# Absorption Enhancement in Hyperbolic Metamaterials by Means of Magnetic Plasma
## 3 Results and Discussion  
Herein, we analytically investigate SPPs excited by a slit waveguide structure. The waveguide is formed by two semi-infinite plasma layers and a thin background dielectric layer, in which one plasma layer is in the presence of the external magnetic field and the other plasma layer is in the absence of a magnetic field. Two magnetic-optical effects are presented, the [PERSON] effect, and the Voigt effect if the plasma is involved with the external magnetic field. However, in this analysis, only the Voigt effect is taken into consideration. The plasma cannot be magnetized or influenced by the applied magnetic field under the transverse magnetic polarization case. Herein, we present a theoretical study by employing Equation (2) and consider the main characteristics of the SPPs. Equation (2) was solved with respect to \(\beta\), aiming to obtain the results. The impact of the applied magnetic field, collision frequency, the dielectric constant, and the thickness of the dielectric layer embedded into the nanostructured metamaterial on the main characteristics of SPPs is studied. A magnetic field \(B_{0}\) is applied parallel to the interface separating two regions. Figure 2 demonstrates the impact of the applied magnetic field on the dispersion diagrams of SPPs. The displayed dispersion curves tend to a stable frequency. The mentioned phenomenon takes place as the SPP modes propagate at the interface under study. The dramatic shift in the SPPs to the higher frequency range is observed, enhancing the external magnetic field. As it is seen in Figure 2b, employment of the nanowire metamaterial media causes the exotic behavior of the dispersion curves. Between the regime of the bound and radiative modes, a frequency gap region with purely imaginary \(\beta\) prohibiting propagation exists. As we can clearly observe in Figure 2b, the case of \(\omega_{c}/\omega_{p}=2\) possesses some discrepancies in this specific region between bound and radiative modes with \(\beta\) being not purely imaginary. Moreover, it can clearly be observed from Figure 2b that \(\beta\) is the complex number with Re(\(\beta\)) \(\
eq\) 0 around \(\omega\) = 6.2 \(\times\) 10\({}^{14}\) Hz. The presence of the real part of the propagation constant between regimes of the bound and radiative modes is treated as the exotic behavior of the proposed structure. Aiming to have a closer look at the nature of the propagating waves, we introduce electric field distributions. Doing so, the case of the nanowires is presented in Figure 3.  
We will further examine this case by engineering dielectric properties of the host media of the nanowire metamaterial along with the metamaterial geometry. Figure 4 is plotted aiming to take into account the impact of the permittivity of the host material when the collision is considered for the plasma. One can conclude that the rise in the dielectric constant will result in the shift in the propagating plasmons to the lower-frequency range. The former phenomenon can be described by the variational principle [14]. In other words, an increase in the dielectric constant ends with the shift in the modes to the lower-frequency range. It should be mentioned that for the instance of planar nanostructured hyperbolic metamaterials, one should expect the absorption enhancement to be a negligible effect because of the lack of any localized plasmons resulting in the field hotspots [15]. Additionally, the high \(k\)-modes cannot be excited by free space illumination and cannot have an impact on the absorption. As it is seen in Figure 4b, the presence of the magnetic plasma significantly enhances the absorption. Figure 2: Dispersion diagrams of SPPs for the case of different external magnetic fields. Other parameters are chosen as follows, i.e., nanolayers (**a**): \(d_{1}\) = 10 nm; \(d_{2}\) = 20 nm; nanowires (**b**): \(d\) = 30 nm, \(S\) = 70 nm.