Coupled-mode analysis for two-dimensional coaxial Bragg structures with helical ripples

Abstract

Making use of field expansion and the equivalent boundary, an analytical model is set up to describe the multi-mode intercoupling in two-dimensional coaxial Bragg structures with either one or both of the conductors corrugated with helical ripples. The coupled-mode equations and the explicit formulae of the coupling coefficients for all possible mode combinations are derived, and the general mode coupling rules are discussed. Based on the analytical model, the dependence of the coupling coefficients on structural parameters of the two-dimensional coaxial Bragg structures with overmoded operation is investigated by numerical calculation. The results show that the additional conductor provides more flexibility for adjustment of coupling coefficients compared with other types of two-dimensional Bragg structures with a single conductor. Taking advantage of this feature, a two-dimensional coaxial Bragg structure can provide strong reflection with high mode purity under overmoded operation by suppressing the parasitic coupling using an optimized combination of corrugated outer and inner conductors. In this way, the structure has potential applications in the design of high-Q improved Bragg resonators for high-power microwave oscillators operating in the millimeter wave or terahertz range.

Bandgap Control of Two-Dimensional Coaxial Bragg Structures With Helically Corrugated Conductors

“…Since the reflectivity/transmission at the Bragg resonance frequency is the key parameter that determines the width and amplitude of a bandgap, one can get a hint from (18) and (19) that bandgap control may be achieved if the coupling coefficient is tunable. According to the coupled-mode analytical model for two-dimensional coaxial Bragg structures established in [31], the coupling coefficient for the helical corrugations described by (1) and (2) can be denoted as…”

“…where ω is the angular frequency; p ik and q ik are variables dependent on the types of mode i and mode k as well as the structure parameters, and their explicit formulas are given in [31]. Once the outer and inner conductors and their corrugated surfaces are processed, the corrugation amplitude l o , l i and the variables p ik , q ik are fixed with a constant value.…”

“…Thus it is possible to exert opposite control effects on the bandgaps associated with different coupled-mode combinations through varying the angular deviation ∆ϕ. Fig.7 shows the transmission responses of structure B within frequency of 30GHz-45GHz, obtained by multimode coupling analysis (solid lines) [31] seen in Fig. 7, when ∆ϕ =0, there is one dominant transmission bandgap centered at 42.48 GHz; when ∆ϕ =180 o , there is also one dominant transmission bandgap, but its center frequency is shifted to 37.52 GHz; when ∆ϕ =117 o , two dominant transmission bandgaps appear with center frequencies of 37.52 GHz and 42.48 GHz, respectively.…”

“…Early investigations of twodimensional Bragg structures mostly concentrated on structures with cylindrical topology. In recent years, growing attention has been paid to Bragg structures in the form of coaxial metallic waveguides, due to their merits in improving the performance of high-power free-electron devices [26]- [31]. It should be noted that, although the coupling coefficients and reflection characteristics of a twodimensional coaxial Bragg structure with one or two helically corrugated conductors were investigated in [31], a method of manipulating the bandgap parameters of two dimensional coaxial Bragg structures is yet to be confirmed.…”