The evolution of nonmonochromatic mode fields in a waveguide with space dispersive medium
DOI:
https://doi.org/10.1109/ICATT.2007.4425143Keywords:
cylindrical waveguide, Maxwell’s equations, constitutive equations, layered space dispersive medium, nonmonochromatic mode fieldsAbstract
We consider a cylindrical waveguide with layered space dispersive medium: there are no free source and charges. The space dispersion is taken in the constitutive equations as a dependence of the electric induction on the electric field and its space derivatives. Electromagnetic fields are; represented as series of nonmonochromatic mode E- and H- fields. In studying the solvability of evolutionary waveguide equations, we obtain a partial differential equation of Sobolev type. We investigate this equation and develop a new numerical method.References
LANDAU, L.D.; LIFSHITZ, E.M. Electrodynamics of Continuous Mediums. Moscow: Fizmatgiz, 1959.
TRET'YAKOV, O.A. Evolutionary waveguide equations. Radiotekhnika i Electronica. 1989, v.34, n.5, p.917-926.
MASHKOVTSEV, B.N.; TSIBIZOV, K.N.; Emelin, B.F. Theory of Waveguides. Moscow-Leningrad: Nauka, 1966.
VLASENKO, L.A. Evolutionary Models with Implicit and Degenerate Differential Equations. Dnepropetrovsk: Sistemnye Tekhnologii, 2006.
RUTKAS, A.; VLASENKO, L. Implicit operator differential equations and applications to electro-dynamics. Mathematical Methods in the Applied Sciences, 2000, v.23, n.1, p.1-15.
RUTKAS, A.G. Mode Fields in a Waveguide with Layered Dispersive Medium. Preprint No. 360. Kharkov: Institute of Radioelectronics of Acad. Sci. of USSR, 1987.
VLASENKO, L.A. A numerical-analytical model of the evolution of electromagnetic field in a waveguide with dispersive medium. Radioelectronika i Informatika, 2005, n.1, p.14-20.
RYABEN'KII, V.S.; PHILIPOV, A.F. On a Stability of Difference Equations. Moscow: Gostekhizdat, 1956.
