Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum

TL;DR

This paper derives analytical formulas for Cherenkov radiation spectra in 2D and 3D photonic crystals, revealing how periodic media modify emission and providing a computationally efficient method validated against numerical simulations.

Contribution

It introduces a new analytical approach for calculating Cherenkov emission spectra in periodic media, simplifying the process and reducing computational demands.

Findings

Analytical expressions match numerical FDTD results.

Cherenkov emission spectra are significantly altered in photonic crystals.

The method simplifies spectral calculations in complex media.

Abstract

The Cherenkov radiation is substantially modified in the presence of a medium with a nontrivial dispersion relation. We consider Cherenkov emission spectra of a point charge moving in general three- (3D) and two-dimensional (2D) photonic crystals. Exact analytical expressions for the spectral distribution of the radiated power are obtained in terms of the Bloch mode expansion. The resulting expression reduces to a simple contour integral (3D case) or a one-dimensional sum (2D case) over a small fraction of the reciprocal space, which is defined by the generalized Cherenkov condition. We apply our method to a specific case of an electron moving with different velocities in a 2D square-lattice photonic crystal. Our method demonstrates an excellent agreement with numerically rigorous finite-difference time-domain calculations while being less demanding on computational resources.