## 2 Materials and Methods
### Experimental Data Processing  
Before the terahertz measurements, the optical circuits of both interferometers were adjusted with respect to the collimated beam of a diode laser (\(\lambda_{0}\) = 635 nm). The adjustment was done with high accuracy, since the difference in the refractive indices of the SPPs on the samples, whose ZnS coatings differed in the thickness by 100 nm, was about \(10^{-4}\). In addition, after the placement of another sample (with a ZnS layer of a different thickness), it was necessary to re-adjust the SPP interferometer circuit, which took a lot of time because of the high accuracy maintained. To reduce the adjustment time and take into account the slight misalignment between the interferometers, we carried out the measurements in two stages. First, two interferograms were measured simultaneously (on the plasmon and BW interferometers), in accordance with the scheme described in Section 2.1, when the SPPs propagated along the sample surface. During the second stage of the measurements, the NovoFEL radiation in the plasmon interferometer was not converted into SPPs; rather, it was directed straight to the beam splitter \(BS_{2}\) to result in an interferogram formed by the source radiation in the environment (air). Simultaneously with that, an interferogram was recorded on the BW interferometer. Thus, with the two stages of the measurements, for each sample (differing in terms of the thickness of the ZnS layer), two pairs of interferograms were obtained. Moreover, for the collection of statistics, the measurements were repeated four times with each of the samples. Figure 2a shows an example of the SPP and BW interferograms. As the movable mirrors of the interferometers move along the \(x\) axis, the amplitudes of the sinusoids first increase, then reach the maximum, and then decrease in the final section of the scanning. This is a typical symmetric form of the autocorrelation function for a coherent radiation source [50]. The amplitude envelope has a Gaussian profile, the width of which determines the length (duration) of coherence, which was 27 mm (90 ps) in this experiment. This is close to the maximum duration of the NovoFEL radiation pulse at operation in a stable mode (100 ps). By means of the Fourier transform, the SPP and NovoFEL radiation spectra were calculated from the interferograms (Figure 2b). The circles indicate the results of the calculations of the components of the Fourier spectrum. The number of calculation points was determined by the length of the measured interferograms, which depends on the coherence length of the NovoFEL radiation (\(l_{\text{coh}}\approx 27\) mm). Next, the spectra were approximated with a Gaussian function of the form \(f(x)=A\cdot\exp\left[-\frac{1}{2}\left(\frac{x-x_{\text{v}}}{w}\right)^{2} \right]+f_{0}\) and normalized to the value (\(A+f_{0}\)). The \(w\) value defined the width of the spectrum. The value of the parameter \(x_{\text{c}}\), which describes the position of the central line of the spectrum, corresponded to the desired wavelength. The plots in Figure 3 show the following wavelengths (central lines of the spectra): \(\lambda_{\text{spp1}}\) and \(\lambda_{\text{0 spp2}}\), found from the interferograms obtained on the plasmon interferometer with and without SPP excitation, respectively; and \(\lambda_{01}\) and \(\lambda_{02}\), the corresponding wavelengths of the NovoFEL radiation in air, as determined with the BW interferometer. Figure 2: **(a)** Example of the interferograms obtained with the plasmon and bulk wave (BW) interferometers for the “Au–ZnS layer 470 nm thick” sample. Left column: interferograms recorded with the plasmon interferometer (upper graph, with SPP excitation; lower graph, without SPP excitation); right column: respective patterns obtained with the BW interferometer. **(b)** Fourier spectra of the SPPs and NovoFEL radiation generating SPPs; circles: reconstruction from the interferograms in **(a)**; lines: approximation of the spectra with the Gaussian function.