Topics studied included the characteristics of a radially polarized electromagnetic field at the strong focus, and spin-orbital conversion at the strong focus of a circularly polarized wave. Numerous follow-up publications relied on the Richards–Wolf formalism to look into the behavior of more general electromagnetic fields with various polarization states. The rigorous description of a linearly polarized electromagnetic field at the strong focus was proposed in a classical work by Richards and Wolf. For a demonstration of the proposed application, the metalens is calculated, which can be a prototype for an optical microsensor based on sharp focusing for measuring roughness. The results obtained in terms of controlling the intensity maxima allow the transverse mode analysis of laser beams in sensorial applications. This spatial separation at the focus of left and right circularly polarized light is a manifestation of the optical spin Hall effect. The longitudinal SAM component is found to be positive, and the polarization vector is shown to rotate anticlockwise in the focal spot regions where the transverse energy flow rotates anticlockwise, and vice versa-the longitudinal SAM component is negative and the polarization vector rotates clockwise in the focal spot regions where the transverse energy flow rotates clockwise. It is interesting that the longitudinal SAM projection changes its sign at the focus 4 m times. The transverse energy flow is also shown to change its handedness an even number of times proportional to the order of the optical vortex via a full circle around the optical axis. We show that light generates 4 m vortices of a transverse energy flow, with their centers located between the local intensity maxima.
The intensity of light in the strong focus is theoretically and numerically shown to have an even number of local maxima located along a closed contour centered at an on-axis point of zero intensity. Reluing on the Richards-Wolf formalism, we deduce analytical expressions that describe E- and H-vector components, intensity patterns, and projections of the Poynting vector and spin angular momentum (SAM) vector at the strong focus.
This type of hybrid polarization combines properties of the m th-order cylindrical polarization and circular polarization. We discuss interesting effects that occur when strongly focusing light with m th-order cylindrical–circular polarization.
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