Two-Dimensional Optical Vortices in Three-Dimensional, Nonvortex, Nonparaxial Beams

It was theoretically and numerically demonstrated that in a nonparaxial light field containing a line of zero intensity in its cross-section, longitudinal optical vortices are formed in the longitudinal cross-section containing the optical axis at isolated points of zero intensity. Energy circulates around these vortices. Moreover, along a segment of this energy circulation path, the energy propagates opposite to the main direction of propagation. The diameter of the region where energy circulates around the intensity zero is approximately 0.2λ. Longitudinal optical vortices appear in pairs. Optical vortices on the one side of the optical axis have the same topological charge (+1 or –1). Optical vortices on the opposite side of the optical axis have topological charges (TC) of opposite signs. If a vortex with a TC of –1 is located to the left of the optical axis (when viewed along the direction of propagation), and a vortex with a TC of +1 is to the right, then light does not pass in the forward direction between these optical vortices. Conversely, if the left optical vortex has TС of +1, and the right vortex has TС of –1, then light does propagate forward between these optical vortices.