The structure of a nonparaxial Gaussian beam near the focus: II. Optical vortices

Exact analytical solutions of Maxwell's equations describing the behavior o f a nonparaxial optical vortex in the vicinity of a focal waist are obtaine d using the Whittaker method of scalar potentials, the point complex source method, and approximate Davis boundary conditions. It is shown that nonpar axial optical vortices in free space fall into three large groups: even and odd vortices with preferential circular polarization and azimuthally symme tric TE and TM vortices. The fields of even and odd nonparaxial vortices ag ree well with the fields of guided homogeneous and inhomogeneous vortices o f a weakly guiding fiber. In the paraxial approximation, the expressions ob tained for the fields are transformed to the fields of paraxial optical vor tices. In the focal region, a nonparaxial beam experiences elliptic deforma tion of the cross section. This elliptic deformation is shown to result fro m the asymmetric location of regions with negative energy flows. The revers al of sign of the topological charge and the helicity of a combination of e ven and odd vortices causes both rotation of the dislocation axis through p i /2 and longitudinal displacement of the focal spot, which are the transve rse and the longitudinal optical Magnus effects. (C) 2001 MAIK "Nauka/Inter periodica".