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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 TM 03  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 TM 0 nlcavity modes that exist in a closed SWS, where  n  and  l  are the radial and axial indices of TM 0n lcavity 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 TM 0 nwaveguide modes of the open SWS are actually not pure TM 0 nmodes, but fascinating combinations of selected portions of the modes with selected portions of all possible lower-order TM 0( n - j )  waveguide modes, where  j =1 … ( n -1). An analytically calculated TM 03  waveguide mode, therefore, turns out to be in fact a combination of three different TM 0 nwaveguide modes sequentially identified by numerically calculated TM 0 nlcavity modes: (i) TM 03 lmode with  l =0 … 4, (ii) TM 01 lmode with  l =13 … 11, and (iii) TM 02 lmode with  l =8 … 9.

journal of electromagnetic waves and applications

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