## 2 Materials and Methods
### Experimental Research Methods and Materials Used
#### 2.2.2 Basic Provisions of the Physical and Mathematical Model
The study of the refractive index \(n_{\infty}(\zeta_{0};E_{0},H_{0},\omega;\mathrm{T;d;b;b;\alpha_{0}})=n_{\infty} (\Omega)(\alpha_{0})\) of the fiber optic material in the most general case should be carried out using the methods of kinetic theory and electrodynamics of a continuous medium [46; 51], which describe the patterns of relaxation processes associated with the interaction of the electric and magnetic fields of an electromagnetic wave (optical signal) with structural elements (ionic and molecular subsystems, electrons of the outer shells of the atoms of the structure, various types of vacancies) of the crystal lattice. Here, the mathematical set of elements \(\Omega=\{\zeta_{0};E_{0},H_{0},\omega;\mathrm{T;d;\theta;b}\}\) is accepted. The influence of crystal structure parameters on the relaxation times of optical-electric processes is determined by the numerical values of the above-mentioned characteristic molecular parameters \(\zeta_{0}\) or groups of parameters related to various substructures (sublattices) that are in a state of stationary interactions with each other, described by the unperturbed Hamiltonian of the crystal lattice, taking into account theoretical model assumptions adopted based on experimental data. The temperature of the substance significantly affects the kinetics of relaxation polarization. The refractive index is influenced by the geometric characteristics of the crystal structure (primarily the type of lattice symmetry, lattice constant, and linear dimensions of the sample d) and optical-geometric parameters (angle of incidence of the beam on the surface of the material \(\theta\) and angle \(\alpha_{0}\) between the wave vector of the optical signal (ray) refracted in the sample and the normal vector to the surface of the photodetector (detection screen) [49; 50; 51]. In the region of anomalously high polarization nonlinearities, the parameters of external field influences (frequency \(\omega\) and amplitude of the wave) and the input (before entering the crystal) intensity of the electromagnetic wave begin to influence the polarization coefficients, complex dielectric and magnetic permeability, and refractive index of the substance. The quantity measured in the experiment is the averaged over angles \(\alpha_{0}\) the function (3). \[P_{\
u_{t},th}^{(\Omega)}=\left\langle P_{\
u_{t}}^{(\Omega)}(\alpha_{0}) \right\rangle=\frac{4\omega}{c\pi}\int\limits_{0}^{\frac{\pi}{2}}I(\alpha_{0} )n_{\infty}(\Omega)(\alpha_{0})\mathrm{d}\alpha_{0} \tag{4}\]  
Thus, within the framework of this paper, we have described a scheme for calculating the physical characteristics of electron-optical processes in fiber-optic elements without using kinetic theory methods (as a simplified model). The connection between the schemes of experiments and the final formulas of the theoretical model (expression (4)) is of a generalized nature, where the angularly averaged distribution of the intensity of the optical signal \(I\) (\(\alpha_{0}\)) registered on the photo plate measured in the experiment is compared with the value of the bulk energy density of the electromagnetic field in the \(P_{\
u_{t},th}^{(\Omega)}\) optical fiber element, the methods of measurement of which will be investigated in the future. Zero approximation of perturbation theory in dimensionless small deformation parameters \(\frac{\mathrm{d}\mathrm{d}}{\mathrm{d}}\), \(\frac{\delta\left(\widehat{\tau}_{0}^{\top}\right)}{\left(\widehat{\tau}_{0} ^{\top}\right)}=\frac{\left(\delta\omega\right)^{2}}{2}\) in expression (4) gives the calculated (theoretical) value of the experimentally measured volumetric power density of the electromagnetic field of the wave detected by a sensitive membrane (photographic plate) after refraction of the outgoing (primary optical signal) in an undeformed fiber optic sample.