Gaussian beams in hollow metal waveguides

Various families of Gaussian beams have been explored previously to represent the propagation of nearly plane electromagnetic waves in media having at most quadratic transverse variations of the index of refraction and the gain or loss in the vicinity of the beam. However, such beams cannot directly represent the wave solutions for propagation in planar or rectangular waveguides, and sinusoidal mode functions are more commonly used for such waveguides. On the other hand, it is also useful to consider the possibility of recurring Gaussian beams that have an approximately Gaussian transverse profile at certain distinct planes along the propagation path. It is shown here that under some conditions recurring Gaussian beams can describe wave propagation in hollow metal waveguides, and they can also lead to efficient coupling between the waveguide fields and free-space beams.