ABSTRACT
A. Zeilinger proposed that photon pairs with entanglement of the orbital angular momentum (OAM) states could be detected in the course of spontaneous parametric down-conversion by illuminating a "fork" hologram (used for generating optical vortices) by a shifted Gaussian beam. Most closely related to the topic of this work are some early papers of the present authors. This chapter discusses both theoretically and experimentally, transformations of optical vortices which occur due to a complex Cartesian shift of the original functions of the complex amplitude. It theoretically and experimentally studies the transformation of the optical vortex proposed, by illuminating an amplitude "fork" hologram by a Gaussian beam with its waist center being shifted in the transverse plane from the hologram center. The chapter considers asymmetric Gaussian optical vortices that can be generated experimentally by diffraction of a Gaussian beam by an amplitude hologram with a typical "fork" at the point of singularity.
