Spontaneous knotting of self-trapped waves

Desyatnikov, Anton S.; Buccoliero, Daniel; Dennis, Mark R.; Kivshar, Yuri S.

doi:10.1038/srep00771

Cited by 34 publications

(26 citation statements)

References 49 publications

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“…These two STOVs, whose axes are along y (perpendicular to page), immediately begin moving apart: one vortex advances in time towards the front of the pulse while the other vortex moves to the back. Similar dynamics are theorized to exist in monochromatic breather solitons, where ring-shaped vortices are formed quasiperiodically throughout propagation [23].…”

Section: Spatiotemporal Optical Vorticesmentioning

confidence: 58%

Spatiotemporal Optical Vortices

et al. 2016

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We present the first experimental evidence, supported by theory and simulation, of spatiotemporal optical vortices (STOVs). A STOV is an optical vortex with phase and energy circulation in a spatiotemporal plane. Depending on the sign of the material dispersion, the local electromagnetic energy flow is saddle or spiral about the STOV. STOVs are a fundamental element of the nonlinear collapse and subsequent propagation of short optical pulses in material media, and conserve topological charge, constraining their birth, evolution, and annihilation. We measure a self-generated STOV consisting of a ring-shaped null in the electromagnetic field about which the phase is spiral, forming a dynamic torus that is concentric with and tracks the propagating pulse. Our results, here obtained for optical pulse collapse and filamentation in air, are generalizable to a broad class of nonlinearly propagating waves.

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Section: Spatiotemporal Optical Vorticesmentioning

confidence: 58%

Spatiotemporal Optical Vortices

et al. 2016

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“…More generally, topological defects are singular points or lines in a distinct scalar, vector or tensor field that can be characterized by topological invariants, including winding number (or index) for two-dimensional, and topological charge for three-dimensional variations of the fields [6,7]. Topological defects have been long known to mediate key processes in a wide range of settings, including knotted flow field stream lines [8], defects in light fields [9], knotted defect lines in complex fluids [10], defects in Type-2 superconductors [11], spontaneous flow in active fluids [12][13][14][15], and even in conduction properties of electron nematics [16].…”

Section: Introductionmentioning

confidence: 99%

Cross-talk between topological defects in different fields revealed by nematic microfluidics

Giomi

Kos

Ravnik

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Topological defects are singularities in material fields that play a vital role across a range of systems: from cosmic microwave background polarization to superconductors and biological materials. Although topological defects and their mutual interactions have been extensively studied, little is known about the interplay between defects in different fields-especially when they coevolve-within the same physical system. Here, using nematic microfluidics, we study the cross-talk of topological defects in two different material fields-the velocity field and the molecular orientational field. Specifically, we generate hydrodynamic stagnation points of different topological charges at the center of starshaped microfluidic junctions, which then interact with emergent topological defects in the orientational field of the nematic director. We combine experiments and analytical and numerical calculations to show that a hydrodynamic singularity of a given topological charge can nucleate a nematic defect of equal topological charge and corroborate this by creating −1, −2, and −3 topological defects in four-, six-, and eight-arm junctions. Our work is an attempt toward understanding materials that are governed by distinctly multifield topology, where disparate topology-carrying fields are coupled and concertedly determine the material properties and response.multifield topology | nematic liquid crystals | topological defects | microfluidics | cross-interactions D efects are ubiquitous in nature and are at the heart of numerous physical mechanisms, including melting in 2D crystals (1), cosmic strings (2), and other topological defects in the early universe (3). Vortices are possibly the most common examples of defects in flowing media (4, 5). In a typical hydrodynamic vortex, the fluid velocity, v, rotates by 2π along any closed loop around the vortex core and has an undefined direction at the core. More generally, topological defects are singular points or lines in a distinct scalar, vector, or tensor field that can be characterized by topological invariants, including winding number (or index) for 2D, and topological charge for 3D variations of the fields (6, 7). Topological defects have been long known to mediate key processes in a wide range of settings, including knotted flow field stream lines (8), defects in light fields (9), knotted defect lines in complex fluids (10), defects in type 2 superconductors (11), spontaneous flow in active fluids (12-15), and even, conduction properties of electron nematics (16).The interaction between topological defects is governed by the defect topology and the underlying energetics. Similar to electrically charged particles, like-sign topological defects, in general, repel each other, whereas defects of opposite sign attract. However, this interaction can be additionally affected by the geometry and surface properties of the environment (17, 18) and the presence of an external stimulus (19-23). Emergence of topological defects in a field and the resulting interactions between them hav...

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“…Here, for simplicity, we don't take into account possible coupling between η 1 and η 2 (term proportional to the product η 1 η 2 ) that could result in orbital angular momentum of elliptical beam as has been shown [47][48][49].…”

Section: Models and Collective-variable Approachmentioning

confidence: 99%

Dependence of beating dynamics on the ellipticity of a Gaussian beam in graded-index absorbing nonlinear fibers

2013

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Using the collective variable approach technique, we analyze propagation of elliptical Gaussian beams in nonlinear waveguides with a parabolic graded-index (GRIN) profile. We considered both saturable and cubicquintic models to describe the nonlinearity, taking into account both linear and nonlinear absorption. For lossless media, we construct diagrams, which define regions of self-focusing and self-diffractive beam propagation for both models in GRIN waveguides and compare them with those for nongraded waveguides. The widths of the propagating elliptic beam exhibit an oscillatory pattern, similar to the "breathing" and "beating" behavior found in nongraded media. Two types of beating oscillations are observed in both models. We calculate the dependence of L beat /L br , the ratio of the "beating" to "breathing" oscillation periods, on the beam ellipticity ρ and the GRIN index g. We find that there is a remarkable difference in this dependence between saturable and cubic-quintic media: in the saturable model, L beat /L br is a monotonic function of ρ, whereas in the cubic-quintic model, it is characterized by singularities, which correspond to transitions between the types of beat oscillations. For lossy media, we discuss the difference between the breathing behavior in nongraded and GRIN waveguides.

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Spontaneous knotting of self-trapped waves

Cited by 34 publications

References 49 publications

Spatiotemporal Optical Vortices

Spatiotemporal Optical Vortices

Cross-talk between topological defects in different fields revealed by nematic microfluidics

Dependence of beating dynamics on the ellipticity of a Gaussian beam in graded-index absorbing nonlinear fibers

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