Electro-optically induced topological reactions of optical indicatrix orientation and polarization state defects

We have studied the behavior of topological defects (TDs) of the optical indicatrix orientation and polarization state, which appear when a divergent optical beam propagates through LiNbO₃ crystals under an external electric field. We have found that the topological reaction of the splitting of a central TD of optical indicatrix orientation, which occurs under the electric field E_X, proceeds according to a scheme 1=1/2+1/2. This reaction splits a doubly charged optical vortex into two singly charged vortices. An increase in the electric field strength leads to angular displacement of the optical vortices, thus making it possible to operate spatial positions of the optical vortices via a Pockels effect. We have found that the lateral TDs with the strengths ±½ represent the defects of the polarization state and are not caused by defects of optical indicatrix orientation. They form topological dipoles and generate optical vortices. These topological dipoles undergo no topological reactions in the external electric field.