Propagation of high-order circularly polarized Bessel beams and vortex generation in uniaxial crystals

We investigate the generation and transformation of Bessel beams through linear and nonlinear optical crystals. We outline the generation of high-order vortices due to propagation of Bessel beams along the optical axis of uniaxial crystals and expand this to the nonlinear regime by outlining a new phase-matching process (full conical phase matching) in second harmonic generation of vector Bessel beams for various symmetries in uniaxial crystals. We demonstrate the principles experimentally in a uniaxial BBO crystal and find excellent agreement between the experimental and theoretical results. The results imply a coupling of the intrinsic and extrinsic optical angular momentum of the resulting fields, which may have importance in studies involving quantum entanglement of the angular momentum basis of light.