Unitary transformation for Poincaré beams on different parts of Poincaré sphere

We construct an experimental setup, consisting of conical refraction transformation in two biaxial cascade crystals and 4f-system, to realize Unitary transformation of light beam and the manipulation of Poincaré beams on the different parts of Poincaré sphere. The spatial structure of the polarization can be controlled by changing the polarization of the incident beam or rotating the angle between these two crystals. The beams with different SoPs covering the full-Poincaré sphere, part-Poincaré sphere and one point on the sphere are generated for the different angles between crystals. The Unitary transformation of light beam is proposed in the experiment with the invariant intensity distribution. Subsequently, the spin angular momentum is derived from the distribution of polarization measured in our experiment. Moreover, the conversion between orbital angular momentum and spin angular momentum of light beam is obtained by changing the angle between crystals. And the conversion progress can also be influenced by the polarization of incident beam. We realized the continuous control of the spatial structure of the angular momentum density, which has potential in the manipulation of optical trapping systems and polarization-multiplexed free-space optical communication.