Electron energy loss and induced photon emission in photonic crystals

TL;DR

This paper investigates how fast electrons lose energy and induce photon emission in photonic crystals by solving Maxwell's equations, revealing the influence of photonic band structures on energy loss spectra.

Contribution

It provides an exact analysis of electron interactions with photonic crystals, highlighting the role of band structure and frequency gaps in energy loss mechanisms.

Findings

Energy loss spectra relate to photonic band structure.

Effective medium theory applies for small lattice constants.

Band structure effects dominate when lattice constants are comparable to wavelength.

Abstract

The interaction of a fast electron with a photonic crystal is investigated by solving the Maxwell equations exactly for the external field provided by the electron in the presence of the crystal. The energy loss is obtained from the retarding force exerted on the electron by the induced electric field. The features of the energy loss spectra are shown to be related to the photonic band structure of the crystal. Two different regimes are discussed: for small lattice constants $a$ relative to the wavelength of the associated electron excitations $\lambda$, an effective medium theory can be used to describe the material; however, for $a\sim\lambda$ the photonic band structure plays an important role. Special attention is paid to the frequency gap regions in the latter case.