Tightly focusing of circularly polarized vortex beams through a uniaxial birefringent crystal

Under the approximation of small birefringence, the properties of circularly polarized vortex beams tightly focused through a uniaxial birefringent crystal are studied. With the proper combination of the topological charge and the birefringence, the small focus, the small bottle beam and the inverse c-shaped intensity pro. le can be obtained. The effects of the focal shift and the Strehl ratio on the birefringence are analysed. A relation between angular momentum (included spin and orbital) and topological Pancharatnam charge is also presented.