
Note that the geometry of the proposed system has typical size values and materials that are used in common photonic integrated circuit technologies. The input and output waveguides can be readily fabricated using excimer laser photolithography, but the feature size of 30 nm at the tapering tips is too small for typical photolithography. Electron beam lithography is one way to obtain such a resolution, but it is not a cost effective way. Alternative method is hybrid lithography where photolithography is used for the entire waveguide system and electron beam lithography is used only for the high-resolution region [24].  
Figure 4: Transmittance against input wavelength at several upper gap sizes. (**a**) 150 nm (50:50 power splitter), (**b**) 200 nm (70:30 power splitter), (**c**) 315 nm (90:10 power splitter), and (**d**) 590 nm (99:1 power splitter) of the upper gap sizes were simulated. The red circles (blue squares) represent the output power ratios through the lower (upper) channel, respectively.  
The waveguide width can be slightly reduced or enlarged by fabrication error, which can result in a different beam-splitter-gap size from its original design. In our scheme, the output split ratio is determined by the relative gap size between the upward and the downward waveguide. If all waveguides shrink or expand in the same way, the difference between the two gap sizes would not change, maintaining the split ratio. To test the effect of this transformation on the splitting ratio, we repeat the computational simulations with an acceptable waveguide width tolerance of \(\pm\) 10 nm in electron beam lithography. From the simulation results, the transmittance of the output changes by up to 1% from the desired splitting ratio values, which can be negligible. This result shows that our optical power splitter scheme is robust to this type of fabrication errors. In addition, when the width or height of the input/output waveguides needs to change under certain experimental conditions, the size of the gap and the selection equation of a power splitting ratio should slightly differ from the current state. Designing a precise beam splitter, though not strictly necessary, should be considered with new conditions.  
In this simulation, only the TE mode is considered. In the TM mode, the evanescent electric field exists at the top and bottom of the waveguides, and the mode profile in the coupling region is complicated and very sensitive to wavelength and geometry dimension variance. In relevant simulations, we observe that the relationship between the gap size and power splitting ratio in the TM mode is different from Equation (1) and is not as simple as that in the TE mode case. We could not find a meaningful and straightforward expression of the relationship as the ratio is too sensitive to the gap size. In addition, we consider the linear optical properties of the proposed design by excluding the nonlinear absorption, power-dependent refractive index, and thermal heating. Further research about the nonlinear optical behaviors of this device is needed.  
Recently, other materials, such as silicon nitride, aluminum nitride, and lithium niobate, are intensively investigated in the fields of photonic integrated circuits. Our suggested structure can be employed not only in silicon but also in other platforms. Due to the different refractive index, mode size, and evanescent profile on other platforms, the parameters in Equation (1) differ from those in silicon than silicon, and further research is required.