Topology of optical vortex lines formed by the interference of three, four, and five plane waves

Spatiotemporal optical vortex reconnections of multi-vortices

Vortex reconnections are ubiquitous events found in diverse media. Here we show that vortex reconnections also occur between spatiotemporal vortices in optical waves. Since vortices exhibit orbital angular momentum (OAM), the reconnections of optical vortices create a variety of connected OAM states. Dispersion and diffraction can cause different reconnection pairs, depending on the orientation of the vortices. The transverse crossing of two vortices with a topological charge of one can produce unique vortex loop reconnection patterns. Higher topological charges result in arrays of vortex loops and connection points. Crossing of three vortices produces spherical structures made of three symmetrical vortex arms. A three vortices reconnection with higher topological charges develops complicated patterns similar to turbulence cascade phenomena in other media. Studying optical vortex interactions may bring insight into vortex reconnections in other fields. We also provide experimental results of two-vortex loop interaction.

Transversal optical singularity induced precision measurement of step-nanostructures

Optical singularities indicate zero-intensity points in space where parameters, such as phase, polarization, are undetermined. Vortex beams such as the Laguerre-Gaussian modes are characterized by a phase factor eilθ, and contain a phase singularity in the middle of its beam. In the case of a transversal optical singularity (TOS), it occurs perpendicular to the propagation, and its phase integral is 2π in nature. Since it emerges within a nano-size range, one expects that TOSs could be sensitive in the light-matter interaction process and could provide a great possibility for accurate determination of certain parameters of nanostructure. Here, we propose to use TOSs generated by a three-wave interference to illuminate a step nanostructure. After interaction with the nanostructure, the TOS is scattered into the far field. The scattering direction can have a relation with the physical parameters of the nanostructure. We show that by monitoring the spatial coordinates of the scattered TOS, its propagation direction can be determined, and as consequence, certain physical parameters of the step nanostructure can be retrieved with high precision.

The singularities of light: intensity, phase, polarisation

In modern optics, light can be described at different levels: as rays, as scalar waves, as vector fields, and as quantum fields. In the first three levels, there are singularities-characteristic features, useful in interpreting phenomena at that level. In geometrical optics, the singularities are ray caustics; in scalar wave optics, they are phase singularities (=wave dislocations= wave vortices = nodal manifolds); in vector waves, they are singularities where the polarisation of light is purely linear or purely circular. The singularities at each level are dissolved at the next level. Similar singularities occur in all waves, not just light.

Vortex array generation based on quasi-Talbot effects

A lens-less method for generating vortex arrays with tunable parameters is proposed based on quasi-Talbot effects. By illuminating a two-dimensional periodic sinusoidal grating with a vortex beam carrying a fourth-order cross-phase, the continuous vortex array structure can be generated in the Fresnel diffraction region. Due to the shaping effect of the fourth-order cross-phase on the vortex beam, by changing the constant parameter of the fourth-order cross-phase, it is possible to shape the generation of optical vortex arrays at different positions. This will somewhat broaden the flexibility of the lens-free optical vortex array in terms of generation position. In addition, the generation of polygonal optical vortex arrays is achieved by higher-order cross-phases of different orders. This technique has potential applications in various fields such as optical tweezers, multi-particle screening, microscopic manipulation, etc.

Generation of optical vortex lattices by in-line phase modulation with partially coherent light

Of late, generation of different kinds of optical vortex lattices has been gaining much attention due to various applications. Several methods have been reported for the generation of optical vortex lattices using a coherent light source involving interferometric, diffractive, and pinhole phase plate methods. Owing to cost effectiveness and ease in optical implementation, these days use of incoherent or partially coherent light beams is becoming popular. In this study, we demonstrate generation of different kinds of optical vortex lattices through in-line modulation of phase distributions employing the phase concatenation approach and a light-emitting diode as a light source. It is a non-interferometric and flexible technique for the selection of the parameters that characterize the optical vortices and their arrays. The proposed method allows generation of an array of optical vortices of different topological charges with zero and non-zero radial indices having different symmetries.

A Third Angular Momentum of Photons

Photons that acquire orbital angular momentum move in a helical path and are observed as a light ring. During helical motion, if a force is applied perpendicular to the direction of motion, an additional radial angular momentum is introduced, and alternate dark spots appear on the light ring. Here, a third, centrifugal angular momentum has been added by twisting the helical path further according to the three-step hierarchical assembly of helical organic nanowires. Attaining a third angular momentum is the theoretical limit for a photon. The additional angular momentum converts the dimensionless photon to a hollow spherical photon condensate with interactive dark regions. A stream of these photon condensates can interfere like a wave or disintegrate like matter, similar to the behavior of electrons.

