Multitwist M\xf6bius Strips and Twisted Ribbons in the Polarization of Paraxial Light Beams

Enrique J Galvez,Kory Beach,Joshua A Jones,Behzad Khajavi,Ishir Dutta,Jon J Zeosky

doi:10.1038/s41598-017-13199-1

Abstract

The polarization of light can exhibit unusual features when singular optical beams are involved. In 3-dimensional polarized random media the polarization orientation around singularities describe 1/2 or 3/2 Möbius strips. It has been predicted that if singular beams intersect non-collinearly in free space, the polarization ellipse rotates forming many-turn Möbius strips or twisted ribbons along closed loops around a central singularity. These polarization features are important because polarization is an aspect of light that mediate strong interactions with matter, with potential for new applications. We examined the non-collinear superposition of two unfocused paraxial light beams when one of them carried an optical vortex and the other one a uniform phase front, both in orthogonal states of circular polarization. It is known that these superpositions in 2-dimensions produce space-variant patterns of polarization. Relying on the symmetry of the problem, we extracted the 3-dimensional patterns from projective measurements, and confirmed the formation of many-turn Möbius strips or twisted ribbons when the topological charge of one of the component beams was odd or even, respectively. The measurements agree well with the modelings and confirmed that these types of patterns occur at macroscopic length scales and in ordinary superposition situations.

Highlights

Electromagnetic waves can produce in 3-dimensions (3-d) unusual patterns of fields that are not immediately obvious
A more recent prediction claimed that singular optical beams would produce 3-d fields that describe many-turn Möbius strips at macroscopic length scales in the intersection of paraxial beams
The largest angle θ that we investigated was of about one degree, which involved about 7 camera pixels from fringe to fringe, yielding a Möbius strip with about 161.5 turns for a circular path with r w

Summary

Introduction

Electromagnetic waves can produce in 3-dimensions (3-d) unusual patterns of fields that are not immediately obvious. Freund proposed that electromagnetic fields involving randomly-polarized fields contain unique features: the polarization ellipse describes Möbius strips of either 1/2 or 3/2 turns along closed paths surrounding a singular point[20,21,22]. These features have been confirmed analytically by independent analysis[23]. A more recent prediction claimed that singular optical beams would produce 3-d fields that describe many-turn Möbius strips at macroscopic length scales in the intersection of paraxial beams These patterns would appear along a macroscopic closed path about the singular point[26,27]. Using this method we were able to successfully reconstruct the 3-d orientations of the polarization ellipse, as shown below

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Results

Conclusion