## 2 Materials and Methods  
Herein, we deal with the plane boundary separating a nanocomposite (NC) semi-infinite layer, which fills the half-space \(x<0\) and adjacent to it, hypercrystal filling the half-space \(x>0\) (Figure 1). It should be stressed that the surface waves under consideration propagate along z axis. It is worthwhile noting that the structure under the study can be constructed by means of molecular beam epitaxy [16], chemical vapor deposition, atomic layer deposition and sacrificial etching [17]. The nanocomposite is presented as a non-conductive transparent matrix with a permittivity \(\varepsilon_{\text{n}}\), in the volume of which regularly distributed semiconductor nanoparticles with permittivity \(\varepsilon_{\text{m}}\). The frequency dependent dielectric function of the TCO based nanoparticles is of particular interest. An emergence of high-conducting metal being transparent has opened wide avenues recently. The issue has attracted lots of interest within the scientific community because of the metal being opaque for light. From the perspectives of the potential applications, transparent conducting metals described by high DC conductivity (\(\sigma_{\text{DC}}\)) are anticipated for optoelectronic devices, ranging from solar cells to electronic paper, touch screens and displays. Though, since \(\sigma_{DC}=n_{e}e^{2}\tau/m\) (with \(\tau\) being relaxation time of the electron and m--electron mass) of a metal is associated with plasmon frequency \(\omega_{p}^{2}=n_{e}e^{2}/\varepsilon_{0}m\) through the free-electron density \(n_{e}\), a high-conducting metal (with a high \(n_{e}\)) is certainly opaque for light because of its permittivity \(\varepsilon\) being typically very negatively affected by its high \(\omega_{\text{p}}\). Conventional techniques to produce transparent conducting metals include the decrease of the \(n_{e}\), by utilizing transparent conducting oxides (TCOs). The parameters of the Drude-Lorentz approach for aluminum-doped zinc oxide (AZO), Ga-doped ZnO (GZO) and indium tin oxide (ITO) gained from experimental data [12] are presented in Table 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **AZO** & **GZO** & **ITO** & **TiN (Deposited at 800 \({}^{\circ}\)C)** & **TiN (Deposited at 500 \({}^{\circ}\)C)** & **ZrN** \\ \hline \(\varepsilon_{\text{b}}\) & 3.54 & 3.23 & 3.53 & 4.86 & 2.49 & 3.47 \\ \hline \(\omega_{\text{p}}\) (eV) & 1.75 & 1.99 & 1.78 & 7.93 & 5.95 & 8.02 \\ \hline \(\gamma_{\text{p}}\) (eV) & 0.04 & 0.12 & 0.16 & 0.18 & 0.51 & 0.52 \\ \hline \(f_{1}\) & 0.51 & 0.39 & 0.39 & 3.29 & 2.04 & 2.45 \\ \hline \(\omega_{1}\) (eV) & 4.29 & 4.05 & 4.21 & 4.22 & 3.95 & 5.48 \\ \hline \(\gamma_{1}\) (eV) & 0.10 & 0.09 & 0.09 & 2.03 & 2.49 & 1.74 \\ \hline \end{tabular}
\end{table} 
Table 1: Drude–Lorentz parameters of plasmonic materials obtained from experimental data. One may approximate the materials dielectric function by the complex dielectric function: \(\varepsilon_{TCO}=\varepsilon_{b}-\frac{\omega_{p}^{2}}{\omega\left(\omega+i \gamma_{\text{p}}\right)}+\frac{f\omega_{1}^{2}}{\left(\omega_{1}^{2}-\omega^{2 }-i\omega\gamma_{1}\right)}\), with the values of the parameters outlined in the table [18]. Here \(\varepsilon_{\text{b}}\) is the polarization response from the core electrons (background permittivity), \(\omega_{\text{p}}\) is the plasma frequency, \(\gamma_{\text{p}}\) is the Drude relaxation rate. The dielectric function of metallic medium in the complex conductivity and frequency domain is written as [19]:  
\[\varepsilon_{r}(\sigma,\,\omega)=1+\left(\chi+\frac{|\sigma|e^{i\phi}}{\omega \varepsilon_{0}}\right) \tag{1}\]  
where \(\chi\) is the susceptibility of the system, \(|\sigma|\) is absolute value of complex conductivity and \(\phi\) is its phase.