Dispersion diagrams of linear slow-wave structures. Identification of electromagnetic waves, all electromagnetic waves: forward-traveling, backward-traveling and standing electromagnetic waves

The analytically calculated dispersion diagram of an overmoded 9-period V-band slow-wave structure (SWS) designed to operate in a high-order transverse-magnetic TM03 waveguide mode of a backward-traveling electromagnetic wave [Ye et al., Phys. Plasmas, 22, 063104 (2015)] is re-examined using the two-dimensional (2D) Poisson SuperFish code allowing to precisely calculate spatial patterns of electric field vectors, wavenumbers and characteristic frequencies of all azimuthally-symmetric TM0nl cavity modes that exist in a closed SWS, where n and l are the radial and axial indices of TM0nl cavity modes, respectively [Main et al., IEEE Trans. Plasma Sci., Vol. 22, No. 5, Oct. 1994, p. 566]. It is shown that the analytically calculated higher-order TM0n waveguide modes of the open SWS are actually not pure TM0n modes, but fascinating combinations of selected portions of the modes with selected portions of all possible lower-order TM0(n-j) waveguide modes, where j=1 horizontal ellipsis (n-1). An analytically calculated TM03 waveguide mode, therefore, turns out to be in fact a combination of three different TM0n waveguide modes sequentially identified by numerically calculated TM0nl cavity modes: (i) TM03l mode with l=0 horizontal ellipsis 4, (ii) TM01l mode with l=13 horizontal ellipsis 11, and (iii) TM02l mode with l=8 horizontal ellipsis 9.