Radiation of a TM mode from an Open End of a Three-Layer Dielectric Capillary

Modern trends in beam-driven radiation sources include the interaction of Cherenkov wakefields with open-ended circular waveguides with complicated dielectric linings, with a three-layer dielectric capillary recently proposed to reduce radiation divergence being a representative example [Jiang S et al. 2020 Opt. Lett. 45 5416]. This paper presents a rigorous approach that allows for an analytical description of the electromagnetic processes that occur when the structure is excited by a single waveguide TM mode. In other words, the corresponding canonical waveguide diffraction problem is solved in a rigorous formulation. This is a continuation of our previous papers which considered simpler cases with a homogeneous or two-layer dielectric filling. Here, we use the same analytical approach based on the Wiener-Hopf-Fock technique and deal with the more complicated case of a three-layer dielectric lining. Using the obtained rigorous solution, we discuss the possibility of manipulating the far-field radiation pattern using a third layer made of a low permittivity material.