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A multiwave interaction formulation of coaxial Bragg structure with either one or both of the conductors sinusoidally corrugated is presented to describe all the forward and backward waves of various propagating modes within the structure. The validity of the formulation is examined in terms of the reported experiments, and good agreement of the theoretical results with the experimental measurements is demonstrated. Comparison of the present formulation with the previous two-wave interaction treatment shows substantial difference, and confirms the significance of the multiwave interaction formulation presented in this paper. Based on the multiwave interaction formulation, interesting information is revealed that a higher-order mode (such as TE6,1) operation at a frequency of hundreds of gigahertz in a coaxial Bragg reflector can be achieved due to the suppression of spurious modes. This peculiarity provides potential application in constructing a high-Q coaxial Bragg resonator for a high-power cyclotron autoresonance maser or a free-electron laser oscillator in the millimeter and submillimeter wave ranges.

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In practice a coaxial Bragg structure always has an eccentricity between the outer-wall and inner-rod axes. Numerical simulations are carried out to analyze the effect of the eccentricity on the transmission in a coaxial Bragg structure. Results demonstrate that the effect of the eccentricity is minimized and becomes negligible when the phase difference between the outer and inner corrugations is π, no matter if the eccentricity is parallel or oblique.