# Cm-Level Photonic-Crystal-Like Subwavelength Waveguide Platform with High Integration Density
## 1 Introduction  
An efficient integrated waveguide is undoubtedly the basis of the development of photonic integrated circuits. A valuable candidate needs to have excellent characteristics such as subwavelength mode constraints, chip scale propagation length, high efficiency waveguide bending, and small center-to-center separation between low crosstalk adjacent waveguides. Recently, reports of plasmonic waveguides such as metal-dielectric-metal (MDM) [1], dielectric-metal-dielectric (DMD) [2], hybrid surface plasmon polariton (HSPP) [3; 4; 5], and dielectric loaded surface plasmon polariton (DLSPP) [6], have generated considerable attention. Plasmonic waveguides can bound light into the deep subwavelength scale, and enhance light-matter interactions [7; 8]. However, due to the collective oscillation of electrons at the interface between metal and medium with Ohm dissipation, the propagation loss is high. It is impossible to achieve medium or even small scale waveguide integration, and the practical prospect is severely limited. On the other hand, photonic crystal (PhC) waveguide [9; 10] can form a superposition of multiple reflection interfaces through multiple lattice cycles, so that the beam can be effectively bound in the core layer. Based on this mechanism, light beam can be effectively guided with very low loss. However, due to the requirement of multiple periods, the transverse width of the waveguide is large, which is not conducive to integration. Therefore, if one can take full advantages of the strong field confinement of an MDM waveguide and the ultra-low propagation loss of a photonic crystal waveguide, a newhybrid waveguide could be designed. For example, utilizing the mirror imaging symmetry of the metal, one can decrease the lateral period number of a PhC waveguide double or more, so that the entire width of the waveguide can be largely decreased. Earlier, our group tried the hybrid waveguide with only one column of air holes and a metal wall (cladding) on each side of the waveguide [11; 12; 13], and preliminarily found that it is of low loss, high isolation (or channel crosstalk) and efficient bending. However, the cm-level PhC-like subwavelength waveguide platforms with various photonic lattice structures have not yet been studied. We carried out numerical investigation on various lattice structures and guiding mechanisms of the PhC-like subwavelength waveguides, in which the tradeoff between the integration density and loss were analyzed to obtain optimal performance. It is also interesting to investigate the guiding mechanism on different geometric constructions of the waveguide platform. This study may pave the way of developing the high-performance PhC-like hybrid waveguide platform for the large-scale photonic integration. The paper is structured as follows. Section 2 describes characters of the subwavelength PhC-like waveguide with trigonal- and tetragonal-latticed PhC structures. Section 3 presents the basic structure of a T-shaped splitter and its performance on the power splitting. This is followed by the conclusions. Propagation Characters of the PhC-Like Hybrid Waveguides with Different Photonic Lattice Structures  
The PhC-like waveguide is formed by introducing a few columns of periodic air holes with one metallic sidewalls on each side of the silicon core of a TE-mode MDM waveguide. The air holes are employed to enhance the mode confinement and to extend the propagation length at the same time. The schematic is shown in Figure 1, where \(d_{1}\) and \(Period\) are, respectively, the distances between the centers of two adjacent air holes in the \(x\) and \(y\) directions, \(R\) denotes the radius of all the air holes. The symbol \(d_{2}\) denotes the widths of metallic sidewalls. The real waveguide structures will be fabricated on the silicon on insulator platform. It should be much better to perform the three-dimensional (3D) simulation than the 2D simulation.