  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.
