# Bloch-Surface-Polariton-Based Hybrid Nanowire Structure for Subwavelength, Low-Loss Waveguiding
## 2 Geometry of the Proposed Hybrid Waveguide  
The structure of interest is schematically shown in Figure 1, which consists of a metallic nanowire placed near the up side of a high-index, dielectric-ridge-loaded 1D PC multilayer structure, with a low-index, nanoscale buffer layer sandwiched between them. The metallic nanowire is buried in air cladding, supporting the subwavelength tightly confined plasmonic mode over a wide wavelengthrange at the surface. With appropriate design, the BSW mode can be excited in the 1D PC multilayer structures for p-polarized incident light for the considered wavelength. The sandwiched buffer layer helps to squeeze the hybrid optical mode within the nanoscale gap region with low modal loss. The hybridization between the BSP and SPP modes is conducted by tuning the structural parameters of the waveguide. In our study, the operating wavelength is set at the telecommunication wavelength \(\lambda\) of 1550 nm. The 1D PC multilayer structure consists of 20 alternating TiO\({}_{2}\) (H, high-index) and SiO\({}_{2}\) (L, low-index) layers, with the thicknesses of \(t_{\rm H}\) = 385 nm and \(t_{\rm L}\) = 350 nm, respectively. The material of the high-index dielectric ridge is selected as TiO\({}_{2}\), the thickness of which is defined as \(t_{\rm r}\) and the width of which is 3 \(\mu\)m. The parameters and materials listed above are designed to be able to excite the BSW mode in the truncated 1D PC multilayer structure according to the formula in Reference [21]. The metal nanowire is chosen as gold for its good optical properties and chemical stability with the radius of r. The material of the buffer layer is selected as SiO\({}_{2}\), the thickness of which is denoted as t\({}_{\rm b}\) and the width of which is the same as the dielectric ridge. The refractive indices of TiO\({}_{2}\), SiO\({}_{2}\), Au, and air at the operating wavelength are \(n_{\rm h}\) = 2.438, \(n_{\rm l}\) = 1.444, \(n_{\rm au}\) = 0.55 + 11.5\(i\) and \(n_{\rm c}\) = 1, respectively. In the following, the characteristics of the hybrid waveguide are investigated by solving the Helmholtz equation with the finite-element method (FEM) method based on COMSOL(tm), the mode analysis is carried out in the frequency domain which belongs to an RF (Radio Frequency) module, and a first-order scattering boundary condition is used in the eigenmode solver. In order to illustrate the local field enhancement of the proposed HBSPP waveguide structure and the hybrid mode, we obtained the result of the coupling between the SPP mode and the BSP mode. The E field distributions are plotted with the same scale and the corresponding effective refractive indices of the SPP that excited with the metal nanowire only, the BSP that excited within the 1D PC only, and the hybrid mode proposed in our paper are respectively marked. The structural parameters of the waveguides are chosen as: \(t_{\rm r}\) = 150 nm, \(t_{\rm b}\) = 10 nm, and \(r\) = 100 nm, respectively. It can be seen in Figure 2 that, for the 1D PC, the enhanced electric field is mostly distributed in the dielectric-ridge layer and the underneath multilayer structure, and the maximum E field enhancement factor is \(\sim\)50; for the metal nanowire, the E field enhancement factor is \(\sim\)280. For the hybrid mode, the E field is strongly confined within the gap between the buffer layer and the metal nanowire with a greatly enhanced factor of \(\sim\)350, which is larger than that of both the SPP mode and BSP mode, and the effective refractive index of the mode is between that of the SPP mode and that of the BSP mode. As far as is observed, the BSP mode and the SPP mode couple with each other and the resulting hybrid mode shows similar characteristics to the SPP mode with a further increased E field enhancement. Figure 1: Schematic diagram of the proposed hybrid waveguide. As a simple demonstration, the electric field distributions of the coupling mode supported by the HBSPP waveguide with different buffer layer thicknesses are investigated.