Unitary transformation in polarization of vector beams via biaxial cascade crystals

Abstract

This research establishes a polarization converter consisting of biaxial cascade crystals and a 4f system. The polarization manipulation of vector beams is investigated theoretically. This paper develops an analytical model for the vector beams created by biaxial cascade crystals based on Belsky–Khapalyuk–Berry paraxial theory. The transformation of the electric field caused by conical refraction is verified to be a unitary transformation, resulting in the inhomogeneous state of polarization with the intensity distribution remaining invariant. The numerical simulation results show that the state of polarization varies with incident polarization and the angle between cascade crystals. In particular, for the angle of zero, the exit beam has the state of polarization covering the whole Poincaré sphere. Moreover, the part-Poincaré beams are generated by rotating the crystal around the optics axis. The details of the state of polarization are mapped on the Poincaré sphere to analyze the distribution rule. This method has the potential to extend the coding degree of freedom for optical communication and the diversity of light and matter interactions. The unitary transformation may have great value in research about optical neural networks.