Polychromatic electric field knots

Manuel F Ferrer-Garcia,Alessio D'Errico,Ebrahim Karimi,Alicia Sit,Hugo Larocque

doi:10.1103/physrevresearch.3.033226

Manuel F Ferrer-Garcia, Alessio D'Errico + Show 3 more

Open Access

https://doi.org/10.1103/physrevresearch.3.033226

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Abstract

The polarization of a monochromatic optical beam lies in a plane, and in general, is described by an ellipse, known as the polarization ellipse. The polarization ellipse in the tight focusing (non-paraxial) regime forms non-trivial three-dimensional topologies, such as M\"obius and ribbon strips, as well as knots. The latter is formed when the dynamics of specific polarization states, e.g., circular polarization states, are studied upon propagation. However, there is an alternative method to generate optical knots: the electric field's tip can be made to evolve along a knot trajectory in time locally. We propose an intuitive technique to generate and engineer the path traced by the electric field vector of polychromatic beams to form different knots. In particular, we show examples of how tightly focused beams with at least three frequency components and different spatial modes can cause the tip of the electric field vector to follow, locally, a knotted trajectory. Furthermore, we characterize the generated knots and explore different knot densities upon free-space propagation in the focal volume. Our study may provide insight for designing current densities when structured polychromatic electromagnetic fields interact with materials.

Highlights

The rapid advancements in the manipulation and control of electromagnetic radiation have allowed researchers to explore solutions of Maxwell’s equations possessing rich topological features
Beams carrying a nonzero value of orbital angular momentum (OAM) [4] became of interest in many applications of classical and quantum optics
Optical beams with well-engineered spectra, polarization, and spatial and temporal structures are nowadays widely used in optical manipulation [5], microscopy [6,7,8], surface and material structuring [9], and classical and quantum communication [10,11]

Summary

INTRODUCTION

The rapid advancements in the manipulation and control of electromagnetic radiation have allowed researchers to explore solutions of Maxwell’s equations possessing rich topological features. More complicated structures can be observed by analyzing an optical beam whose properties are not entirely defined within a two-dimensional plane, but within a three-dimensional volume It is, predicted that the free-space trajectories of field dislocations can form closed loops [12,13] with nontrivial topologies, e.g., links and knots [14]. While in the monochromatic case the electric field vector describes an ellipse, more complicated curves occur when multiple waves with different temporal frequencies are superimposed This new “zoo” of polarization states, as mentioned before, remains almost unexplored; the only accurately described cases are the ones in which two fields oscillate in the same plane. A general scheme has been proposed in which three-dimensional superpositions of plane waves with different frequencies can create an electric field wherein its tip locally traces a knotted curve [28]. We localize and identify the knotted trajectories in different planes in the focal volume

KNOTTED POLARIZATION CURVES

KNOTTING LIGHT BY TIGHT-FOCUSING STRUCTURED POLYCHROMATIC LIGHT

RESULTS AND DISCUSSION