A numerical method for solving a system of integral equations in the problem of electromagnetic waves’ propagation in a graphene rod 

Yuriy G. Smirnov, Doctor of physical and mathematical sciences, professor, head of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), mmm@pnzgu.ru
Marina A. Moskaleva, Candidate of physical and mathematical sciences, associate professor of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), mmm@pnzgu.ru

Background. The problem of electromagnetic waves’ propagation in a dielectric rod of arbitrary cross-section covered with a layer of graphene, which is considered infinitely thin, is considered. The main problem in describing the process of wave propagation in the waveguiding structure is to obtain and analyze the system of integral equations to determine propagation constants. Materials and methods. Maxwell’s equations are solved in the frequency domain. The coupling conditions contain the conductivity of graphene. The method of Green’s functions is applied. Results and conclusions. The system of integral equations for determining the propagation constants is solved numerically. Numerical results are presented.

graphene, integral equation, Green’s function, numerical method

Smirnov Yu.G., Moskaleva M.A. A numerical method for solving a system of integral equations in the problem of electromagnetic waves’ propagation in a graphene rod. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki =  University proceedings. Volga region. Physical and mathematical sciences. 2023;(4):60–74. (In Russ.). doi: 10.21685/2072-3040-2023-4-6