Generating multiple focal structures with circularly polarized double ring shaped beam and axial birefringence

The properties of circularly polarized double ring shaped beam tightly focused through a uniaxial birefringent crystal are studied numerically by the use vectorial diffraction theory for small birefringence. Novel focal structures such as splitting of single focal spot into multiple spots and the focal shift of maximum intensity can be obtained with the proper combination of the topological charge [n], birefringence [Δn], and the pupil to beam ratio [β] of the input circularly polarized double ring shaped beam.