Nonlinear singular optics
01 Mar 1998-Pure and Applied Optics: Journal of The European Optical Society Part A (IOP Publishing)-Vol. 7, Iss: 2, pp 301-311
TL;DR: The physical background of singular optics dealing with phase singularities in light waves is reported as a new chapter in modern optics in this paper, and a review of the current status of nonlinear singular optics is presented.
Abstract: The physical background of singular optics dealing with phase singularities in light waves is reported as a new chapter in modern optics. A review of the current status of nonlinear singular optics is presented.
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TL;DR: In this paper, an isolated dark ring is created within a light beam, with an analytical description of the field, and a screw wave-front dislocation has a feature that the spatial structure of the wave front has the form of a helicoid around the dislocation axis.
Abstract: Singular optics is a branch of modern physical optics that involves a wide class of effects associated with the phase singularities in wave fields and with the topology of wave fronts. Optical singularities (optical vortices) exhibit some fundamental features absent in the "usual" fields with smooth wave fronts. Namely, optical vortices possess orbital angular momentum, topological charge for helical wave front of beams with well-defined direction of propagation. As a result, an interesting spatial evolution can be generated such as optical vortices "nucleation" and "annihilation" by pairs with participation of phase saddles, often called "optical chemistry." To study the structure of the circular edge dislocation, an isolated dark (zero-amplitude) ring is created within a light beam, with an analytical description of the field. A screw wave-front dislocation has a feature that the spatial structure of the wave front has the form of a helicoid around the dislocation axis. The chapter also describes reflection, refraction, interference and diffraction of OVs. Both frequency up- and down-conversion processes possess essential peculiarities for light beams with OVs. The chapter discusses the topology of wave fronts and vortex trajectories. Gouy phase shift in singular optics is also described in the chapter.
725 citations
381 citations
18 May 2006
TL;DR: In this paper, a liquid crystal is defined as a mixture of a liquid and a columnar phase, and the following properties of the liquid crystal: 1 1.1 What is a Liquid Crystal? 2 1.2 Cholesterics.
Abstract: 1 What is a liquid crystal 2 1.1 Nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Cholesterics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Smectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Columnar phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Lyotropic liquid crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
325 citations
Cites background from "Nonlinear singular optics"
...They exist almost in every branch of physics: biological systems [18], superfluid helium [19], ferromagnets [20], crystalline solids [21, 22], liquid crystals [23, 24, 25, 26, 27], quantum Hall fluids [28], and even optical fields [29] playing an important role in such phenomena as response to external stresses, the nature and type of phase transitions....
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TL;DR: In this article, a pedagogical overview of liquid crystals is presented based on lectures for postgraduate students given at the International Max Planck Research School "Modeling of Soft Matter".
227 citations
Cites background from "Nonlinear singular optics"
...They exist almost in every branch of physics: biological systems, superfluid helium, ferromagnets, crystalline solids, liquid crystals [64–67], quantum Hall fluids, and even optical fields [68], playing an important role in such phenomena as a response to external stresses and the nature and type of phase transitions....
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TL;DR: A brief overview of the major advances in the study of optical vortices in different types of nonlinear media, with emphasis on the properties of vortex solitons, can be found in this paper.
Abstract: Optical vortices are phase singularities nested in electromagnetic waves that constitute a fascinating source of phenomena in the physics of light and display deep similarities to their close relatives, quantized vortices in superfluids and Bose-Einstein condensates. We present a brief overview of the major advances in the study of optical vortices in different types of nonlinear media, with emphasis on the properties of {\em vortex solitons}. Self-focusing nonlinearity leads, in general, to the azimuthal instability of a vortex-carrying beam, but it can also support novel types of stable or meta-stable self-trapped beams carrying nonzero angular momentum, such as ring-like solitons, necklace beams, and soliton clusters. We describe vortex solitons created by multi-component beams, by parametrically coupled beams in quadratic nonlinear media, and in partially incoherent light, as well as discrete vortex solitons in periodic photonic lattices.
193 citations
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TL;DR: In this paper, it was shown that dislocations are to be expected whenever limited trains of waves, ultimately derived from the same oscillator, travel in different directions and interfere -for example in a scattering problem.
Abstract: When an ultrasonic pulse, containing, say, ten quasi-sinusoidal oscillations, is reflected in air from a rough surface, it is observed experimentally that the scattered wave train contains dislocations, which are closely analogous to those found in imperfect crystals. We show theoretically that such dislocations are to be expected whenever limited trains of waves, ultimately derived from the same oscillator, travel in different directions and interfere - for example in a scattering problem. Dispersion is not involved. Equations are given showing the detailed structure of edge, screw and mixed edge-screw dislocations, and also of parallel sets of such dislocations. Edge dislocations can glide relative to the wave train at any velocity; they can also climb, and screw dislocations can glide. Wavefront dislocations may be curved, and they may intersect; they may collide and rebound; they may annihilate each other or be created as loops or pairs. With dislocations in wave trains, unlike crystal dislocations, there is no breakdown of linearity near the centre. Mathematically they are lines along which the phase is indeterminate; this implies that the wave amplitude is zero.
1,984 citations
TL;DR: In this paper, a spiral phaseplate can convert a TEM00 laser beam into a helical wavefront beam with a phase singularity at its axis, and the diffractive-optical effect of the spiral phase plate is implemented by index matching a macroscopic structure in an optical immersion.
1,393 citations
TL;DR: In this paper, a mode converter based on the Gouy phase was proposed to transform a Hermite-gaussian mode of arbitrarily high order to a Laguerre-Gaussian mode and vice versa.
1,275 citations
TL;DR: In this article, the properties of light beams carrying phase singularities, or optical vortices, were studied both in theory and experiment, and the general rule for angular-momentum density distribution in a combined beam was established.
Abstract: We analyze the properties of light beams carrying phase singularities, or optical vortices. The transformations of topological charge during free-space propagation of a light wave, which is a combination of a Gaussian beam and a multiple charged optical vortex within a Gaussian envelope, are studied both in theory and experiment. We revise the existing knowledge about topological charge conservation, and demonstrate possible scenarios where additional vortices appear or annihilate during free propagation of such a combined beam. Coaxial interference of optical vortices is also analyzed, and the general rule for angular-momentum density distribution in a combined beam is established. We show that, in spite of any variation in the number of vortices in a combined beam, the total angular momentum is constant during the propagation.
491 citations
TL;DR: In this paper, the free space propagation of an array of optical vortices nested in a smooth (Gaussian) beam is studied in the paraxial regime, and it is shown that their relative positions, as well as their positions within the host beam are invariant upon propagation.
Abstract: Free space propagation of an array of optical vortices nested in a smooth (Gaussian) beam is studied in the paraxial regime. It is found that when the vortices have all the same charge, their relative positions, as well as their positions within the host beam are invariant upon propagation. The array simply expands or contracts with the host beam and rotates rigidly. Vortices of opposite charges, in contrast, attract each other. Pairs can collide and annihilate. As an illustration, numerical simulation is used to compare the propagation of a pair of vortices of equal charges with that of a pair of opposite charges.
410 citations