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By using the recently introduced parametrization of an n-dimensional density matrix in terms of the indices of population asymmetry and the intrinsic coherences, we define descriptors in both integer and continuous forms of the effective dimension that take place for a complete description of a density matrix, thus providing accurate information beyond the rank of the density matrix. The concepts of dimensional folding, hidden dimensional purity, and dimensional entropy are introduced and discussed in view of the new approach presented. The results are applicable to any physical system represented by a density matrix, such as n-level quantum systems, qutrits, sets of interacting pencils of radiation, classical polarization states, and to transformations of density matrices, as occurs with quantum channels.

Making use of exact and quasistatic expressions for the field in near-field imaging of a point dipole by a thin silver slab, we calculate the point-spread function and the associated image resolution. We show that the resolution, which depends on the silver slab thickness and the dipole orientation, generally is better than the conventional diffraction limit and can be as high as λ/8. The results substantially agree with recent theoretical and experimental studies on 2D objects.

We show that for a stationary, quasi-monochromatic, partially polarized beam the temporal electromagnetic degree of coherence is specified by the modulation contrasts of the Stokes parameters in Michelson’s interferometer. We also demonstrate how the polarization modulations are transferred into intensity variations, thereby enabling the measurement of the time-domain degree of coherence and the associated coherence time. Our results are analogous to those found earlier for spatial electromagnetic coherence in Young’s interferometer and form an extension to the customary scalar treatment of Michelson’s interferometer. Our work also highlights the relationship between polarization and electromagnetic coherence and the time-domain analyses of these quantities in terms of the traditional (polarization) Stokes parameters and the recently introduced coherence (two-time) Stokes parameters.

The polarization of light is important in a great variety of optical phenomena, ranging from transmission, reflection and scattering to polarimetric imaging of scenes and quantum-mechanical selection rules of atomic and molecular transitions. Among some less-well-known phenomena that illustrate the vectorial nature of light are the Pancharatnam1 (or geometric2) phase, singularities in the polarization pattern of clear sky3 and polarization of microwave background radiation4. Here, we examine the partial polarization of focused light. We experimentally demonstrate a rather surprising phenomenon, where the focusing of unpolarized light results in rings of full polarization in the focal plane of the focusing optics. The polarization rings are imaged with a resolution of