Theoretical and numerical investigation of internal conical refraction of structured light beams

TL;DR

This paper provides a comprehensive numerical analysis of internal conical refraction in biaxial crystals for structured light beams, deriving exact equations from fundamental principles without approximations.

Contribution

It introduces a novel ab-initio numerical method for analyzing conical refraction of structured light in biaxial crystals, applicable to various beam types and polarization states.

Findings

Refraction cone appears within the crystal under realistic conditions.

Shape of the refraction cone is highly sensitive to initial beam conditions.

Exact equations enable precise modeling without analytical approximations.

Abstract

We present an ab-initio numerical investigation of the internal conical refraction of structured light beams in a biaxial crystal. Starting from the solutions of the Fresnel equation, a theoretical analysis is developed without assuming any analytical approximation, thus obtaining a set of exact equations that can be solved by standard methods of integration for any impinging light beam. As examples of applications, we consider the particular cases of linearly and circularly polarized Gaussian and Bessel beams inside a KTP crystal. The numerical calculations follow the evolution of the refracted beam inside the crystal. It is seen that for realistic boundary conditions, a refraction cone appears in a certain range of distances within the crystal and its shape is rather sensitive to the initial conditions.