Supermodes of oversized Talbot-type cavities

The use of a Talbot-type supermode as the primary operating mode can be a means of providing a selective single-mode operation of terahertz electron masers with an oversized beam-wave interaction system. However, as the first step to justifying this approach, it is necessary to show the existence of a set of orthogonal supermodes by which the wave field can be decomposed, to identify the hierarchy and properties of these orthogonal supermodes, and to investigate the issue of their competition. In this paper, all these questions are addressed in the simplest model of a Talbot-type cavity, namely, in a planar 2D cavity with an equidistant spectrum of the transverse wave numbers of the partial waveguide modes. The development of this approach for more complex types of cavities is also briefly discussed.