Multi-twist polarization ribbon topologies in highly-confined optical fields

Thomas Bauer,Lorenzo Marrucci,Gerd Leuchs,Robert W Boyd,Frédéric Bouchard,Ebrahim Karimi,Peter Banzer,Enrico Santamato,Sergej Orlov

doi:10.1088/1367-2630/ab171b

Abstract

Electromagnetic plane waves, solutions to Maxwell’s equations, are said to be ‘transverse’ in vacuum. Namely, the waves’ oscillatory electric and magnetic fields are confined within a plane transverse to the waves’ propagation direction. Under tight-focusing conditions however, the field can exhibit longitudinal electric or magnetic components, transverse spin angular momentum, or non-trivial topologies such as Möbius strips. Here, we show that when a suitably spatially structured beam is tightly focused, a three-dimensional polarization topology in the form of a ribbon with two full twists appears in the focal volume. We study experimentally the stability and dynamics of the observed polarization ribbon by exploring its topological structure for various radii upon focusing and for different propagation planes.

Highlights

Since the inception of electromagnetic theory, the polarization of light, i.e. the oscillation direction of the electric field vector, has been a central concept to our understanding of optics, giving rise to countless applications [1]
For plane waves and in paraxial beams, the polarization has been recognized as a transverse quantity and, it can be represented by a set of two orthogonal basis vectors
Spatially structured light fields with field components along the propagation direction were predicted by Freund to show so-called optical polarization Mobius strips and twisted ribbons [14, 15], with the former recently confirmed experimentally in tightly focused fields [16] as well as the originally proposed scheme of crossing beams [17]

Summary

Introduction

Since the inception of electromagnetic theory, the polarization of light, i.e. the oscillation direction of the electric field vector, has been a central concept to our understanding of optics, giving rise to countless applications [1]. The ratio and the relative phase between the two polarization components define the oscillations of the electric field vector’s tip upon propagation or in time, and its trajectory in the plane transverse to its propagation direction, typically given by an ellipse [1] This description of the light field by a socalled polarization ellipse at each point in space is even valid in highly confined fields exhibiting out-of-plane field components, as long as the field itself is monochromatic. This ellipse becomes singular [2, 3, 4]: (i) the ellipse’s major and minor axes are undefined, resulting in circular polarization (C-point); (ii) the minor axis of the ellipse is zero and its surface normal is undefined, and the polarization is linear (L-line) These so-called polarization singularities in general arise in light fields with spatially inhomogeneous polarization distributions, which we refer to as spacevarying polarized light beams. We will experimentally demonstrate the generation and stability of the latter in highly confined fields, looking at the dynamics of the twisted ribbon when propagating through the focal volume of a tailored spacevarying polarized light beam

Space-varying polarized beams under tight focusing

Experimental Realization

Conclusion