There may be four groups of mode types for a metallic closed waveguide structure where the variation of the field along the propagation direction is [e.
This is a different case from classical closed waveguide structures in which the complex wave modes appear in an adjacent frequency region of backward wave modes in the phase constant region as given in [21-31].
The surface waves were explained separately for two subclasses of waveguide, closed waveguides and open waveguides in  which presents some comments on the classification of waveguide modes.
In a classic study, Schelkunoff derived the transverse field component from the potential and the stream functions for the general structure of closed waveguides.
Mittra, "Energy considerations in open and closed waveguides," IEEE Trans.