Electro-optical coupling of a circular Airy beam in a uniaxial crystal

This paper investigates theoretically and numerically on the electro-optical coupling (EOC) for a circular Airy beam (CAB) propagating along the optical axis of a uniaxial crystal after deducing the wave coupling equations of EOC. For a circularly polarized incident CAB, EOC can be used to generate vortex beam by coupling the incident left-handed component into the right-handed vortex component with a vortex topological charge of 2. What's more, EOC plays important role in enhancing or suppressing the abrupt autofocusing, the most important property of CABs, for both left-handed and right-handed components. Near the focal plane, EOC can result in electrically controllable optical "needle" and "cage", which shall be interesting in micromanipulation. In addition, EOC can influence or even forbid the exchange between spin angular momentum (SAM) and orbit angular momentum (OAM). For a linearly polarized incident CAB, its two Cartesian field components of the beam cannot only couple their powers to each other, but also lead to the changes of the intensity pattern and polarization distributions. The polarization state becomes spatially inhomogeneous, and possesses vortex phase with a topological charge of 2 during propagation. EOC presents a new way to control an Airy beam fast and efficiently.