This paper deals with the propagation of electromagnetic waves in cylindrical
waveguides with irregularly deformed cross-sections. The general theory of
electromagnetic waves is of high interest because of its practical use as a
transmission medium. But only in a few special cases, an analytic solution of
Maxwell's equations and the appropriate boundary conditions can be found

Rayleigh was the first to describe the transmission of electromagnetic waves
in hollow and perfect conducting waveguides

However, practical waveguides are usually not uniform in their cross-section
due to the manufacturing process. So in case of nonuniform waveguides the
method of separation does not work.

Based on the earlier work of

It is well known that the solution of Maxwell's partial differential equation
can be reduced to the determination of a vector and a scalar potential. In
1889, Hertz showed that it is possible to define an electromagnetic field
with a single vector function

There are different kinds of boundary conditions to model the actual boundary of a waveguide.
One of the most commonly used boundary conditions is the perfect electric conductor (PEC)

In case of small irregular deformations of the cross-section, it is
appropriate to use the perturbation theory. The surface of the waveguide can
be represented in cylindrical coordinates

In the previous section, the boundary condition for an irregular deformed
waveguide was modeled. The imperfections on the surface

Change of transverse field pattern of the electric and magnetic
field along the

Coupling modes in the irregularly deformed waveguide.

Change of transverse field pattern of the electric and magnetic
field along the

In this section, we will present the method of computing the stochastic GTE's.
After substituting the field components of the IBC Eq. (

All the basis coefficients

Parameters for simulation of excited TE

In this paper it was shown, that it is possible to derive stochastic
generalized telegraphist's equation for irregular deformed waveguides for a
specific random process. In the case of the impedance boundary condition from
Leontovich (IBC), the mathematical derivation and first numeric results were
presented. The changes of the transverse field pattern of a circular electric
wave (TE

There are no underlying research data for the presented work. All results can be reproduced with the equations and parameters given directly in the paper.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Kleinheubacher Berichte 2017”. It is a result of the Kleinheubacher Tagung 2017, Miltenberg, Germany, 25–27 September 2017.The publication of this article was funded by the open-access fund of Leibniz Universität Hannover.Edited by: Thomas Eibert Reviewed by: two anonymous referees