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

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. 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.