Spatial distribution of Cherenkov radiation in periodic dielectric media

TL;DR

This paper develops an analytical theory for the spatial distribution of Cherenkov radiation in periodic dielectric media, validated by numerical simulations, revealing how the medium's dispersion influences radiation patterns.

Contribution

It introduces a general analytical framework for Cherenkov radiation in 2D and 3D periodic media using Bloch mode expansion, bridging theory and numerical validation.

Findings

Analytical expressions match numerical FDTD results.

Dispersion relations significantly affect Cherenkov radiation patterns.

The theory applies to arbitrary periodic dielectric structures.

Abstract

The nontrivial dispersion relation of a periodic medium affects both the spectral and the spatial distribution of Cherenkov radiation. We present a theory of the spatial distribution of Cherenkov radiation in the far-field zone inside arbitrary three- and two-dimensional dielectric media. Simple analytical expressions for the far-field are obtained in terms of the Bloch mode expansion. Numerical examples of the Cherenkov radiation in a two-dimensional photonic crystal is presented. The developed analytical theory demonstrates good agreement with numerically rigorous finite-difference time-domain calculations.