## 1 Introduction  
The ability to tune an antenna's main lobe angle is a desirable property. In leaky-wave antennas, which use the dielectric waveguide as a guiding element and incorporate periodic grating as a scattering object, the period and parameters of the waveguide significantly affect the angle of the main lobe at a certain frequency [1]. The variation of the wavelength of the natural wave (eigenwave) of the waveguide can lead to the variation of the angle of the main lobe. This can be achieved by changing the structural parameters. Another approach is to leave the geometrical parameters unchangeable, but to use material with dynamically controllable properties [2; 3; 4; 5]. Graphene is one such material, which has an almost infinitely thin resistive surface with complex-valued conductivity, denoted as \(\sigma=\sigma(f,\mu_{c},\tau,T)\). The conductivity is a function of four parameters: the frequency \(f\), chemical potential \(\mu_{c}\), electron relaxation time \(\tau\) and temperature \(T\). The conductivity \(\sigma\) can be controlled dynamically by the application of electrostatic or magnetostatic doping and by changing the chemical potential \(\mu_{c}\). Graphene strips are capable of supporting plasmon-polariton waves and corresponding plasmon resonances in the low THz range. Together with the extraordinary hardness and flexibility of graphene, these properties open up wide opportunities for its inclusion in the construction of tunable antennas, absorbers, sensors, polarizers, lasers, etc. [6; 7; 8; 9; 10; 11]. In [12], dynamic single- and dual-channel graphene Q-switching in an Yb:YAG waveguide with controlled power-splitting ratios for application in lasers is demonstrated. A commonly employed technique for studying the graphene structures is the finite-difference time-domain (FDTD) method with modifications [8; 9]. The modifications are proposed due to the mesh size dependency on the size of the scatterers, particularly the thickness of the graphene elements. Given that the graphene is ideally monolayer, extremely dense mesh is need. The finite element method (FEM) is used in [11] to study the graphene-based sensor. FDTD or commercial packages based on FEM use approximate radiation conditions and do not take into account the edge condition, which limits the accuracy of the results. In [13], a graphene antenna at frequencies up to 0.8 THz is proposed. CST microwave studio analysis software is used for the modelling. In this frequency range, the resonance frequency is only slightly influenced by the chemical potential and almost cannot be controlled by electrostatic or magnetostatic biasing. Approximate methods allow a solution to be obtained in much less computation time, and some physical effects to be studied analytically, but at the cost of accuracy. In [14], the graphene patch antenna is considered with the use of the equivalent circuit. The omnidirectional radiation pattern is comparable to that of the conventional metal implementations. However, the resonance frequency is controlled by variation of the chemical potential. In [15], the authors study the graphene bowtie antenna properties for different values of chemical potential, arm length, relaxation time and substrate thickness based on the equivalent circuit. In [16], the leaky-wave antennas based on a single dielectric slab and a double dielectric slab, with an infinite graphene plane or infinite graphene strips excited by dipole, are investigated. An approximate solution is obtained. The radiation patterns demonstrate a controllable elevation angle of the main lobe that depends on the chemical potential of the graphene, accompanied by a noticeable reduction in the maximum of the main lobe. Plasmon wave propagation along the infinite graphene strip is considered in [17]. The authors achieved a change in the elevation angle by modulating the value of the chemical potential of the strip according to a sinusoidal law.