# Cm-Level Photonic-Crystal-Like Subwavelength Waveguide Platform with High Integration Density
## 3 T-Shaped Splitter Based on the Subwavelength Waveguides  
The passive power splitter is one of the fundamental components. It is widely applied in optical switches, wavelength-selective filters, light modulators, etc. [20; 21]. However, the splitter based on a PhC-like waveguide has not been proposed in the previous study. At present, there are many types of power splitters, such as dielectric waveguide splitter [22], photonic-crystal waveguide splitter [23], plasma metal waveguide splitter [24; 25] and hybrid structure waveguide splitter [26]. Dielectric waveguide splitter can only be used at a small splitting angle. Photonic crystal waveguide splitter and plasmonic waveguide splitter can realize the beam splitting at a large angle. Here, we propose a T-shaped splitter, which can split the light symmetrically with \(90^{\circ}\) angle and with high efficiency. Figure 10: The band gap versus the Period. The insert shows the band gap drifting with the increasing of the Period. Figure 9: Propagation loss and integration density versus column number of air holes in the square-lattice hybrid waveguide at the wavelength of \(1.55\,\mathrm{\SIUnitSymbolMicro m}\). Figure 11 shows an optimized structure of a T-shaped splitter. The illustration in the lower left corner is the \(E_{z}\) field at an incident wavelength of 1.55 \(\upmu\)m.  
The T-type splitter can be physically analyzed in the scattering matrix theory [27] as follows:  
\[ \begin{pmatrix}E_{1}^{out}\\ E_{2}^{out}\\ E_{3}^{out}\end{pmatrix} =S \begin{pmatrix}E_{1}^{in}\\ E_{2}^{in}\\ E_{3}^{in}\end{pmatrix}  \tag{1}\]  
where  
\[S= \begin{bmatrix}r_{1}&s_{12}&s_{13}\\ s_{21}&r_{2}&s_{23}\\ s_{31}&s_{32}&r_{2}\end{bmatrix}  \tag{2}\]  
\(r_{i}\) (i = 1,2,3), \(t_{1}=(s_{21}=s_{31})\), \(t_{2}=(s_{12}=s_{13})\) and \(s_{23}=s_{32}\) are, respectively, the reflection and splitting coefficient of the corresponding port caused by the structure; and \(E_{i}^{in}\) and \(E_{i}^{out}\) stand for the fields of incident and output beams at Port i, respectively. Using Equation (1) and the law of conservation of energy for only one input beam of Port 1, one can obtain \(E_{1}^{out}=r_{1}E_{1}^{in},E_{2}^{out}=t_{1}E_{1}^{in},E_{3}^{out}=t_{1}E_{1}^ {in}\), and \((E_{1}^{in})^{2}=(r_{1}E_{1}^{in})^{2}+(t_{1}E_{1}^{in})^{2}+(t_{1}E_{1}^{in})^ {2}\). It finally gives  
\[t_{1}^{2}=(1-r_{1}^{2})/2 \tag{3}\]  
Therefore, to get the maximum energy transmittance \(t_{1}^{2}\) of \(1/2\), one has to optimize the reflectivity \(r_{1}\) of the design to be very small, even close to 0. The performance of varied radius and the positions of several air holes on the loss at the branch is simulated, and a triangular metal Ag with suitable \(L\) and \(h\) is used to achieve high splitting efficiency. After the optimization, a splitter with a transmission efficiency of 0.422 can be obtained with the parameters of \(L=1.58\upmu\)m, \(h=0.52\upmu\)m, \(R_{a}=0.10\upmu\)m (the positions of air holes a and \(a^{\prime}\) are deviated from the original position with \(\Delta x=\pm 0.01\upmu\)m, \(\Delta y=0.02\upmu\)m), and \(R_{b}=0.08\upmu\)m. It gives an excess loss of the T-type splitter less than 0.4 dB. The right insert of Figure 11 is the spectrum of the T structure. It gives the operation wavelength range (1.45-1.51 \(\upmu\)m, 1.52-1.56 \(\upmu\)m) of T-type splitter. If the angle of T-type splitter is changed, it will become a Y-type splitter. One can design a Y-type splitter with an  
Figure 11: The structure of a T-type splitter with its beam propagation in the lower left inset. The right insert of Figure 11 is the spectrum of the T structure. arbitrary angle based on the same optimization process. By adjusting the sizes and positions of the air holes and the size of the metal at the junction, the branching effect can be optimized. The minimal size of the air holes and the smallest width among the metal walls are, respectively, 130 nm and 100 nm, which are all larger than the resolution (\(\sim\)5 nm) of a typical electron-beam lithography (EBL) system.