## 4 Conclusions  
In conclusion, a new method has been proposed to mediate the propagation constant of the SPP mode on a very thin Ag NW (diameter as low as 70 nm), when placed on a dielectric multilayer. Both the effective refractive index and propagation distance or cutoff wavelength of this mode can be tuned with the thickness of the top dielectric (SiO\({}_{2}\)) layer. When the Ag NW of the same diameter was placed on a commonly used glass or silicon substrate, the SPP mode here (H1X mode or plasmonic leaky mode)  
Figure 5: FFP images of the plasmon’s propagations. Three Ag NWs of the same diameter (about 70 nm) were put on three substrates with different thickness of the top SiO\({}_{2}\) layer. The top SiO\({}_{2}\) layer’s thickness was (**a,b**) t = 160 nm; (**c,d**) t = 180 nm, and (**e,f**) t = 250 nm, respectively. The incident wavelength was selected as 590 nm. On (**b,d,f**), the blue solid line is an exponential fit to the data (red dots) and was used to extract the propagation distance of the plasmonic mode as 13 \(\upmu\)m (at t = 160 nm), 11 \(\upmu\)m (at t = 180 nm), and 10 \(\upmu\)m (at t = 250 nm). The scale bar in (**a**) is also applicable for (**c,e**).  
disappeared, and only the plasmonic bound mode could remain, but with very short propagation distance [34]. With this method, the Ag NW can be placed on any location of the substrate and can be moved flexibly to be integrated with other components. There is no need to coat another surface cladding, and will avoid damaging the smooth NW surface. For future applications, the top SiO\({}_{2}\) layer can be replaced with a layer made of piezoelectric materials, such as LiNbO\({}_{3}\), whose thickness or refractive index can be tuned with external electric signals, providing an approach for realizing active nano-devices. This tuning of the effective refractive index and propagation distance of the SPP waveguide modes on an Ag NW can be used to understand a serial of Boolean logic functions in on-chip integrated circuits for next-generation information technology and nanoscale optical sensing. We note that the field intensity is stronger confined near the NW surface Figure 3e. This confinement will result in a small observed volume, which is of interest for biophotonic applications [39; 40; 41; 42].  
This work was supported by MOST (2013 CBA01703 and 2016 YFA0200601), NSFC (61427818, 11774330 and 11374286), and the Science and Technological Fund of Anhui Province for Outstanding Youth (160808502), and the Longshan academic talent research supporting program of SWUST (17 LZX626). This work was also supported by grants from the National Institute of Health (GM107986, EB006521, EB018959, and OD019975). This work was partially carried out at the University of Science and Technology of China's Centre for Micro and Nanoscale Research and Fabrication. We thank [PERSON], [PERSON] and [PERSON] for their help on the micro/nano fabrication steps.  
[PERSON] conceived the idea and drafted the manuscript. [PERSON] carried out the optical experiments. [PERSON] and [PERSON] performed the numerical calculations. [PERSON], [PERSON], and [PERSON] fabricated the dielectric multilayer. [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] assisted in drafting the manuscript. All authors discussed the results and contributed to the writing and editing of the manuscript. [PERSON] and [PERSON] contributed equally to this work.  
The authors declare no competing financial interests.