Geometric descriptions for the polarization for nonparaxial optical fields: a tutorial

Abstract

This tutorial provides an overview of the local description of polarization for nonparaxial light, for which all Cartesian components of the electric field are significant. The polarization of light at each point is characterized by a $3$ component vector in the case of full polarization or by a $3\times 3$ polarization matrix for partial polarization. Standard concepts for paraxial polarization like the degree of polarization, the Stokes parameters and the Poincaré sphere then have generalizations for nonparaxial light that are either not unique or not trivial. This work aims to clarify some of these discrepancies, present some new concepts, and provide a framework that highlights the similarities and differences with the description for the paraxial regimes. Particular emphasis is placed on geometric interpretations.

72 pages, 19 figures

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• Nonlinear vortex dichroism in chiral molecules
• Topological-charge-dependent dichroism and birefringence of optical vortices
• Spin angular momentum and optical chirality of Poincaré vector vortex beams
• Bridging Coherence Optics and Classical Mechanics -- A Universal Light Polarization-Entanglement Complementary Relation
• On the orbit-induced spin density of tightly focused optical vortex beams: ellipticity and helicity
• Spectral Bounds on Entropy and Ergotropy via Statistical Effective Temperature in Classical Polarization and Quantum Thermal States
• Generating optical angular momentum through wavefront curvature
• Intrinsic Meron Spin Textures in Generic Focused Fields
• Unfolding unstable skyrmionic polarization textures
• Non-diffracting meronic spin defects of light