Analytical solution for the stopping power of the Cherenkov radiation in a uniaxial nanowire material

TL;DR

This paper derives analytical formulas for the Cherenkov radiation stopping power in uniaxial nanowire materials, revealing velocity-dependent emission without a threshold and extending the formalism to dispersive media.

Contribution

It provides the first closed-form analytical expressions for Cherenkov stopping power in uniaxial wire media, including effects of material dispersion.

Findings

Stopping power proportional to charge velocity in non-dispersive media

No velocity threshold for Cherenkov emission in this medium

Optimal charge velocity for maximum emission can be less than light speed

Abstract

We derive closed analytical formulae for the power emitted by moving charged particles in a uniaxial wire medium by means of an eigenfunction expansion. Our analytical expressions demonstrate that in the absence of material dispersion the stopping power of the uniaxial wire medium is proportional to the charges velocity, and that there is no velocity threshold for the Cherenkov emission. It is shown that the eigenfunction expansion formalism can be extended to the case of dispersive lossless media. Furthermore, in presence of material dispersion the optimal charge velocity that maximizes the emitted Cherenkov power may be less than the speed of light in vacuum.