Optical Sensing of Electron-Beam Position with Twin Silver Nanotube Antenna Tuned to Hybrid Surface Plasmon Resonance

Considered is the diffraction radiation of a flat modulated beam of electrons flowing between two identical circular nanotubes made of silver. The electromagnetic field of such a beam is a two-dimensional H-polarized surface wave, which propagates in the same direction as the beam, with the phase velocity equal to the beam velocity. This field excites the currents on the nanotubes that radiate even if the beam does not touch the scatterers. For numerical solution, we use the method of partial separation of variables and the addition theorems for cylindrical functions that reduces the diffraction radiation problem to a matrix equation. On casting this equation to the Fredholm second-kind form, we compute far-field scattering cross-sections and field patterns with controlled accuracy. The obtained results show that a shift of the beam trajectory from the central-symmetric position triggers the excitation of certain resonances, which are absent otherwise. This may serve as a basis for the design of novel optical-range beam position monitors of nanoscale dimensions.