Generalized Telegraphist's Equations for Waveguides

In this payer Maxwell's -partial differential equations and the boundary conditions for waveguides jllled with a heterogeneous and non-isotropic medium are converted into an infinite system of ordinary differential equations. This system represents a generalization of "telegraphist's equations" for a single mode transmission to the case of multiple mode transmission. A similar set of equations is obtained for spherical waves. Although such generalized telegraphist's equations are very complicated, it. is very likely that usef ul results can be obtained by an appropriate modal analysis. From a purely mathematical point of view the problem of electromagnetic wave propagation inside a metal waveguide reduces to obtaining that solution of Maxwell's equations which satisfies certain boundary conditions along the waveguide and certain terminal conditions at the ends of the waveguide. If the medium inside the waveguide is homogeneous and isotropic and if the cross-section of the waveguide is either rectangular or circular or elliptic, the desired solution is obtained by the method of separating the variables. The method works for some other special cross-sections. It works also if the medium inside a rectangular waveguide consists of homogeneous, isotropic strata parallel to one of its faces. Similarly, it works if the medium inside a circular waveguide consists of coaxial, homogeneous, isotropic layers. But in general if the medium is either nonhomogeneous or non-isotropic or both, the method does not work.