  We investigate the dynamical properties of a type-II optical parametric
oscillator pumped by a structured light beam carrying orbital angular momentum.
Different dynamical regimes are theoretically derived and experimentally
demonstrated, depending on the anisotropy effects imposed by the nonlinear
medium. In a weakly anisotropic regime, fine-tuning of the orbital angular
momentum transfer is obtained by adjusting the crystal parameters. Under strong
anisotropy, orbital angular momentum transfer is not possible and a sharp
dynamical behavior is observed, with abrupt switching between different
transverse modes.
