ABSTRACT
Hollow metallic elliptical waveguides are used extensively; they have modes similar to those of circular waveguides. This chapter discusses wave functions in the elliptical cylindrical coordinate system. The elliptical cylindrical coordinate system is based on orthogonally intersecting sets of confocal elliptical cylinders, confocal hyperbolic cylinders, and transverse planes. The boundary conditions parallel those for the circular cylinder, namely, that the field functions be finite throughout the interior of the waveguide, and that the tangential component of E and the normal component of B vanish at the waveguide surface. A circular or elliptical tube of highly conducting material will transmit electromagnetic waves of sufficiently high frequency much as a rectangular waveguide will. Both transverse-electric (TE) and transverse-magnetic (TM) modes are possible. Total reflection at the boundary between two concentric dielectric cylinders is the principle for propagation in the fiber optic cable.
