Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam.

We demonstrate that the conversion of spin-to-orbital angular momentum in a focused vectorial light beam can be forbidden or enhanced by the electric-field-erased or increased spatial anisotropy of a uniaxial crystal undergoing the Pockels effect. A focused right-handed circularly polarized quasi-Gaussian beam incident on an electro-optic crystal strontium barium niobate is taken to illustrate the effect, and a conversion-forbidden electric field E(0)=-16.87 kV/cm is found. Of special interest is that single photons generated in this effect exhibit an entanglement of 2 deg of freedom of spin and orbital angular momentum, and it is electro-optically controllable.