Electromagnetic Design of Beam Position Monitor Based on Diffraction Radiation from Twin Dielectric Nanowires

Abstract

The diffraction radiation of a modulated beam of charged particles, which flow between twin dielectric circular nanowires is considered. This nanowire configuration can be considered as a pair of optically coupled dielectric open resonators. In the free space, the electron beam field is a slow wave, which decays exponentially from the beam trajectory and is anti-symmetric with respect to that trajectory. We use the Fourier expansions in local polar coordinates of each wire and the addition theorems for the cylindrical functions in order to reduce the wave-scattering problem to discrete form. As soon as we cast the derived matrix equation to the Fredholm second-kind type, the convergence is guaranteed. The considered optical open resonator supports supermodes of four orthogonal symmetry classes. The optical diffraction radiation power shows the resonanses at the supermode wavelengths, some of which appear only if the beam trajectory has non-zero rotation angle from the symmetric position. This effect can be used in the beam position monitoring. It can be scaled to the other wavelength ranges.