Eigen waves of a double periodical system of coupled
metal waveguides

**S. E.
Bankov **** **^{1}**,
G. G. Grachev **** **^{1}**, M. D. Duplenkova**^{2}

** **^{1 }
**Kotel'nikov Institute of
Radio-engineering and Electronics of RAS,**

**
**^{2
}**
National Research University Moscow Power Engineering Institute,
Development Bureau**

Received October 28, 2011

** **

**Abstarct.** Eigen modes of an infinite double periodical system
of coupled metal waveguides are considered. Coupling between waveguides is
produced by an infinite system of rectangular holes periodically placed along
longitudinal axis. Boundary problem for waveguides with perfectly conducting
and infinitely thin walls is formulated and reduced to a system of integral
equations relatively electric fields in holes. The system is solved with help
of Galerkin’s technique that gives a dispersion equation relatively eigen modes
propagation constants. Their behavior in a quasi-periodical regime is
investigated. Approximate solution for eigen modes is obtained with help of
phenomenological coupled waves theory. This solution is compared with
electromagnetic solution. Parameters of approximate model are determined.

**Keywords:** coupled waveguides, theory of coupled waves,
waveguide array.