## 5 Conclusions  
This paper presents the frequency dependencies of the transmission and reflection coefficients for a \(TM\) wave propagating in a symmetric MCR structure with dielectric BMs. The active layer, which is a periodic graphene-containing structure with the controlled material parameters of individual layers, completely fills the working cavity of the resonator. When the cavity is filled with a structure with quantum wells (graphene monolayers), a regime of strong exciton-photon interaction between the defective cavity mode and quantum well excitons is realized. This leads to the splitting of the exciton and photon levels into two polariton states and to a significant transformation of the transmission and reflection spectra.  
It is shown that the transformation of the spectra in an MCR with the \"dielectric/graphene\" structure occurs due to a change in the conductivity of the graphene monolayers when their Fermi energy changes under the action of an external electric field, and in an MCR with the \"semiconductor/graphene\" structure, it also occurs due to a change in the permittivity of the semiconductor layers when exposed to the external magnetic field. The conductivity real part of the graphene layers, through which a direct electric current flows, can become negative in the range \(f\leq 2\) THz, which leads to terahertz radiation amplification in a structure with graphene layers at the charge carrier drift velocities lower than the phase velocity of an electromagnetic wave. In the frequency range \(f\simeq 0.5\) THz, when modeling photon spectra, the method of transfer matrices was used to describe the optical properties of the BMs and the active layer. Numerical results show that the transmission and reflection spectra in the studied terahertz region can be effectively controlled and transformed both due to a change in the Fermi energy of graphene monolayers by an external electric field, and as a result of a change in an external magnetic field.  
Such an MCR structure can find wide practical application, in particular, it can serve as an effective filter in the narrow frequency region of the defect mode, as well as a polarizer in the region where a wave of only one polarization is transmitted. The operating frequency range of the MCR can be changed over a fairly wide range by choosing the material of the layers, their thickness, the type and concentration of carriers, as well as by choosing the period of the BMs.  
Conceptualization, D.I.S.; methodology, S.V.E. and I.V.F.; software, S.V.E. and I.V.F.; formal analysis, S.V.E. and I.V.F.; investigation, S.V.E., I.V.F. and D.I.S.; resources, D.I.S.; data curation, I.V.F.; writing--original draft preparation, S.V.E. and D.I.S.; writing--review and editing, S.V.E.; supervision, D.I.S. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Ministry of Science and Higher Education of the Russian Federation within the framework the State task No.FEUF-2023-0003.  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} MCRs & microresonators \\ BMs & Bragg mirrors \\ PBGs & photonic band gaps \\ \end{tabular}