Tuning of the Cut-Off Frequency in Effective Medium Approximation and Long Range Surface Plasmon Excitation in Graphene and Black Phosphorus

In this study, we modulate the effective cut-off frequency on the basis of computer simulations of a multilayer dielectric system by increasing the number of layers of the 2D material (graphene or phosphorene) and reducing the thickness of the dielectric, thereby enhancing the frequency. Additionally, another method to modulate the aforementioned effective frequency, \(\varvec{\omega _{p,eff}}\) ${\mathit{\omega }}_{\mathit{p}\mathbf{,}\mathit{e}\mathit{f}\mathit{f}}$ , is by varying the Fermi energy of both 2D materials. Expressions were derived to approximate the dielectric thickness required to estimate the frequency at which the effective \(\varvec{\omega _p}\) ${\mathit{\omega }}_{\mathit{p}}$ occurs, all under normal incidence. Furthermore, we investigated long-range surface plasmons in the Sarid et al. structure (substrate-glass-metal-glass-air) using both graphene and phosphorene. By introducing the 2D material, an additional Lorentzian was obtained with graphene, even with high intensity, whereas phosphorene produced only a slight increase in field amplification. The tunneling of the Lorentzians by modifying the Fermi energy was moderate for both materials. The modulation of the effective frequency and the acquisition of an additional Lorentzian hold potential for the design of sensors and optoelectronic devices.