Fermionic transformation rules for spatially filtered light beams in conical refraction

In conical refraction, when a collimated light beam passes along the optic axis of a biaxial crystal it refracts conically giving rise to a characteristic conical refraction (CR) ring. At each point of the CR ring the light electric field is linearly polarized with the polarization plane rotating along the ring such that every two opposite points of the ring present orthogonal linear polarizations. With a pinhole we have spatially filtered a small part of the CR ring and experimentally reported that this filtered light does not yield a ring pattern when it refracts along the optic axis of a second biaxial crystal, called the CR-analyzer in what follows. Instead, after crossing the CR-analyzer the filtered beam splits into two beams with orthogonal linear polarizations that correspond to two opposite points of the otherwise expected CR ring. We have experimentally derived the transformation rules of the filtered beam. For a CR-analyzer rotated by an angle ω around the optic axis, the filtered beam splits in two beams with intensities following the fermionic transformation rule cos2 (ω / 2) , in contrast to the Malus law of cos 2ω followed by double refraction.