One of the urgent tasks of the development of modern radio electronics is the creation of an element base based on graphene nanostructures. Such a base can be used both in the well–studied microwave, and in the sub–terahertz, terahertz, infrared and optical ranges, which have not been previously used and studied due to the lack of coherent reception sources and receivers. To study the properties and functionality of devices based on nanostructured materials and the corresponding components of these ranges, the unified approach to their mathematical modeling is necessary. It follows from the results of mathematical modeling that there is resonant minimum of the transmission coefficient (non– transmission band) due to the resonance in the cells (Fabry–Perot resonators) in the sub–THz and THz ranges. The bandwidth is determined by the values of the chemical potential μc, while the non–transmission band at μc=1.0 eV is twice as wide as at μc=0.5 eV. It follows from the results of electrodynamic calculation that with an increase in the number of graphene sheets (N=33, 47, 60), the transmission coefficient in the non–transmission band decreases significantly. As the simulation results show, by changing the chemical potential of μc by applying an external electric field, which leads to the change in graphene conductivity, it is possible to control the characteristics of filters of the microwave, sub–THz, THz, infrared and optical ranges based on multilayer nanostructures of "graphene–dielectric" type. So, at the value of the chemical potential μc=0 eV (there is no external electric field), attenuation of THz radiation in the non–transmission band is 2 – 4.5 dB (depending on the number N=33 – 60, respectively). When an external electric field is applied, which corresponds to the chemical potential μc=1 eV, the radiation attenuation increases to 20 – 40 dB (when the number of N graphene sheets changes to the values N=33 – 60). Therefore, it is shown that broadband filters of microwave, sub–THz, THz, infrared and optical ranges of planar design can be controlled by an electric field and quickly rearranged in the range of small changes in the energy level when using periodic layered nanostructures of the “graphene–dielectric” type.

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