## 3 Results
Figure 3b also reveals another interesting phenomenon; with increasing top layer thickness, the cutoff wavelength for this H1X mode will be increased. For example, when the top layer thickness is t = 160 nm, this mode will be cut off with the incident wavelength longer than 620 nm, whereas when the thickness is increased into 250 nm, this mode can also appear when the incident wavelength is 660 nm. In our experiment, FFP images of the plasmon propagating along this 70 nm diameter Ag NW at different wavelengths and top layer thicknesses are shown in Figure 4. The selected wavelengths were 580, 600, 620, and 640 nm. Figure 4a-d shows the top layer thickness was approximately 160 nm, and it is clear that at 620 nm wavelength, we could barely find the plasmon propagating along the Ag NW. On the contrary, in Figure 4i-l, the top layer was at the thickness of approximately 250 nm,  
Figure 3: Simulated effective refractive index of the SPP waveguide mode. (**a**) The effective refractive index of Bloch surface wave mode versus the thickness of top SiO\({}_{2}\) layer, in the case of three selected incident wavelengths (570, 590, and 610 nm); (**b**) The effective refractive index of BSW mode versus the incident wavelength with three different thicknesses of top SiO\({}_{2}\) layer; (**c**) The electric field distribution of H1X mode with thickness t = 200 nm and wavelength \(\lambda\) = 590 nm. The arrows with white colour denote the directions of the electric fields, which shows that the mode is the H1X mode. The diameter of the Ag nanowire was 70 nm. and the plasmon could be clearly observed propagating along the NW even if the wavelength was 640 nm. Experiments and simulations verified that the top layer thickness can be used to tune the cutoff wavelength of the plasmonic H1X mode on the Ag NW. To further confirm the mechanism of the above phenomena, the projected photonic band structure of the dielectric multilayer for transverse electronic (TE) polarization was simulated as shown in Figure 4m [38]. The dispersion relations of H1X mode at the three top layer thicknesses were also plotted in this figure. The three curves (t = 160, 180, and 250 nm) of the dispersive (dispersion) relations are all located inside the stop band gap (the yellow zone on Figure 4m) of this multilayer and lie on the right side of the light line, which is the fundamental reason that the plasmons can be confined and propagate along this very thin Ag NW. As shown in Figure 4m, we can locate the cutoff wavelength for the plasmonic mode, which decreases with the decreasing of the top layer thickness. This phenomenon also can be analysed from the change of effective index of the plasmonic mode with the incident wavelength and top layer thickness. As shown in Figures 2 and 3, in the case of a thin top dielectric layer (e.g., t = 160 nm), its refractive index is smaller than that of a thicker one (t = 250 nm), and with the  
Figure 4: Controlling the propagation distance of the SPP waveguide mode with the top SiO\({}_{2}\) layer’s thickness. **(a–d)** The thickness of the top dielectric layer is t = 160 nm; **(e–h)** the thickness of the top dielectric layer is t = 180 nm; **(i–l)** the thickness of the top dielectric layer is 250 nm. The incident wavelength varied from 580 to 640 nm with 20 nm step, as labelled from **(a)** to **(l)**. The scale bar in **(a)** is also applicable for the images in **(b–l)**. The diameter of the Ag NW was about 70 nm in all these images; **(m)** Simulated band structure of the multilayer and dispersion relation of the SPP waveguide mode. The projected photonic band structure of the dielectric multilayer for transverse electronic (TE) polarization. The yellow zone denotes the stop band. The solid lines denote the dispersion relations of BSW modes with different thickness of the top SiO\({}_{2}\) layer (t = 160, 180, and 250 nm). increasing of the incident wavelength, the refractive index of this SPP mode will decrease accordingly. When this index approaches 1.0, this mode will be cut off.