Diffraction at the Open-Ended Dielectric-Loaded Circular Waveguide: Rigorous Approach

Abstract

A rigorous approach for solving canonical circular open-ended dielectric-lined waveguide diffraction problems is presented. This is continuation of our recent paper [1] where a simpler case of uniform dielectric filling has been considered. Here we deal with the case of an open-ended circular waveguide with layered dielectric filling which is closer to potential applications. The presented method uses the solution of corresponding Wiener-Hopf-Fock equation and leads to an infinite linear system for reflection coefficients (S-parameters) of the waveguide, the latter can be efficiently solved numerically using the reducing technique. As a specific example directly applicable to beam-driven radiation sources based on dielectric-lined capillaries, diffraction of a slow TM symmetrical mode at the open end of the described waveguide is considered. A series of such modes forms the wakefield (Cherenkov radiation field) generated by a charged particle bunch during its passage along the vacuum channel axis. Calculated S-parameters were compared with those obtained from COMSOL simulation and an excellent agreement was shown. This method is expected to be very convenient for analytical investigation of various electromagnetic interactions of Terahertz (THz) waves (both free and guided) and charged particle bunches with slow-wave structures prospective in context of modern beam-driven THz emitters, THz accererators and THz-based bunch manipulation and bunch diagnostic systems.

Radiation of a TM mode from an open end of a three-layer dielectric capillary

“…is always supposed that R is so large that limits values of θ lie in area 4). In our case, the saddle point is isolated and we obtain [17]…”

“…Sim-ilar to Refs. [17,18], an input end of the waveguide was supported by a series of numerical ports, one separate port for each propagating mode (the port that corresponds to the incident mode was set to be active). The corresponding eigenmodes were determined numerically, with analytically calculated longitudinal wavenumbers k zm being used as guess values.…”

“…( 9) in Ref. [17]. Functions F (1,2,3) are determined using the continuity of E ωρ and H ωϕ for z = 0, ρ < d (see Ref.…”

“…Functions F (1,2,3) are determined using the continuity of E ωρ and H ωϕ for z = 0, ρ < d (see Ref. [17] for details), therefore 2πF (1)…”

“…[16] For further development of the discussed topics, a rigorous approach allowing the analytical study of both the radiation from such an open-ended capillary and its excitation by an external source (bunch or electromagnetic pulse) would be extremely useful. In our recent papers, [17,18] we presented an efficient rigorous method for solving circular open-ended waveguide diffraction problems and illustrated this method using the case of a uniform dielectric filling and a two-layer lining of the waveguide. Here we deal with a more complicated geometry offered in Ref.…”