Theoretical study on the diffraction-based generation of a 2D orthogonal lattice of optical beams: physical bases and application for a vortex beam multiplication

A comprehensive theoretical study on the generation of a 2D orthogonal lattice of optical beams based on the near-field diffraction and Talbot effect is presented. First we investigate the near-field diffraction of an optical beam with a finite lateral extension from an infinite 2D orthogonal grating. It is shown that the resulting diffraction patterns over the Talbot planes depend on the following parameters: the period and opening ratio (OR) of the grating, wavelength and spatial spectral bandwidth of the incident beam, and the propagation distance. In terms of these parameters, we find multiplication conditions: the certain conditions under which a 2D orthogonal lattice of the Fourier transform of the incident beam is generated on the Talbot planes. Therefore, if the incident beam is Fourier-invariant and all the established multiplication conditions are fulfilled, the intensity profile of each of the individual Talbot images resembles the intensity profile of the incident beam. We consider the Laguerre-Gaussian beams having zero radial index as an important class of the vortex beams. We explicitly show that these beams are Fourier-invariant and we calculate their spatial spectral bandwidth. As a result, in the illumination of a 2D orthogonal binary grating with this kind of vortex beam, a 2D orthogonal lattice of the incident optical vortex is generated at the Talbot planes. Considering the obtained multiplication conditions, for the first time, to our knowledge, we determine a multiplication interval. This interval covers the propagation distances at which the vortex beam multiplication occurs. Moreover, we obtain the maximum possible value of the grating's OR for the realizations of the vortex multiplication. It is shown that both the multiplication interval and the maximum value of the OR depend on the topological charge (TC) of the incident beam. With the aid of some practical examples and defining a multiplication quality factor, the mentioned results are verified quantitatively. In addition to the vortex beam multiplication effect, we consider another interesting phenomenon that results from the interference of the grating's first diffraction orders. We call this phenomenon the first diffraction orders interference (FDOI) effect. We show that both the multiplication and the FDOI effects occur simultaneously but at different propagation distances. It is also shown that the multiplication and FDOI intervals separate and distance from each other by increasing the TC of the incident beam.

Topological constant-intensity waves

Topological constant-intensity (TCI) waves are introduced in the context of non-Hermitian photonics. Unlike other known examples of topological defects, the proposed TCI waves exhibit a counterintuitive behavior because a phase difference occurs across space without any accompanying intensity variations. Such solutions exist only on non-Hermitian systems, because the associated nonzero phase difference is directly related to the real and imaginary parts of the potential. The free space diffraction and the existence of such waves in two spatial dimensions are also discussed in detail.

Shaping the topology of light with a moving Rabi-oscillating vortex

Quantum vortices are the analogue of classical vortices in optics, Bose-Einstein condensates, superfluids and superconductors, where they provide the elementary mode of rotation and orbital angular momentum. While they mediate important pair interactions and phase transitions in nonlinear fluids, their linear dynamics is useful for the shaping of complex light, as well as for topological entities in multi-component systems, such as full Bloch beams. Here, setting a quantum vortex into directional motion in an open-dissipative fluid of microcavity polaritons, we observe the self-splitting of the packet, leading to the trembling movement of its center of mass, whereas the vortex core undergoes ultrafast spiraling along diverging and converging circles, in a sub-picosecond precessing fashion. This singular dynamics is accompanied by vortex-antivortex pair creation and annihilation and a periodically changing topological charge. The spiraling and branching mechanics represent a direct manifestation of the underlying Bloch pseudospin space, whose mapping is shown to be rotating and splitting itself. Its reshaping is due to three simultaneous drives along the distinct directions of momentum and complex frequency, by means of the differential group velocities, Rabi frequency and dissipation rates, which are natural assets in coupled fields such as polaritons. This state, displaying linear momentum dressed with oscillating angular momentum, confirms the richness of multi-component and open quantum fluids and their innate potentiality to implement sophisticated and dynamical topological textures of light.

