The propagation of the TM-wave in a flat semi-open dielectric layer with nonlocal nonlinearity 

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
Stanislav V. Tikhov, Postgraduate student, Penza State University (40 Krasnaya street,Penza, Russia)

Background. The article considers the problem of propagation of electromagnetic waves in a dielectric layer filled with a medium whose permittivity is characterized by the integral form of the Kerr law. The main task in describing the process of wave propagation in a waveguide structure is to obtain a dispersion equation for propagation constants and study its solvability. Materials and methods. Maxwell’s equations are solved in the frequency domain. The system contains the dependence on the square of the modulus of the electric field strength. Results and conclusions. A system of dispersion equations is obtained, which in fact is a system of dispersion equations for TM waves in the structure. The results of calculations of propagation constants depending on the parameters of the problem are presented.

 nonlinear media, modified Kerr law, nonlocal nonlinearity, eigenwaves, eigenvalue problem, system of dispersion equations

Smirnov Yu.G., Tikhov S.V. The propagation of the TM-wave in a flat semiopen dielectric layer with nonlocal nonlinearity. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2023;(1):40–53. (In Russ.). doi: 10.21685/2072-3040-2023-1-4