## 3 Results
This value of \(\text{Re}(\varepsilon_{\text{m}})\) is in agreement with the estimates given in earlier publications on the THz SPP refractometry of deposited gold without a dielectric coating layer, as implemented on a TDS spectrometer [31] and with FEL radiation [24]. However, as follows from the above, this value of the \(\text{Re}(\varepsilon_{\text{m}})\) differs from its real value of \(-7000\) almost \(10\) times. In our opinion, the erroneous estimation of the \(\text{Re}(\varepsilon_{\text{m}})\) in previous works on the THz SPP refractometry was because of the unaccounted for significant radiative losses of the SPPs on a metal surface free without a coating layer. It is important to note that the obtained errors for the metal effective permittivity (see Figure 7) are very large (reach 50%). It is clear that its more reliable determination via the proposed method of the SPP refractometry requires higher accuracy in terms of finding the real part of the SPP refractive index from the recorded interferograms. For the accuracy of the determination of the metal permittivity to be \(20\%\) (for thicknesses \(d\geq 500\) nm), it is necessary to determine the \(n_{\text{s}}\) with an error not worse than \(10^{-4}\) (with an actual error of \(10\%\) for the \(x_{\text{s}}\), which depends on the signal-to-noise ratio, adjustment, and stability of the intensity of NovoFEL radiation). For such accuracy for the \(n_{\text{s}}\), the stability of the radiation source in terms of the wavelength during the recording of the interferogram must not be worse than \(0.01\)\(\upmu\)m (for \(\lambda_{0}=141\)\(\upmu\)m), while the width of the generation line must be an order of magnitude smaller than \(1.0\div 1.5\)\(\upmu\)m in the normal operation mode. This can be achieved via the reduction of the measurement time with faster and more sensitive detectors, as well as with sources of coherent THz radiation that are more stable than FELs, such as gas lasers [56], backward wave oscillators [57], gyrotrons [58], and quantum-cascade lasers [59]. Note that it is possible to increase the stability of the NovoFEL radiation to temporal variations in the radiation wavelength at an operation in the mode of negative detuning of the electron bunch repetition rate from the repetition rate of light pulses inside the  
\[\varepsilon_{\rm m}(\omega)=1-\frac{{\omega_{p}}^{2}}{\omega^{2}+{\omega_{\rm \tau}}^{2}}+i\,\frac{{\omega_{\rm\tau}}\cdot{\omega_{p}}^{2}}{\omega\cdot({ \omega^{2}+{\omega_{\rm\tau}}^{2}})} \tag{4}\]2 (**a**) Real and (**b**) imaginary parts of the gold permittivity \(\varepsilon_{\text{m}}\) vs. the thickness \(d\) of the ZnS layer (blue circles), as calculated by Formula (9) with the \(\widetilde{n}_{\text{s}}(d)\) values found from the results of the measurements presented in \[\varepsilon_{\rm m}(\omega)=1-\frac{{\omega_{p}}^{2}}{\omega^{2}+{\omega_{\rm \tau}}^{2}}+i\,\frac{{\omega_{\rm\tau}}\cdot{\omega_{p}}^{2}}{\omega\cdot({ \omega^{2}+{\omega_{\rm\tau}}^{2}})} \tag{4}\]3 Red dotted lines: values of both parts of the gold permeability, found via the approximation method; rectangular areas filled with oblique red lines: corresponding standard deviation ranges. FEL optical resonator, accompanied by a decrease in the average radiation power [60]. In operation in this mode, a stable single-mode generation regime was established, the linewidth of which reached the maximum possible narrow value (0.25%) [50], while the wavelength shift in 15 min was not more than 0.1 of the width of the generated radiation spectrum (0.04 \(\upmu\)m at \(\lambda_{0}\) = 141 \(\upmu\)m), which is close to the desired accuracy. However, to achieve such a generation mode, a long and laborious adjustment of the NovoFEL parameters is necessary. In addition, the precision of the translation stages, which shift the movable mirrors \(M_{2}\) and \(M_{5}\) (Figure 1), has a significant effect on the accuracy of the interferometric measurements.