Evolution of vortices created by conical diffraction in biaxial crystals versus orbital angular momentum

Light states evolution versus their fractional orbital angular momentum (OAM) has been analyzed in the conical diffraction process occurring through biaxial crystals. Experimental results are provided by a non-degenerate cascade of KGd(WO$_2$)$_4$ and Bi$_2$ZnOB$_2$O$_6$ biaxial crystals. The continuous $0\to 1\to 2$ $\hbar$/photon increasing of the fractional OAM in passing through integer values was operated with the help of the spin-orbit coupling in the Bi$_2$ZnOB$_2$O$_6$ crystal. The phase of the state light and its vortices were visualized by interference patterns with a reference beam. The evolution of the fractional OAM value is accompanied by a continuous evolution of pairs of vortices with opposite signs and linked by a $-\pi/+\pi$ discontinuous phase line. The phase pattern evolution around half-integer OAM is observed to be continuous. In other cases, the evolution can be interrupted by the breaking of a $-\pi/+\pi$ discontinuous phase line and a new pair of vortices with opposite charges is born.