Generation of an asymmetric optical vortex array with tunable singularity distribution

Light beams with multiple phase singularities, namely, optical vortex arrays (OVAs), can be generated via coherent superpositions of symmetric laser modes, e.g., the combination of a circular vortex beam and a Gaussian beam. Further, a non-trivial evolution of the singularity structure can be obtained when the system's symmetry is broken. In this paper, we propose an asymmetric OVA (AOVA) with a highly tunable structure. The AOVA is generated by the coaxial superposition of a vortex beam and an elliptical Gaussian beam in the waist plane. After the interference of the two beams, the original high-order phase singularity residing on the beam axis breaks up into multiple +1 and -1 order vortices. The vortices are located at discrete azimuthal angles and different distances from the beam center. Unlike previous OVAs with annular shapes, the AOVA can present various singularity structures devoid of rotational symmetry, which are decided by the radii of the elliptical Gaussian beam and the topological charge of the vortex beam. Furthermore, we theoretically show that the number, sign, and distribution of local singularities can be modulated by defining two azimuthal discriminant functions. Numerical simulations and visualizations are also carried out. This work provides a new perspective for designs of connected OVAs and may find potential applications, especially in particle manipulation, optical communication, and optical metrology.

Anomalous ring-connected optical vortex array

In this study, an anomalous ring-connected optical vortex array (ARC-OVA) via the superposition of two grafted optical vortices (GOVs) with different topological charges (TCs) has been proposed. Compared with conventional OVAs, the signs and distribution of the OVs can be individually modulated, while the number of OVs remains unchanged. In particular, the positive and negative OVs simultaneously appear in the same intensity ring. Additionally, the size of the dark core occupied by the OV can be modulated, and the specific dark core is shared by a pair of plus-minus OVs. This work deepens our knowledge about connected OVAs and facilitates new potential applications, especially in particle manipulation and optical measurement.

Accurate and rapid measurement of optical vortex links and knots

Optical vortices can evolve in light fields, of which the singularity evolution forms dark lines with complex topological structures, knotted or linked. We propose a method to more accurately and rapidly measure the topology of optical vortex fields. To accurately locate the phase singular points, phase measurement based on digital holography and, further, a numerical search algorithm, are utilized. A motor-driven right-angle prism enables the implementation of a single exposure of hologram for each measurement along the propagation direction, greatly improving the measurement speed. The three-dimensional (3D) spatial distributions of several typical vortex links and knots are experimentally reconstructed. The proposed method is expected to rapidly observe the 3D evolution of other complicated, or even vector, fields.

Characterizing vortex beams from a spatial light modulator with collinear phase-shifting holography

We demonstrate collinear phase-shifting holography for measuring complex optical modes of twisted light beams with orbital angular momentum (OAM) generated by passing a laser through a spatial light modulator (SLM). This technique measures the mode along the direction of propagation from the SLM and requires no additional optics, so it can be used to aid alignment of the SLM, to efficiently check for the effects of beam wander, and to fully characterize generated beams before use in other experiments. Optimized error analysis and careful SLM alignment allow us to generate and measure OAM with purity as high as 99.9%.

Close-packed optical vortex lattices with controllable structures

As a spatial structured light field, the optical vortex (OV) has attracted extensive attention in recent years. In practice, the OV lattice (OVL) is an optimal candidate for applications of orbital angular momentum (OAM)-based optical communications, microparticle manipulation, and micro/nanofabrication. However, traditional methods for producing OVLs meet a significant challenge: the OVL structures cannot be adjusted freely and form a close-packed arrangement, simultaneously. To overcome these difficulties, we propose an alternative scheme to produce close-packed OVLs (CPOVLs) with controllable structures. By borrowing the concept of the close-packed lattice from solid-state physics, CPOVLs with versatile structures are produced by using logical operations of expanding OV primitive cells combined with the technique of phase mask generation. Then, the existence of OAM states in the CPOVLs is verified. Furthermore, the energy flow and OAM distribution of the CPOVLs are visualized and analyzed. From a light field physics viewpoint, this work increases the adjustment dimensions and extends the fundamental understanding of the OVL, which will introduce novel applications.

