The Plane-Wave Resolution of Guided Waves

Wave propagation in cylindrical guides of both rectangular and circular cross section is treated by representing the proper solutions to Maxwell's equation through a plane-wave expansion of the Hertzian vector. In the case of a rectangular wave guide only a finite number of plane waves (two or four) is required to represent a given mode, while for the circular guide an infinite manifold is required. The plane waves are uniform, traveling with the velocity of light in the medium at an angle to the cylindrical axis which is determined by the frequency and the eigenvalue of the mode under consideration.