Synthesis and characterization of non-uniformly totally polarized light beams: tutorial

Polarization of a light beam is traditionally studied under the hypothesis that the state of polarization is uniform across the transverse section of the beam. In such a case, if the paraxial approximation is also assumed, the propa- gation of the beam reduces to a scalar problem. Over the last few decades, light beams with spatially variant states of polarization have attracted great attention, due mainly to their potential use in applications such as optical trapping, laser machining, nanoscale imaging, polarimetry, etc. In this tutorial, an introductory treatment of non- uniformly totally polarized beams is given. Besides a brief review of some useful parameters for characterizing the polarization distribution of such beams across transverse planes, from both local and global points of view, several methods for generating them are described. It is expected that this tutorial will serve newcomers as a starting point for further studies on the subject.