Chip-scale optical vortex lattice generator on a silicon platform

An optical vortex (OV) with an isolated field singularity has been extensively studied in a variety of fields. An OV lattice with a network of optical vortices may find more advanced applications in widespread areas such as optical metrology, optical manipulation, and quantum processing. An OV lattice generated by traditional approaches relies on a number of bulky diffractive optical elements with large volumes and long working distances. Here we present a simple and compact on-chip OV lattice emitter on silicon photonics platforms. The principle relies on three-plane-wave interference. We design, fabricate, and demonstrate an on-chip OV lattice emitter consisting of three parallel waveguides with etched tilt gratings. The tilt gratings facilitate flexible light emission in a wide range of directions, enabling the generation of an OV lattice above the silicon chip. The demonstrated on-chip OV lattice emitter may open a door to generate, manipulate, and detect an OV lattice using photonic integrated circuits.

Orbital angular momentum 25 years on [Invited]

Twenty-five years ago Allen, Beijersbergen, Spreeuw, and Woerdman published their seminal paper establishing that light beams with helical phase-fronts carried an orbital angular momentum. Previously orbital angular momentum had been associated only with high-order atomic/molecular transitions and hence considered to be a rare occurrence. The realization that every photon in a laser beam could carry an orbital angular momentum that was in excess of the angular momentum associated with photon spin has led both to new understandings of optical effects and various applications. These applications range from optical manipulation, imaging and quantum optics, to optical communications. This brief review will examine some of the research in the field to date and consider what future directions might hold.

Singularimetry of local phase gradients using vortex lattices and in-line holography

We have developed a differential form of singularimetry, which utilizes phase vortices or intensity gradient singularities as topological fiducial markers in a structured illumination context. This approach analytically measures phase gradients imparted by refracting specimens, yielding quantitative information that is both local and deterministic. We have quantified our phase gradient experiments to demonstrate that lattices of wave field singularities can be used to detect subtle phase gradients imparted by a spherical specimen and fiber optic cylinders.

Singular optical lattice generation using light beams with orbital angular momentum

In this Letter we numerically and experimentally demonstrated that a lattice with an optical vortex distributed over the entire lattice can be generated in the Fourier space using three higher-order Laguerre-Gauss beams placed at the vertices of an equilateral triangle in real space. In this scheme the optical vortice's lattice presents a topological defect in its central region. Probing the net topological charge of the whole lattice, we found that it corresponds to the topological charge associated with the orbital angular momentum of each beam in real space.

Light's twist

That light travels in straight lines is a statement of the obvious. However, the energy and momentum flow within light beams can twist to form vortices such as eddies in a stream. These twists carry angular momentum, which can make microscopic objects spin, be used to encode extra information in communication systems, enable the design of novel imaging systems and allow new tests of quantum mechanics.

Generation of second-order vortex arrays with six-pinhole interferometers under plane wave illumination

We propose a method based on six-pinhole interferometers to generate vortex arrays with topological charge 2, only with plane wave illumination. The six-pinhole interferometer is composed of two concentric symmetrical three-pinhole interferometers with different radial distances of the pinholes and a relative rotation of 60 deg from each other. In the Fourier domain, the vortices with second-order topological charge are generated when the radial distances of the two three-pinhole interferometers satisfy some certain ratios. Due to the symmetry of the six-pinhole interferometer, such vortices are distributed at the vertices of some symmetrically distributed regular hexagons. The experimental results obtained in a focal-to-focal system show satisfactory coincidence with the calculations.

Transport of intensity phase retrieval of arbitrary wave fields including vortices

The phase problem can be considered as one of the cornerstones of quantum mechanics intimately connected to the detection process and the uncertainty relation. The latter impose fundamental limits on the manifold phase reconstruction schemes invented to date, in particular, at small magnitudes of the quantum wave. Here, we show that a rigorous solution of the transport of intensity reconstruction (TIE) scheme in terms of a linear elliptic partial differential equation for the phase provides reconstructions even in the presence of wave zeros if particular boundary conditions are given. We furthermore discuss how partial coherence hampers phase reconstruction and show that a modified version of the TIE reconstructs the curl-free current density at arbitrary (in)coherence. Our results open the way for TIE-based phase retrieval of arbitrary wave fields, eventually containing zeros such as phase vortices.

Formation of optical vortices through superposition of two Gaussian beams

We observe phase singularities in the superposed field of two Gaussian beams. It is seen that the formation of these singularities depends on the tilt between two Gaussian beams and the separation of their beam axes. By reversing the angle or the position of the beams, one can change the sign of the vortex. We have shown the formation of single as well as multiple vortices by changing the tilt angle and the position of two Gaussian beams. The experimental results are verified with theoretical analysis. We also observe that such a vortex structure can be formed through superposition of two backreflected Gaussian beams from any optical element with two flat surfaces, as illustrated through a beam splitter and a neutral density filter. This technique is very useful for generation of vortices with high-power lasers where one cannot use a spatial light modulator.

