Polarimetric dimension and nonregularity of tightly focused light beams

Polarimetric dimension and nonregularity are newly introduced concepts that characterize three-dimensional (3D) polarization states of light. We analyze the spectral polarimetric dimension and the degree of nonregularity associated with two kinds of tightly focused beams: a radially fully polarized Gaussian Schell-model (GSM) beam and a partially polarized beam composed of an incoherent superposition of two orthogonally polarized (coherent) plane-wave modes. We show that for both beams the focal field can exhibit genuine 3D and nonregular character, with even perfect nonregularity encountered for the tightly focused two-mode beam. These features originate from the partial spatial coherence and partial polarization of the incident beams, and in the limit of full coherence and polarization the three-dimensionality and nonregularity of the focal field vanish. We also find that the GSM beam can generate a nanoscale region around the focus where the field is essentially 3D unpolarized. The results demonstrate the rich polarimetric structure of focal fields and may find uses in optical particle manipulation and sensing.