Transition radiation on semi-infinite plate and Smith-Purcell effect

TL;DR

This paper develops a theoretical approach to describe high-frequency Smith-Purcell and transition radiation using eikonal approximation for dielectric plates, extending understanding beyond metallic grating models.

Contribution

It introduces a simplified eikonal approximation model for radiation on semi-infinite dielectric plates, applicable at high frequencies where materials behave as dielectrics.

Findings

Derived formulae for radiation on dielectric plates

Unified description of transition and Smith-Purcell radiation

Applicable to high-frequency regimes exceeding plasma frequency

Abstract

The Smith-Purcell radiation is usually measured when an electron passes over the grating of metallic stripes. However, for high frequencies (exceeding the plasma frequency of the grating material) none material could be treated as a conductor, but ought to be considered as a dielectric with plasma-like permittivity. So for describing Smith-Purcell radiation in the range of high frequencies new theoretical approaches are needed. In the present paper we apply the simple variant of eikonal approximation developed earlier to the case of radiation on the set of parallel semi-infinite dielectric plates. The formulae obtained describe the radiation generated by the particles both passing through the plates (traditionally referred as "transition radiation") and moving in vacuum over the grating formed by the edges of the plates (traditionally referred as "diffraction radiation", and, taking into account the periodicity of the plates arrangement, as Smith-Purcell radiation).