Microwave magnetoelectric fields and their role in the matter-field interaction

We show that in a source-free subwavelength region of microwave fields, there can exist field structures with a local coupling between the time-varying electric and magnetic fields differing from the electric-magnetic coupling in regular-propagating free-space electromagnetic waves. To distinguish such field structures from regular electromagnetic (EM) field structures, we term them as magnetoelectric (ME) fields. We study a structure and conservation laws of microwave ME near fields. We show that there exist sources of microwave ME near fields-the ME particles. These particles are represented by small quasi-two-dimensional ferrite disks with magnetic-dipolar-oscillation spectra. The near fields originating from such particles are characterized by topologically distinctive power-flow vortices, nonzero helicity, and a torsion degree of freedom. The paper consists of two main parts. In the first one, we give a theoretical background of properties of the electric and magnetic fields inside and outside of a ferrite particle with magnetic-dipolar-oscillation spectra resulting in the appearance of microwave ME near fields. In the second main part, we represent numerical and experimental studies of the microwave ME near fields and their interactions with matter. Based on the obtained properties of the ME near fields, we discuss possibilities for effective microwave sensing of natural and artificial chiral structures.

Electron vortex production and control using aberration induced diffraction catastrophes

An aberration corrected electron microscope is used to create electron diffraction catastrophes, containing arrays of intensity zeros threading vortex cores. Vortices are ascribed to these arrays using catastrophe theory, scalar diffraction integrals, and experimentally retrieved phase maps. From measured wave function phases, obtained using focal-series phase retrieval, the orbital angular momentum density is mapped for highly astigmatic electron probes. We observe vortex rings and topological reconnections of nodal lines by tracking the vortex cores using the retrieved phases.

Instability of higher-order optical vortices analyzed with a multi-pinhole interferometer

Higher-order optical vortices are inherently unstable in the sense that they tend to split up in a series of vortices with unity charge. We demonstrate this vortex-splitting phenomenon in beams produced with holograms and spatial light modulators and discuss its generic and practically unavoidable nature. To analyze the splitting phenomena in detail, we use a multi-pinhole interferometer to map the combined amplitude and phase profile of the optical field. This technique, which is based on the analysis of the far-field interference pattern observed behind an opaque screen perforated with multiple pinholes, turns out to be very robust and can among others be used to study very 'dark' regions of electromagnetic fields. Furthermore, the vortex splitting provides an ultra-sensitive measurement method of unwanted scattering from holograms and other phase-changing optical elements.

Phase measurement using an optical vortex lattice produced with a three-beam interferometer

A new phase-measurement technique is proposed, which utilizes a three-beam interferometer. Three-wave interference in the interferometer generates a uniform lattice of optical vortices, which is distorted by the presence of an object inserted in one arm of the interferometer. The transverse displacement of the vortices is proportional to the phase shift in the object wave. Tracking the vortices permits the phase of the object to be reconstructed. We demonstrate the method experimentally using a simple lens and a more complex object, namely the wing of a common house fly. Since the technique is implemented in real space, it is capable of reconstructing the phase locally.

Tailored complex 3D vortex lattice structures by perturbed multiples of three-plane waves

As three-plane waves are the minimum number required for the formation of vortex-embedded lattice structures by plane wave interference, we present our experimental investigation on the formation of complex 3D photonic vortex lattice structures by a designed superposition of multiples of phase-engineered three-plane waves. The unfolding of the generated complex photonic lattice structures with higher order helical phase is realized by perturbing the superposition of a relatively phase-encoded, axially equidistant multiple of three noncoplanar plane waves. Through a programmable spatial light modulator assisted single step fabrication approach, the unfolded 3D vortex lattice structures are experimentally realized, well matched to our computer simulations. The formation of higher order intertwined helices embedded in these 3D spiraling vortex lattice structures by the superposition of the multiples of phase-engineered three-plane waves interference is also studied.

