Abstract
A waveguide with a constant, simply connected section S is considered under the condition that the substance filling the waveguide is characterized by permittivity and permeability that vary smoothly over the section S, but are constant along the waveguide axis. Ideal conductivity conditions are assumed on the walls of the waveguide. On the basis of the previously found representation of the electromagnetic field in such a waveguide using 4 scalar functions, namely, two electric and two magnetic potentials, Maxwells equations are rewritten with respect to the potentials and longitudinal components of the field. It appears possible to exclude potentials from this system and arrive at a pair of integro-differential equations for longitudinal components alone that split into two uncoupled wave equations in the optically homogeneous case. In an optically inhomogeneous case, this approach reduces the problem of finding the normal modes of a waveguide to studying the spectrum of a quadratic self-adjoint operator pencil.
Highlights
Consider a waveguide representing a cylinder of constant cross-section S filled with an optically inhomogeneous substance, which we will characterize with a permittivity and a permeability
The normal waves of the waveguide turned out to be eigenfunctions of some non-self-adjoint quadratic operator pencil acting in a space specially selected by the functional
We were able to reduce the problem of wave propagation in a waveguide filled with an inhomogeneous substance to a linear second-order partial differential equation (9), the coefficients of which are self-adjoint operators
Summary
Consider a waveguide representing a cylinder of constant cross-section S filled with an optically inhomogeneous substance, which we will characterize with a permittivity and a permeability. In the attempt to study a general case undertaken in the beginning of 2000s [3]–[5], it was not possible to introduce potentials and the problem was investigated with respect to three randomly chosen field components With this approach, the normal waves of the waveguide turned out to be eigenfunctions of some non-self-adjoint quadratic operator pencil acting in a space specially selected by the functional. In a series of numerical experiments [7]–[9], it was shown that the propagation constants of the normal modes of an axially symmetric waveguide with a dielectric core can leave the real and imaginary axes of the β complex plane To calculate these eigenvalues, we used the truncation method and standard solvers to find the eigenvalues of non-self-adjoint matrices. Below we seek the solution of Maxwell’s equations in a waveguide in the form (2) without any loss of generality
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Discrete and Continuous Models and Applied Computational Science
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
