## 2 Material Parameters of the Structure
The propagation constant of this wave \(k_{s}=k_{0}\sqrt{\varepsilon_{s\perp}}\), where \(k_{0}=\omega/c\) and \(\varepsilon_{s\perp}=\varepsilon-\varepsilon_{a}^{2}/\varepsilon\) is the effective permittivity. Figure 3a shows the frequency dependencies of the real and imaginary parts of the effective permittivity for the \(n-InSb\) semiconductor, obtained at \(H_{0}=0,5,10,15,20\) kOe (black, red, blue, green, violet curves, color online only) and the values of the parameters used in the numerical analysis: \(\varepsilon_{l}=17.8\), \(m^{*}=0.014\)\(m_{e}\), \(n_{0}=10^{15}\) cm\({}^{-3}\), \(\omega_{p}=3.5\cdot 10^{12}\) s\({}^{-1}\), \(\
u=5\cdot 10^{10}\) s\({}^{-1}\). We note the resonant character of these dependencies: for each value \(H_{0}\) in a narrow region near the frequency \(\omega_{res}\simeq\sqrt{\omega_{p}^{2}+\omega_{c}^{2}}\), a sharp increase in the imaginary part of the effective permittivity is observed, which should lead to sharp dips in the transmission spectrum for the semiconductor layer at these frequencies. Increasing the magnetic field shifts the resonant peak to higher frequencies and lowers the height of the resonant peak. It can be seen that the magnetic field can be used to effectively control the permittivities of the semiconductor layers. Graphene monolayers can be both in the unexcited and active states. In unexcited graphene, the Fermi energy \(E_{F}\) (chemical potential) is at the Dirac point and is equal to zero. In this case, the valence band is completely filled, the conduction band is completely free, and the band gap is absent. The chemical potential can be shifted into the conduction band or valence band and thereby change the surface conductivity of the graphene sheet by applying a voltage of different polarity between the graphene monolayer and the substrate. A planar magnetic field does not affect the electronic subsystem of graphene due to its 2D geometry. The terahertz response of graphene for frequencies below the electron-electron collision frequency is determined by its conductivity. The expression for the conductivity of graphene, which is valid for the region \(f<5\,\)THz and obtained using the hydrodynamic approach when solving the equations of the electromagnetic field, the balance of momentum and energy of charge carriers, as well as the continuity equation, has the form [32; 33]:  
\[\frac{\sigma_{g}}{\sigma_{0}}=\frac{4\omega E_{F}[2i(\beta-1)(\omega-ku)-3 \gamma\beta]}{\pi\hbar\sqrt{1-\beta}[k^{2}V_{F}^{2}(ku\chi_{1}+\chi_{3})+ \omega^{2}\chi_{2}(\gamma/\omega-i)+ku\chi_{4}]}, \tag{5}\]  
where \(\sigma_{0}=e^{2}/4\hbar\) is the surface static conductivity, \(e\) is the charge of an electron, \(\hbar\) is [PERSON]'s constant and \(\tau\) is the momentum relaxation time of charge carriers in the graphene monolayer, \(\beta=(u/V_{F})^{2}\), \(u\) is the charge carrier drift velocity and the Fermi velocity in graphene \(V_{F}=10^{6}\) m/s, \(E_{F}\) is the Fermi energy (or chemical potential) in graphene. The following notation is also introduced: \(\gamma=1/\tau\), \(\chi_{1}=2\beta-1\), \(\chi_{2}=3\gamma\beta+i\omega(\beta-2)\), \(\chi_{3}=\omega-\beta(3i\gamma+4\omega)\), \(\chi_{4}=\omega[i\gamma(2\beta+5)+\omega(4-\beta)]\). Graphene conductivity (5) in the hydrodynamic regime was obtained by solving the balance equations for the momentum and energy of charge carriers, as well as the continuity Equation [29; 31]. To solve the hydrodynamic equations, they are linearized, and the charge carrier velocity, the effective mass density of the electron liquid, the charge density and the current density are expanded in the powers of the amplitude of the acting electric field, with only the stationary and linear expansion terms being preserved.