# Cm-Level Photonic-Crystal-Like Subwavelength Waveguide Platform with High Integration Density
## 1 Introduction
### A Triangular Lattice of Circular Air-Holes
#### 2.1.2 The High Isolation of Photonic Crystal-Like Waveguides  
Because isolation or crosstalk between adjacent waveguides determines how closely two waveguides can be laterally placed in the integrated plane, the isolation versus the width of the common silver sidewall was examined. The isolation (or crosstalk) between adjacent waveguides determines how closely two waveguides can be laterally placed in the integrated plane. The isolation is defined to be \(I_{so}=10\times log(P_{3}/P_{2})\), where \(P_{2}\) and \(P_{3}\) are the powers monitored at the output ports for the channel waveguide and its adjacent waveguide, respectively.  
In Figure 6, we give examples of two closely spaced waveguides with 0.5 and 1 column air holes, respectively, and with a metallic sidewall width of \(0.1\,\upmu\)m between them to show the isolation between left and right waveguides. The light beam is launched at the input port of each left waveguide at the wavelength of \(1.55\,\upmu\)m. It can be seen that the beam propagating along each left waveguide can be well confined and the right waveguide is well isolated from the left one. The two silver sidewalls of the proposed waveguide can be approximately treated as two perfect mirrors, which can form mirror images of the realistic silicon core to equivalently double column number of air holes. The simulation of two adjacent waveguides shows the isolation between them is \(31.85\) dB for the propagation distance of \(100\,\upmu\)m in the waveguide with 0.5 column air holes at the wavelength of \(1.55\,\upmu\)m, as shown in Figure 6a. The width of 100 nm far exceeds the skin depth of the silver (\(\sim\)21 nm at \(\lambda=1.55\,\upmu\)m). Therefore, the width of 100 nm is safe enough for silver wall to achieve high isolation. If the number of air-hole columns increases, the isolation will be better, as shown in Figure 6b.  
Figure 5: The \(E\) fields of waveguides with different column numbers of air holes without metallic sidewall ((**a–c**) for \(1.0,2.0,3.0\) columns, respectively) at the wavelength of \(1.55\,\upmu\)m.  
2.1.3. The Propagation Loss and Integration Density Versus Column Numbers of Triangular Lattice Air-Holes Waveguide  
At the wavelength of 1.55 \(\upmu\)m, we obtained the propagation loss from the definition of \(Loss=10\,log\frac{P_{out}}{P_{in}}\), where \(P_{in}\) and \(P_{out}\) are, respectively, the input and output powers of the waveguide in 17 periods of air holes at the propagation direction. The loss per length is averaged from the definition of \(Loss/length\), where the \(length\) is the distance (of 17 periods) between the two monitors in the propagation direction of the waveguide, to obtain the propagation loss per centimeter for the subwavelength waveguides with different column number of lateral air holes, as shown in Figure 4. It can be seen that the propagation loss is also small in the centimeter-level transmission distance as the waveguide with 1.5 columns of air holes or more. Many micron-scale devices can be integrated in the cm-level waveguide platforms. There are few reports on cm-level waveguide with subwavelength confinement in the integration plane in the literature.  
Next, the integration density is defined as the number of parallel-integrated waveguides with high isolation (>30 dB) in one millimeter in the lateral direction, the integrated density is further compared to obtain the optimal performance. As shown in Figure 4, the integration density decreases for subwavelength waveguides with a larger column number of air holes. Therefore, there is a tradeoff between the propagation loss and the integration density. One can choose different column number of the waveguide for different application requirement. Since the intersection of the loss curve and the integration curve does not fall within the structure range of the triangular lattice waveguide, we continue to explore the square lattice waveguide for the balance between the loss and integration density.