# Tailorable and Broadband On-Chip Optical Power Splitter
## 2 Materials and Methods  
The simulations are performed by Lumerical's MODE solution, which offers the 2.5D finite-difference time-domain method. The mesh accuracy used in the simulation is the predefined value 6 in Lumerical, which is small enough for the narrow tips in the tapered region in Figure 1. The time step is about 0.04 fs. The boundary conditions are the perfect matched layer condition in the \(x\)- and \(y\)-directions and the metal boundary condition in the \(z\)-direction. This metal boundary condition can reduce the simulation time and does not affect the simulation results as light is tightly confined in the waveguides. A 3D diagram of the proposed beam splitter is illustrated in Figure 1a, and the top-down view of the power splitter system with various geometric parameters is shown in Figure 1b. The 1 \(\times\) 2  
Figure 1: Proposed photonic power splitter based on 1\(\times\)2 interleaved tapered waveguides (**a**) 3D schematic representation of a 1\(\times\)2 ITW. (**b**) Pictorial representation of the splitter from the top-down view. All waveguides have a width of W = 400 nm and a thickness of h = 220 nm. The tapering length is L = 15 \(\upmu\)m, and the sharp end of each tapered waveguides has the width of 30 nm. (**c**)–(**e**) Cross-sections of the proposed power splitter at several positions. The location of each cross-section is marked on Figure 1b with green dashed lines as (**c**) A, (**d**) B, and (**e**) C.  
interleaved tapered waveguide (ITW) structure consists of an input port with one tapered waveguide and two output ports with tapered waveguides next to the input channel in the opposite direction. The waveguides are tapered in from 400 nm to 30 nm across the coupling length L (15 \(\upmu\)m), as shown in Figure 1b. Since the tapering angle of the input and output waveguides is identical, two slot waveguides are created, approaching each other along the propagation direction. The minimum tapering size of 30 nm is determined from typical and affordable electron beam lithography resolution. Divided optical power comes through two curved waveguides with a bending radius of 30 \(\upmu\)m. The cross-sectional views of the power splitter system at locations A, B, and C in Figure 1b are shown in Figure 1c-e, respectively. The silicon waveguides in this scheme are surrounded by a SiO2 cladding and have a thickness (**h**) of 220 nm and a width (W) of 400 nm, as seen in Figure 1c-e. The performance of this structure is simulated for various geometrical conditions. The gap size between the input tapered waveguide and the upper output waveguide in Figure 1b varies lithographically from d\({}_{1}\) = 150 nm to 600 nm. By means of changing this gap d\({}_{1}\), the output ratio can be designed to achieve a desired split ratio. The lower gap of d\({}_{2}\) = 150 nm and the coupling length of L = 15 \(\upmu\)m are fixed. The gap sizes d\({}_{1}\), d\({}_{2}\) and the coupling length L are larger than those in reference [20]. The gap size of 150 nm is slightly larger than the decaying depth of the evanescent wave. The gap size of less than 150 nm can yield complicated coupling between waveguides due to long evanescent tails, and the power splitting becomes sensitive to fabrication errors. The gap size of 150 nm is large enough to prevent complicated coupling and to achieve tailorable power relatively readily. On the other hand, simulation results show that a beam splitter with larger gap size than d\({}_{1}\) = d\({}_{2}\) = 150 nm and shorter coupling length than L = 15 \(\upmu\)m significantly increases its insertion loss. With the optimized gap size of 150 nm, the coupling length should be at least 15 \(\upmu\)m to achieve transition with the fundamental mode and to compensate the loss induced by the large gap. Note that this method is designed with only one polarization direction in silicon waveguides. The computational simulation is conducted with only transverse electric (TE)-like modes as many photonic integrated circuits support one polarization mode (mostly TE-like mode).