Spin angular momentum density in the tight focus of a light field with phase and polarization singularities

For a light field with both phase and polarization singularities at its center, expressions are obtained that describe the distribution of the spin angular momentum (SAM) density in the sharp focal spot of an aplanatic system. These expressions include the radial, azimuthal, and longitudinal SAM components. As special cases, focusing of optical vortices with radial, azimuthal, and saddle polarizations is studied. Using the Bessel beam as an example, it is shown that in some areas in the focal plane the longitudinal SAM component is zero (resulting in a photonic wheel), while in others it is an order of magnitude less than the transverse component.

Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system

An investigation is made of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source. First the case of a linearly polarized incident field is examined and expressions are derived for the electric and magnetic vectors in the image space. Some general consequences of the formulae are then discussed. In particular the symmetry properties of the field with respect to the focal plane are noted and the state of polarization of the image region is investigated. The distribution of the time-averaged electric and magnetic energy densities and of the energy flow (Poynting vector) in the focal plane is studied in detail, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor. The case of an unpolarized field is also investigated. The solution is riot restricted to systems of low aperture, and the computational results cover, in fact, selected values of the angular semi-aperture a on the image side, in the whole range 0 ≤ α ≤ 90°. The limiting case α → 0 is examined in detail and it is shown that the field is then completely characterized by a single, generally complex, scalar function, which turns out to be identical with that of the classical scalar theory of Airy, Lommel and Struve. The results have an immediate bearing on the resolving power of image forming systems; they also help our understanding of the significance of the scalar diffraction theory, which is customarily employed, without a proper justification, in the analysis of images in lowaperture systems.