Generic optical singularities and beam-field phenomena due to general paraxial beam reflection at a plane dielectric interface

Abstract

A single paraxial beam reflection at a plane dielectric interface, configured appropriately, can lead to the formation of a polarization singularity in the inhomogeneously polarized output beam field for any central angle of incidence. In this paper we derive the necessary condition to realize this effect. We explore the phase singularity characteristics associated with this polarization-singular field and explore the dynamics of the singularities due to controlled variations of the input polarization. The simulation-generated exact field information lead to the exploration of the unique Goos-H\"anchen, Imbert-Fedorov, and spin shifts of the optical-singular fields and the anticipation of an exact mathematical characterization of spin-orbit interaction phenomena involved therein. The formation of a phase singularity independent of a polarization singularity is explained subsequently. Interrelating these seemingly unconnected beam-field phenomena and generic optical singularities can lead to a significant and fundamental understanding of the inhomogeneously polarized beam field; additionally, our singularity generation method can find potential application in experimental characterization of the involved dielectric media.