Conical diffraction and transformation of Bessel beams in biaxial crystals

As shown previously, the propagation of a Bessel light beam along the optical axes of a biaxial crystal results in conversion of the order of a Bessel function. The Bessel beam changes its order by one due to the effect of the crystal anisotropy, which results in the generation of a vortex beam. In this work we demonstrate a simple derivation of the equations describing the conversion and propagation of the vortex field. These equations are applied to study the conversion of a strongly truncated Bessel beam. The results can be used for developing crystal-based Bessel beam converters and generating vortex optical fields.