  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.
