Optical M0bius Strips in Three Dimensional Ellipse Fields: Lines of Linear Polarization

Abstract

The minor axes of, and the normals to, the polarization ellipses that surround singular lines of linear polarization in three dimensional optical ellipse fields are shown to be organized into Mobius strips and into structures we call rippled rings (r-rings). The Mobius strips have two full twists, and can be either right- or left-handed. The major axes of the surrounding ellipses generate cone-like structures. Three orthogonal projections that give rise to 15 indices are used to characterize the different structures. These indices, if independent, could generate 839,808 geometrically and topologically distinct lines; selection rules are presented that reduce the number of lines to 8,248, some 5,562 of which have been observed in a computer simulation. Statistical probabilities are presented for the most important index combinations in random fields. It is argued that it is presently feasible to perform experimental measurements of the Mobius strips, r-rings, and cones described here theoretically.

References in corpus (3)

• Geometric interpretation of the 3-dimensional coherence matrix for nonparaxial polarization
• Optical Mobius Strips in Three Dimensional Ellipse Fields: Lines of Circular Polarization
• Statistics of diffusive and localized fields in the vortex core

Cited by in corpus (6)

• Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects
• Knotting fractional-order knots with the polarization state of light
• Optical Mobius Strips in Three Dimensional Ellipse Fields: Lines of Circular Polarization
• Fermionic out-of-plane structure of polarization singularities
• Generation and characterization of complex vector modes with digital micromirror devices
• Evolution of the Stokes parameters, polarization singularities, and optical skyrmion