## 3 Results  
The experiments were carried out with a set of samples with flat substrates containing non-transparent layers of sputtered gold coated with a ZnS layer of thickness \(d\) = 0-3000 nm. Figure 4a,b show the real part without unity \(n_{\rm s}-1\) and the imaginary part \(\kappa_{\rm s}\) of the SPP refractive index, respectively, which were found via the above methods, versus the \(d\) value. In these figures, the black lines show the calculated dependences obtained via the numerical solution of the dispersion equation for the \"gold-ZnS layer-air\" structure at \(\lambda_{0}\) = 141 \(\upmu\)m. In these calculations, the refractive index of ZnS was taken as \(n_{\rm d}=2.943+i\!\cdot\!0.01\)[7], and the gold permittivity \(\varepsilon_{\rm m}\) was calculated by the Drude model with the use of the reference  
Figure 3: SPP intensity attenuation on the “Au–ZnS layer 470 nm thick” sample at the displacement of the mirror \(M_{2}\) (see Figure 1) in the plasmon interferometer; fixed mirror \(M_{1}\) closed by dump: blue line—experimental data, red line—approximation curve. values of the plasma frequency \(\omega_{\rm p}=1.37\times 10^{16}\) s\({}^{-1}\) and frequency of the collisions of the conduction electrons \(\omega_{\rm\tau}=4.05\times 10^{13}\) s\({}^{-1}\)[1]:  
\[\varepsilon_{\rm m}(\omega)=1-\frac{{\omega_{p}}^{2}}{\omega^{2}+{\omega_{\rm \tau}}^{2}}+i\,\frac{{\omega_{\rm\tau}}\cdot{\omega_{p}}^{2}}{\omega\cdot({ \omega^{2}+{\omega_{\rm\tau}}^{2}})} \tag{4}\]  
where \(\omega=2\pi c/\lambda_{0}=1.34\times 10^{13}\) s\({}^{-1}\) (c is the speed of light in a vacuum). From Figure 4a, one can see that the value of \(n_{\rm s}-1\) monotonically increases with \(d\), with all its experimental values lying above the calculated curve, which indicates that the real part \(\rm Re(\varepsilon_{\rm m})\) of the dielectric constant of the deposited gold is less than the value predicted by the Drude model--according to the SPP theory, a decrease in the \(\rm Re(\varepsilon_{\rm m})\) must be accompanied by an increase in the \(n_{\rm s}\). Note that the determination errors for \(n_{\rm s}-1\) for small thicknesses of ZnS (\(d\leq 300\) nm) and \(d=3000\) nm are noticeably larger than those for \(300\) nm \(<d<3000\) nm. The reason for this is the low intensity of the useful signal from the SPPs due to the low efficiency of the SPP generation in the plasmon interferometer at such thicknesses of the dielectric layer. The value of the SPP refractive index on uncoated gold was \(n_{\rm s}\approx 1.0005\), which corresponds to the SPP phase velocity \(\phi_{\rm ph}=c/n_{\rm s}\approx 0.9995\)\(c\). Similar values of SPP phase velocities were also obtained for thick aluminum wire in experiments performed on a TDS spectrometer [53], where \(\phi_{\rm ph}\) was determined from the time delay of a THz SPP pulse relative to a light pulse propagating in air. As for the imaginary part \(\kappa_{\rm s}\) of the SPP refractive index, which characterizes the SPP decay, at an increase in the thickness \(d\) of the cover layer, the measured values (blue circles in Figure 4b) first decrease, reach the minimum at \(d\approx 300\) nm, and then grow monotonically. This behavior of \(\kappa_{\rm s}\) was explained in [35] and is associated with the decrease in the radiative losses of the SPPs at the deposition of a dielectric layer onto the metal surface. At some \(d=d_{0}\) (300 nm in our case), the integral losses of the SPPs reach the minimum, and at \(d>d_{0}\), their growth is due to the predominance of the Joule losses over the radiative losses because of the monotonic increase in the fraction of the SPP field energy transferred into the metal with \(d\) growth. A small discrepancy between the experimental values of \(\kappa_{\rm s}\) and the numerical solution at \(d>d_{0}\) can be caused by the thickness inhomogeneity of the ZnS coating, which can lead to the inaccuracy of the measurements of the absorption part of the refractive index of the SPPs.