# Design of Power Splitters Based on Hybrid Plasmonic Waveguides
## 3 Results and Discussion
In Figure 2b, the positions of 3-fold images were at \(L_{A}/3\), as shown by the arrows C. When z = 3.2 \(\upmu\)m, the field intensity of the 2 nd and the 4 th waveguides was zero, in which the field energy was coupled to the 3 rd and the 5 th waveguides. If we reduced the length of the 2 nd and the 4 th waveguides to 3.2 \(\upmu\)m, a \(1\times 3\) power splitter could be obtained. The scheme is shown in Figure 5a. The intensity distribution is shown in Figure 5b. The field distribution is shown in Figure 5c. It can be seen that the incident field was transmitted into the 1 st, 3 rd, and 5 th waveguides. The ratio of the output power was about 1:1:1. The transmission efficiency, \(\eta=P_{\text{out}}/P_{\text{in}}\), was 91%, where \(P_{\text{out}}\) was the power in the output and \(P_{\text{in}}\) was the power in the input. The output power \(P_{\text{out}}\) was the sum of the 1 st, 3 rd, and 5 th waveguides. The energy loss mainly came from two aspects. One was due to the reflection of the waveguide port. When the input field was transmitted in the 2 nd and 4 th waveguides, part of the energy was reflected by the waveguide ports. The other aspect was the ohmic loss of the waveguide itself [3]. We could also design a \(1\times 2\) power splitter according to the field intensity distribution of Figure 5b. We reduced the length of the 3 rd waveguide to 2.6 \(\upmu\)m, as shown in Figure 6a. The field intensity distribution is shown in Figure 6b. The incident field was transmitted into the 1 st and 5 th waveguides. The ratio of the output power was 1:1. The output power was the sum of the 1 st and 5 th waveguides. The transmission efficiency \(\eta\) was 77%. Figure 5: (**a**) Schemes of \(1\times 3\) power splitter based on five HPWs. (**b**) The intensity distribution of SPPs in the power splitter. (**c**) The field distribution of SPPs in the power splitter. Another scheme for \(1\times 2\) power splitter could be designed by three HPWs, as shown in Figure 7a. The length of the middle waveguide was 2.6 \(\upmu\)m. The field intensity distribution is shown in Figure 7b. The incident field was coupled to the adjacent waveguides. The ratio of the output power was also 1:1. The transmission efficiency \(\upeta\) was 92%, which was more efficient than the scheme of Figure 6. The principal reason was that the number of the middle waveguides in Figure 6 was three and the number in Figure 7 was one, in which the input energy was reflected by the output ends of the middle waveguides. We compared the power splitters proposed in this work with other power splitters previously published, which are shown in \[H_{s}(x,z)=\sum_{n=1}^{N}C_{s,n}\psi_{n}(x,z) \tag{1}\]0 The previous power splitters were mainly based on 2D MIM waveguides. Here, the power splitter was based on 3D HPWs, which was more suitable for integrated photonics structures and had a higher transmission efficiency. \[H_{s}(x,z)=\sum_{n=1}^{N}C_{s,n}\psi_{n}(x,z) \tag{1}\]1 (**a**) Schemes of \(1\times 2\) power splitter based on five HPWs. (**b**) The intensity distribution of SPPs in the power splitter. \[H_{s}(x,z)=\sum_{n=1}^{N}C_{s,n}\psi_{n}(x,z) \tag{1}\]2 (**a**) Schemes of \(1\times 2\) power splitter based on three HPWs. (**b**) The intensity distribution of SPPs in the power splitter.