# Propagation of Elastic Waves in a One-Dimensional High Aspect Ratio Nanoparticle Phononic Crystal
## 3 Results and Discussion
### Infiltration with a Liquid
When we compare the two dispersion curves, one can see that the branches of the 1D nanoridges structure infiltrated with Cargille can be associated to the fundamental modes of the 1D infinite multilayer array. In addition, due to the finite size effect of the nanoridges in the vertical direction, the fundamental modes are followed by many others that correspond to higher orders of vibration (harmonic modes). For propagation in the direction perpendicular to the nanoridges (Figure 8b), we also show in blue the dispersion curves of the infinite 1D periodic epoxy/Cargille multilayer. The dispersion curves of the actual structures, under the condition \(P_{yz}(w,q)\geq 80\%\), can qualitatively be distinguished into the following three categories. (i) Above the SiO\({}_{2}\) transverse velocity (red line), the selected modes are localized inside the 1D periodic structure, but can couple to the semi-infinite substrate. Such modes are known as leaky waves. (ii) The modes situated below the transverse velocity of SiO\({}_{2}\) (red solid line) and above the lower blue branch are dispersive modes that result from propagation inside the multilayer and interact with the surface of the substrate. They are analogous to the Sezawa waves that are associated with an ad-layer deposited on a substrate. (iii) The branches below the lower blue curve are almost flat, which represents a signature of their localization in the 1D periodic nanostructure. Indeed, as the flat bands fall below the longitudinal velocity of sound in the fluid (Cargille), these modes do not propagate in the fluid. In Figure 9, we discuss the evolution of the dispersion curves as a function of the height of the liquid filling the grooves. The left panel in Figure 9 recalls the dispersion curves corresponding to the nanoridges with a height of 540 nm without infiltration. The middle and right panels in Figure 9 present the calculation when the grooves are filled with two different heights of the liquid polymer:  
Figure 8: Dispersion curves of the one-dimensional (1D) nanoridge structure of high aspect ratio (\(AR\)) (\(h=2.7\) μm) infiltrated with the liquid (Cargille) (**a**) for the direction parallel to the nanoridges under the condition \(P_{xy}\) (\(w\), \(q\)) \(\geq 80\%\) (black curves) and (**b**) for the direction perpendicular to the nanoridges under the condition \(P_{yz}\) (\(w\), \(q\)) \(\geq 80\%\) (black curves). The dispersion curves of an infinite 1D epoxy/Cargille multilayer array are reported in blue. 270 nm and 540 nm, respectively. In each case, one can see that the level of liquid drastically modifies the dispersion curves with the creation of new branches. As discussed previously, these new dispersive branches present a group velocity that is different from zero, and associated with propagating waves at and above the surface of the semi-infinite glass substrate. This propagation can be understood as the ridges now being connected through the grooves filled with a liquid. Therefore, the modes can now propagate through the 1D multilayer array on top of the semi-infinite substrate.