Fractality of Light’s Darkness

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

doi:10.1103/physrevlett.100.053902

Cited by 92 publications

(95 citation statements)

References 29 publications

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“…The best known example of this is laser speckle, observed whenever an expanded laser beam is scattered from a rough surface; each of the observed dark specks is, in fact, a phase singularity [31]. 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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Section: Orbital Angular Momentum and Phase Singularitiesmentioning

confidence: 99%

Orbital angular momentum: origins, behavior and applications

Yao

Padgett²

2011

Adv. Opt. Photon.

Self Cite

2,801

1,573

View full text Add to dashboard Cite

show abstract

“…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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“…We then introduce a specific and a general solution, which is more useful in the context of the practical electron vortex beams which are usually generated under bandwidthlimited conditions. In general, the vortex lines can be curved, closed and knotted (O'Holleran et al, 2008), but they can be regarded as a superposition of the simpler straight vortex lines introduced below.…”

Section: B Vortex Beam Solutions Of the Schrödinger Equationmentioning

confidence: 99%

Electron vortices: Beams with orbital angular momentum

et al. 2017

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The recent prediction and subsequent creation of electron vortex beams in a number of laboratories occurred after almost 20 years had elapsed since the recognition of the physical significance and potential for applications of the orbital angular momentum carried by optical vortex beams. A rapid growth in interest in electron vortex beams followed, with swift theoretical and experimental developments. Much of the rapid progress can be attributed in part to the clear similarities between electron optics and photonics arising from the functional equivalence between the Helmholtz equations governing the free space propagation of optical beams and the time-independent Schrödinger equation governing freely propagating electron vortex beams. There are, however, key di↵erences in the properties of the two kinds of vortex beams. This review is concerned primarily with the electron type, with specific emphasis on the distinguishing vortex features: notably the spin, electric charge, current and magnetic moment, the spatial distribution as well as the associated electric and magnetic fields. The physical consequences and potential applications of such properties are pointed out and analysed, including nanoparticle manipulation and the mechanisms of orbital angular momentum transfer in the electron vortex interaction with matter.

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Fractality of Light’s Darkness

Cited by 92 publications

References 29 publications

Orbital angular momentum: origins, behavior and applications

Orbital angular momentum: origins, behavior and applications

Universal statistics of vortex lines

Electron vortices: Beams with orbital angular momentum

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