This talk will provide an overview of the local description of polarization for nonparaxial fields, for which all three Cartesian components of the vector field are significant. The polarization of light at each point is characterized by a 3x3 polarization matrix, as opposed to the 2x2 matrix used in the study of polarization for paraxial light. For nonparaxial light, concepts like the degree of polarization, the Stokes parameters and the Poincare sphere have generalizations that are neither unique nor trivial. This presentation aims to clarify some of these discrepancies and provide a framework that highlights the similarities and differences with the standard description for the paraxial regime, emphasizing geometric interpretations. Finally, the application of these concepts to super-resolution fluorescence microscopy will be presented.
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