Spin-Orbital Conversion of a Strongly Focused Light Wave with High-Order Cylindrical-Circular Polarization.

Victor V Kotlyar,Anton G Nalimov,Sergey S Stafeev,Elena S Kozlova

doi:10.3390/s21196424

Victor V Kotlyar, Anton G Nalimov + Show 2 more

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https://doi.org/10.3390/s21196424

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Abstract

We discuss interesting effects that occur when strongly focusing light with mth-order cylindrical–circular polarization. This type of hybrid polarization combines properties of the mth-order cylindrical polarization and circular polarization. Reluing on the Richards-Wolf formalism, we deduce analytical expressions that describe E- and H-vector components, intensity patterns, and projections of the Poynting vector and spin angular momentum (SAM) vector at the strong focus. The intensity of light in the strong focus is theoretically and numerically shown to have an even number of local maxima located along a closed contour centered at an on-axis point of zero intensity. We show that light generates 4m vortices of a transverse energy flow, with their centers located between the local intensity maxima. The transverse energy flow is also shown to change its handedness an even number of times proportional to the order of the optical vortex via a full circle around the optical axis. It is interesting that the longitudinal SAM projection changes its sign at the focus 4m times. The longitudinal SAM component is found to be positive, and the polarization vector is shown to rotate anticlockwise in the focal spot regions where the transverse energy flow rotates anticlockwise, and vice versa—the longitudinal SAM component is negative and the polarization vector rotates clockwise in the focal spot regions where the transverse energy flow rotates clockwise. This spatial separation at the focus of left and right circularly polarized light is a manifestation of the optical spin Hall effect. The results obtained in terms of controlling the intensity maxima allow the transverse mode analysis of laser beams in sensorial applications. For a demonstration of the proposed application, the metalens is calculated, which can be a prototype for an optical microsensor based on sharp focusing for measuring roughness.

Highlights

The rigorous description of a linearly polarized electromagnetic field at the strong focus was proposed in a classical work by Richards and Wolf [1]
Numerous follow-up publications relied on the Richards–Wolf formalism to look into the behavior of more general electromagnetic fields with various polarization states
We experimentally demonstrate the possibility of generating a second-order hybrid beam with a vortex half-wave plate

Summary

Introduction

The rigorous description of a linearly polarized electromagnetic field at the strong focus was proposed in a classical work by Richards and Wolf [1]. Studies of the focusing of promising beams with hybrid polarization have been conducted [15,16,17,18,19] For this type of polarization, the transposed Jones vector takes the form E = (exp(iδ), exp(−iδ)), where δ = αr + β, r is a radial variable, α, β are constant, and E is the initial light field. This type of hybrid polarization is linear along some radii and circular on the others, while being independent of the polar angle φ.

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