Polarized grating transition radiation from a 2D photonic crystal

Abstract

Transition radiation (TR) is widely used as a radiation source in a wide spectral range, from terahertz to x rays. Conventional flat surfaces are usually used, but with the development of applications using microscopically structured surfaces, periodic surface structures are beginning to be studied. The periodicity of the surface dramatically changes the characteristics of TR, so this type of radiation received its own name: grating transition radiation (GTR). In this work, we investigate the polarization properties of GTR from a two-dimensional (2D) photonic crystal consisting of small particles arranged in a flat lattice (a 2D photonic crystal slab). We show theoretically that the polarization properties of GTR differ significantly from those of the kindred types of radiation: conventional TR and Smith–Purcell radiation. Since we found that the asymptotic behavior depending on the electron velocity for GTR and classical TR diverges, we performed homogenization and show that the results for GTR after homogenization are in perfect agreement with those for classical TR. This means that different dependence on the electron velocity for TR from a slab and for GTR from a 2D photonic crystal slab is caused by the fundamental difference between a conventional slab and a 2D photonic crystal due to its microscopic structure. The constructed theory contains the coordinates of the particles the photonic crystal consists of, which allows considering structures of finite size, both symmetrical and asymmetric. For asymmetric targets, the polarization of the radiation proves to be very sensitive to the electron’s trajectory. This sensibility of polarization characteristics opens up good opportunities for studying fine fundamental effects connected with the electron trajectory, such as the effect of the quantum nature of free electrons which manifests itself in the properties of radiation generated by free electrons. Also, the obtained results may find application in the design of compact sources of polarized radiation based on microscopically structured surfaces.