Singular knot bundle in light

Abstract

As the size of an optical vortex knot, imprinted in a coherent light beam, is decreased, nonparaxial effects alter the structure of the knotted optical singularity. For knot structures approaching the scale of wavelength, longitudinal polarization effects become non-negligible and the electric and magnetic fields differ, leading to intertwined knotted nodal structures in the transverse and longitudinal polarization components which we call a knot bundle of polarization singularities. We analyze their structure using polynomial beam approximations, and numerical diffraction theory. The analysis reveals features of spin-orbit effects and polarization topology in tightly-focused geometry, and we propose an experiment to measure this phenomenon.

Optical framed knots as information carriers

“…Furthermore, non-paraxial methods would enable the generation of knots with a more manageable longitudinal extent. Indeed, a wealth of structures, including the trefoil and cinquefoil knots investigated here, are predicted to form over a distance comparable to the optical field's wavelength 34 .…”

Interference and polarization beating of independent arbitrarily polarized polychromatic optical waves

“…This fact can be used to extract additional information about the field source and propagation medium. Furthermore, significant progress has been recently achieved in structuring the polarization state of optical beams [15][16][17][18][19]. As an example, it has been shown that interference of an optical wave * andriy.shevchenko@aalto.fi with its orthogonally polarized frequency-shifted copy, such as its second harmonic, can result in complex polarization Lissajous curves instead of polarization ellipses and form optical beams with fractional-order angular momenta [15].…”

“…As an example, it has been shown that interference of an optical wave * andriy.shevchenko@aalto.fi with its orthogonally polarized frequency-shifted copy, such as its second harmonic, can result in complex polarization Lissajous curves instead of polarization ellipses and form optical beams with fractional-order angular momenta [15]. Such beams, as well as other optical fields with designed twoand three-dimensional polarization profiles [16][17][18][19], can show a variety of new spatially distributed dynamic polarization and interference effects.…”

Tying Polarization‐Switchable Optical Vortex Knots and Links via Holographic All‐Dielectric Metasurfaces

“…However, in order to make the polynomial beams physically realizable, the polynomial is multiplied by a Gaussian amplitude function with width w. Therefore, the topological configuration is closely related to w. With the decrease of w, this gap gradually disappears and the vorticity lines just reconnect into knot or link at the plane of z→± ∞, likewise, the isolated topological structure disappears. [15] This means that the size of topological configuration is dependent on the balance of coefficient parameters and w. As a result, the topological configurations here have transversal size about 220 µm, nevertheless, their longitudinal sizes are far greater than the transversal one, which is adverse for further creating smaller topological structures.…”

“…Since the orbital angular momentum associated with the spiral phase of Laguerre-Gaussian (LG) beams was demonstrated by Allen et al in 1992, [1] the light fields that contain phase singularities have been extensively investigated and applied to various realms, including optical imaging, [2,3] particle manipulation, [4][5][6] optical information storage, communication, and so on. [7][8][9][10][11] Recently, a new family of null solutions to Maxwell's equations in 3D, whose vorticity line (connected phase singularities in 3D space) is connected as isolated loop in the forms of knots and links, [12][13][14][15] has been reported and attracted increasing interest, because of its nontrivial spatial feature. On the other hand, after the theoretical proposal of Lord Kelvin, [16] the knots and links were conjectured to play a fundamental role in a wide range of Dr. X. Guo, Prof. P. Li physical branches such as spanning plasma, [17] quantum field theory, [18,19] classical fluid dynamics, [20][21][22] and liquid crystals.…”