# Bloch-Surface-Polariton-Based Hybrid Nanowire Structure for Subwavelength, Low-Loss Waveguiding
## 3 Optical Properties and Modal Analysis of the Proposed Hybrid Waveguide
Although the mode confinement decreases as the nanowire grows larger, the calculated effective mode area--shown in Figure 5c--can still maintain a deep-subwavelength scale with _Aeff/A_0 lower than \(10^{-3}\). The calculations further reveal that the power confined in the considered region is reasonable and relatively stable with the change of the metallic nanowire radius. Figure 4: Dependence of the proposed modal properties on the buffer layer for different dielectric ridges (\(r=100\) nm): (**a**) modal effective index (\(n_{\textit{eff}}\)); (**b**) propagation length (\(L\)); (**c**) normalized mode area (\(A_{\textit{eff}}\)/\(A_{0}\)); (**d**) confinement factor in the considered gap region (\(\Gamma_{gap}\)), which is schematically shown in the inset in (**d**). To further benchmark the properties of the proposed hybrid waveguide structure, the quantitative comparison of key parameters such as propagation length and effective mode area between the proposed HBSPP waveguide and a typical hybrid surface plasmon polariton (HSPP) waveguide structure is carried out simultaneously. As is known, the excitation of the BSP mode is based on the internal reflection and refraction of the 1D PC multilayer structures, resulting in a weak confinement of the optical mode. Meanwhile, owing to the absence of metal, the excited low-loss BSP mode in the all-dielectric structure improves the propagation distance dramatically. Therefore, the hybridization of the BSP mode with the SPP mode effectively provides a good propagation distance with strong mode confinement. For fair comparison, the HSPP waveguide structure consists of a nanowire topped on the high-index dielectric ridge with the low-index buffer layer sandwiched between them, as shown in the inset of Figure 6b. The structural parameters and materials of the HSPP waveguide are the same as the proposed HBSPP waveguide, with the absence of the periodical 1D PC. During the comparison, the thickness of the buffer layer is changed to calculate the propagation length (\(L\)) and the normalized mode area (\(A_{\textit{eff}}\)/\(A_{0}\)). For intuitive comparison of the modal properties, the 2D plots of the HBSPP waveguide and the HSPP waveguide are depicted in Figure 6a,b, respectively. The results of the HSPP waveguide are calculated using the same method as the proposed HBSPP waveguide shown above. As clearly illustrated in Figure 6, for the proposed hybrid waveguide, a \(\sim\)2 times larger propagation length of the proposed HBSPP waveguide can be achieved compared to that of the HSPP waveguide, although the effective mode area of the HBSPP waveguide increases slightly compared to the corresponding HSPP counterparts. The results indicate that the hybridization of the BSP mode with the SPP mode could help to reduce the propagation loss with a certain sacrifice in the mode confinement. Figure 5: Dependence of the proposed modal properties on the radius of the metallic nanowire for different buffer layer (\(t_{\text{r}}=150\) nm): (**a**) modal effective index (\(n_{\textit{eff}}\)); (**b**) propagation length (\(L\)); (**c**) normalized mode area (\(A_{\textit{eff}}\)/\(A_{0}\)); (**d**) confinement factor in the considered gap region (\(\Gamma_{\text{gap}}\)) which is schematically shown in the inset in Figure 4d.