## 2 Materials and Methods
### Experimental Research Methods and Materials Used
#### 2.2.2 Basic Provisions of the Physical and Mathematical Model
Then, taking the displacement current due to the electric field in the form \(\overrightarrow{j}(t)=\frac{\partial\overrightarrow{a}}{\partial t}=i\omega \varepsilon_{0}\varepsilon_{\infty}\overrightarrow{E}(t)+\frac{\partial \overrightarrow{P}_{Tp}(t)}{\partial t}\), where, \(\varepsilon_{\infty}\) is the inductive (high-frequency) component of the complex dielectric permittivity (CDP) of the optical fiber material, and neglecting the relaxation (low-frequency) polarization of the sample \(\frac{\partial\overrightarrow{P}_{Tp}(t)}{\partial t}\to 0\)[47; 48], we calculate the volumetric power density of the electric field of an electromagnetic wave in an optical fiber in the following form [46]:  
\[\mathrm{P}_{\partial Vt}=\left\langle\mathrm{Re}\left(\overrightarrow{E}(t) \right)\times\mathrm{Im}\left(\overrightarrow{j}(t)\right)\right\rangle\approx \frac{1}{2}\omega\varepsilon_{0}\varepsilon_{\infty}\overrightarrow{E}_{0}^{2} \tag{1}\]  
The volumetric power density of the magnetic field of an electromagnetic wave in a non-magnetic optical fiber is calculated based on approximate equalities \(\overrightarrow{H}=\overrightarrow{H}_{0}\cdot\exp\left(i\omega t- \overrightarrow{k}\overrightarrow{r}\right)\approx\overrightarrow{H}_{0} \cdot\exp(i\omega t)\), and is reduce to the following form:  
\[\mathrm{P}_{mVt}=\left\langle\mathrm{Re}\left[\overrightarrow{H}(t)\right] \mathrm{Im}\left[\frac{\partial\overrightarrow{B}(t)}{\partial t}\right] \right\rangle\approx\frac{1}{2}\omega\upsilon_{0}\overrightarrow{H}_{0}^{2} \tag{2}\]  
The volumetric power density of the electromagnetic field of the wave is calculated, taking into account the identity \(\upsilon_{0}\overrightarrow{H}_{0}=\varepsilon_{0}\varepsilon_{\infty} \overrightarrow{E}_{0}\), from the expression \(\mathrm{P}_{Vt}=\mathrm{P}_{\partial Vt}+\mathrm{P}_{mVt}\approx\omega \varepsilon_{0}\varepsilon_{\infty}\overrightarrow{E}_{0}\). Taking into account the fact that, in this approximation, when estimating the dielectric permittivity of the sample, only the processes of induction polarization realized in the high-frequency range are taken into account, we assume the refractive index of a light wave in a non-magnetic optical fiber in the form \(n\approx\sqrt{\varepsilon_{\infty}}=n_{\infty}(\varepsilon_{0};E_{0},H_{0}, \omega;T;d;\theta;b;\alpha_{0})\). The calculation of the intensity of the electromagnetic wave \(I=\left\langle\mathrm{Re}\left[\left|\overrightarrow{E}(t)\right|\right] \mathrm{Im}\left[\left|\overrightarrow{H}(t)\right|\right]\right\rangle\)\(\approx\frac{1}{2}\left|\overrightarrow{E}_{0}\right|\left|\overrightarrow{H}_{0}\right|\) in the form \(I\approx\frac{1}{2}\sqrt{\frac{\varepsilon_{0}\varepsilon_{\infty}}{\mu_{0}} \overrightarrow{E}_{0}^{2}}\) gives the distribution of the volumetric power density of the electromagnetic field of the wave at angles \(\alpha_{0}\) (between the direction of the wave vector of the wave and the normal to the surface of the sensitive light-receiving plate). \[\mathrm{P}_{Vt}(\zeta_{0};E_{0},H_{0},\omega;T;d;\theta;b;\alpha_{0})=2\omega \sqrt{\varepsilon_{0}\mu_{0}\varepsilon_{\infty}}I(\alpha_{0})\approx 2\omega \,\frac{n_{\infty}(\zeta_{0};E_{0},H_{0},\omega;T;d;\theta;b;\alpha_{0})}{ \zeta}I(\alpha_{0}). \tag{3}\]The calculated value of the refractive index of an optical fiber is performed in a generalized analytical form \(n_{\infty}(\zeta_{0};E_{0},H_{0},\omega;\mathrm{T;d;b;b;\alpha_{0}})\), and its experimental value (necessary for comparing the results of theory and experiment) is calculated from expression (3).