## 1 Introduction  
One-dimensional photonic-crystal microresonators (MCRs) have attracted the close attention of researchers in recent years, which is largely due to their wide use in various optical devices for the selective separation and amplification of an optical signal based on the interaction of optical modes in MCRs and resonances in the active medium that fills its cavity [1; 2; 3; 4; 5]. The possibility of the controlled tuning of the resonant frequency of the microresonator by changing the external parameters is important for many practical applications. The efficient rearrangement of the MCR transmission and reflection spectra can be achieved by introducing layers into the cavity between the mirrors, the material parameters of which depend on easily changeable external factors [6; 7; 8; 9]. MCR's schemes are used to create a wide class of radiation control devices (switches, modulators, filters), performing the function of amplifying various types of light interaction with the propagation medium [10; 11; 12; 13; 14; 15; 16; 17]. To form a symmetric microresonator, two identical Bragg mirrors (BMs) are required with a change in the order of the layers in one of them. The area between the mirrors (the working cavity), as a rule, is filled with an active medium. If the distance between the BMs is a multiple of half the wavelength of the propagating radiation, standing waves (resonator modes) are established in the working cavity of the MCR, and transmission resonances are observed in the photonic band gaps (PBGs). The graphene monolayer is one of the most promising photonics materials and various planar structures are based on it. Graphene monolayer, being a 2D structure, has a number of unique properties such as zero band gap, high electron mobility, high optical transparency and mechanical strength [18; 19]. The chemical modification of graphene structures makes it possible to obtain structures with a non-zero band gap: the fluorination of graphenemakes it possible to obtain a dielectric with a band gap of 3 eV [20]; doping with nitrogen and boron makes it possible to obtain n- and p-type semiconductors [21]; and partial hydrogenation leads to the manifestation of ferromagnetic properties in graphene [22]. Unique mechanical and electronic properties make graphene a promising candidate for creating flexible electronic devices, field-effect transistors, solar cells and energy storage devices. In this regard, the practical application of graphene and other 2D materials is currently one of the priority areas of both fundamental and applied research [23; 24]. In addition to chemical modification, the parameters of graphene-containing structures can be effectively controlled by changing its chemical potential (Fermi energy) using an applied voltage [25; 26; 27; 28]. Graphene monolayers with an inverse population of charge carriers, realized as a result of optical, injection, or diffusion pumping, are the active layers of a medium that amplifies THz radiation. However, the creation of an inverse population is associated with a number of fundamental and technical difficulties (to achieve amplification, a long-lived inverse population is required, which, in turn, requires the creation of high-purity graphene samples). Therefore, alternative mechanisms are of interest to implement the amplification of THz radiation in graphene. It was shown in [29; 30; 31; 32; 33] that graphene with charge carrier drift has the properties of an amplifying medium, i.e., graphene in the active state can be obtained using current pumping. At carrier drift velocities that are greater than the phase velocity of an electromagnetic wave, the real part of graphene conductivity becomes negative, and amplification is achieved in the THz range due to the Vavilov-Cherenkov effect.