Analysis and characteristics of the continuous spectrum of modes of the axially slotted coaxial line

The discrete modes of the axially slotted coaxial line were investigated in many articles. However, the continuous spectrum of modes has not been investigated before. The complete spectrum (discrete and continuous) is required to solve radiation and discontinuity problems of such cylindrical slot/strip lines using modal methods such as the mode matching technique. In this work, the problem of the continuous spectrum of the relevant line is solved using the Riemann-Hilbert problem technique. The analysis reveals the existence of two sets of modes with perpendicular polarizations: one of Ez-even-Hz-odd symmetry about the plane of symmetry of the line, and the other of Hz-even-Ez-odd symmetry. The continuous modes propagating along the line are standing waves in the radial direction. For each propagation constant of the continuous spectrum there are different possible dependencies on the angular dimension, thereby constituting what may be called "transverse patterns" or "angular modes". The characteristics and field configurations of a variety of such modes are investigated in this work. Interesting results of continuous transformations of one angular mode to another when varying the longitudinal propagation constant, the operating frequency and the slot width, are shown in this paper.