Electromagnetic waves in uniaxial crystals: General formalism with an application to Bessel beams

TL;DR

This paper develops a comprehensive mathematical framework for electromagnetic wave propagation in uniaxial crystals, including refraction, reflection, and Bessel beam analysis, with numerical insights into optical vortex behavior.

Contribution

It introduces a general formalism for electromagnetic waves in birefringent media and applies it to analyze Bessel beams and optical vortices in detail.

Findings

Formulas for refraction and reflection at interfaces

Analysis of Bessel beam interactions with uniaxial crystals

Numerical results on optical vortex formation and destruction

Abstract

We present a mathematical formalism describing the propagation of a completely general electromagnetic wave in a birefringent medium. Analytic formulas for the refraction and reflection from a plane interface are obtained. As a particular example, a Bessel beam impinging at an arbitrary angle is analyzed in detail. Some numerical results showing the formation and destruction of optical vortices are presented.