Topology of Light’s Darkness

O’Holleran, Kevin; Dennis, Mark R.; Padgett, Miles J.

doi:10.1103/physrevlett.102.143902

Cited by 66 publications

(56 citation statements)

References 19 publications

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“…Universal aspects of vortex statistics have been examined numerically in a wide range of contexts, including cosmic strings, beginning with the simulations of Vachaspati and Vilenkin [7,8,10,[13][14][15], line defects in random light fields, known as 'optical vortices' [9,16], vortices in the XY [17,18] and Abelian Higgs models [19][20][21][22], in turbulent superfluids [23], and in a Potts-like model introduced to describe polymers [6]. In addition, similar scaling behaviour has been observed in simulations of lattice models of completely-packed loops [24,25].…”

Section: Introductionmentioning

confidence: 99%

Universal statistics of vortex lines

Nahum

Chalker

2012

Phys. Rev. E

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We study the vortex lines that are a feature of many random or disordered three-dimensional systems. These show universal statistical properties on long length scales, and geometrical phase transitions analogous to percolation transitions but in distinct universality classes. The field theories for these problems have not previously been identified, so that while many numerical studies have been performed, a framework for interpreting the results has been lacking. We provide such a framework with mappings to simple supersymmetric models. Our main focus is on vortices in shortrange correlated complex fields, which show a geometrical phase transition that we argue is described by the CP k|k model (essentially the CP n−1 model in the replica limit n → 1). This can be seen by mapping a lattice version of the problem to a lattice gauge theory. A related field theory with a noncompact gauge field, the 'N CCP k|k model', is a supersymmetric extension of the standard dual theory for the XY transition, and we show that XY duality gives another way to understand the appearance of field theories of this type. The supersymmetric descriptions yield results relevant, for example, to vortices in the XY model and in superfluids, to optical vortices, and to certain models of cosmic strings. A distinct but related field theory, the RP 2l|2l model (or the RP n−1 model in the limit n → 1) describes the unoriented vortices which occur for instance in nematic liquid crystals. Finally, we show that in two dimensions, a lattice gauge theory analogous to that discussed in three dimensions gives a simple way to see the known relation between two-dimensional percolation and the CP k|k sigma model with a θ term.

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Section: Introductionmentioning

confidence: 99%

Universal statistics of vortex lines

Nahum

Chalker

2012

Phys. Rev. E

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“…In three dimensions these vortex lines map out complex paths that are fractal in nature [32] and even form complicated topological features like loops and knots as shown in Fig. 4 [33,34].…”

Section: Orbital Angular Momentum and Phase Singularitiesmentioning

confidence: 99%

Orbital angular momentum: origins, behavior and applications

Yao

Padgett²

2011

Adv. Opt. Photon.

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2,801

1,573

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As they travel through space, some light beams rotate. Such light beams have angular momentum. There are two particularly important ways in which a light beam can rotate: if every polarization vector rotates, the light has spin; if the phase structure rotates, the light has orbital angular momentum (OAM), which can be many times greater than the spin. Only in the past 20 years has it been realized that beams carrying OAM, which have an optical vortex along the axis, can be easily made in the laboratory. These light beams are able to spin microscopic objects, give rise to rotational frequency shifts, create new forms of imaging systems, and behave within nonlinear material to give new insights into quantum optics

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“…A variety of knotted and linked optical vortices can be synthesized with tailored superpositions of free-space modes2831, successfully implemented in experiments with Gaussian laser beams controlled by holograms293031. However, knot topology appears rare if these superpositions are not chosen carefully3637. A similar approach to the construction of knotted optical fields2831 was employed for vortex knots in BECs22.…”

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confidence: 99%

Spontaneous knotting of self-trapped waves

Desyatnikov

Buccoliero

Dennis

et al. 2012

Sci Rep

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We describe theory and simulations of a spinning optical soliton whose propagation spontaneously excites knotted and linked optical vortices. The nonlinear phase of the self-trapped light beam breaks the wave front into a sequence of optical vortex loops around the soliton, which, through the soliton's orbital angular momentum and spatial twist, tangle on propagation to form links and knots. We anticipate similar spontaneous knot topology to be a universal feature of waves whose phase front is twisted and nonlinearly modulated, including superfluids and trapped matter waves.

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Topology of Light’s Darkness

Cited by 66 publications

References 19 publications

Universal statistics of vortex lines

Universal statistics of vortex lines

Orbital angular momentum: origins, behavior and applications

Spontaneous knotting of self-trapped waves

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