Generation of optical vortex array with transformation of standing-wave Laguerre-Gaussian mode

We develop a novel method of creating optical vortex array by the conversion of a standing-wave Laguerre-Gaussian (LG) mode. Theoretically, by employing the transformational relation, the standing-wave LG mode is verified to be transformed from a pair of crisscrossed Hermite-Gaussian (HG) modes, embedded with optical vortex array, consists of a TEM_n,m mode and a TEM_m,n mode. Due to close correspondence between the transformational relation and the mode conversion of astigmatic lenses, we successfully generate the optical vortex array by transforming a standing-wave LG mode into the crisscrossed HG modes via a π/2 cylindrical lens mode converter. The investigation may provide useful insight in the study of the vortex light beam and its further applications.

Symmetry breaking of optical vortices: birth and annihilation of singularities in the evanescent field

The interaction of optical vortices (or phase singularities, or screw dislocations) with ordinary matter is treated with a simple approach. Using the total internal reflection phenomenon and the superposition of four plane waves incident on a material with a refractive index lower than the original propagating medium, we are able to show the birth and annihilation of optical vortices in an evanescent field with curved topological features. Until now, this phenomenon has been explored only in free space propagation. By a suitable tuning process involving the incident angles and the amplitudes of the incident plane waves, it is possible to create unusual topological features of optical vortices in the vicinity of the material. We believe that this work can open new aspects of curved optical vortex manipulation in near-field optics.

Modulated vortex solitons of four-wave mixing

We experimentally demonstrate the vortex solitons of four-wave mixing (FWM) in multi-level atomic media created by the interference patterns with superposing three or more waves. The modulation effect of the vortex solitons is induced by the cross-Kerr nonlinear dispersion due to atomic coherence in the multi-level atomic system. These FWM vortex patterns are explained via the three-, four- and five-wave interference topologies.

Optical vortices and singularities due to interference in atomic radiation near a mirror

We consider radiation emitted by an electric dipole close to a mirror. We have studied the field lines of the Poynting vector, representing the flow lines of the electromagnetic energy, and we show that numerous singularities and subwavelength optical vortices appear in this energy flow pattern. We also show that the field line pattern in the plane of the mirror contains a singular circle across which the field lines change direction.

Topology of light's darkness

We numerically study the topology of optical vortex lines (nodal lines) in volumes of optical speckle, modeled as superpositions of random plane waves. It is known that the vortex lines may be infinitely long, or form closed loops. Loops are occasionally threaded by infinite lines, or linked with other loops. We find the probability of a loop not being threaded decays exponentially with the length of the loop. This behavior has a similarity to scaling laws studied in superfluid turbulence, and polymers modeled as random walks.

Generation and dynamics of vortex lattices in coherent exciton-polariton fields

Vortex dynamics in coherent ensembles of exciton polaritons (condensates) is studied in the framework of the polarization-dependent Gross-Pitaevskii equation. Vortex lattices can be resonantly excited in the polariton field by the interference of three or more optical pumps. Vortex-antivortex pairs can also appear in polariton condensates due to scattering with disorder. The nonlinear vortex dynamics is characterized by interactions of vortex cores and vortex-antivortex recombination.

Polarization singularities in 2D and 3D speckle fields

The 3D structure of randomly polarized light fields is exemplified by its polarization singularities: lines along which the polarization is purely circular (C lines) and surfaces on which the polarization is linear (L surfaces). We visualize these polarization singularities experimentally in vector laser speckle fields, and in numerical simulations of random wave superpositions. Our results confirm previous analytical predictions [M. R. Dennis, Opt. Commun. 213, 201 (2002)] regarding the statistical distribution of types of C points and relate their 2D properties to their 3D structure.

Fractality of light's darkness

Natural light fields are threaded by lines of darkness. For monochromatic light, the phenomenon is familiar in laser speckle, i.e., the black points that appear in the scattered light. These black points are optical vortices that extend as lines throughout the volume of the field. We establish by numerical simulations, supported by experiments, that these vortex lines have the fractal properties of a Brownian random walk. Approximately 73% of the lines percolate through the optical beam, the remainder forming closed loops. Our statistical results are similar to those of vortices in random discrete lattice models of cosmic strings, implying that the statistics of singularities in random optical fields exhibit universal behavior.

Symmetric array of off-axis singular beams: spiral beams and their critical points

We consider conditions of structural stability under which the array of singular beams preserves its topological structure and intensity distribution while slightly perturbing its intrinsic parameters. The orbital angular momentum of the array as a function of the array parameters is a characteristic function, and its extreme points correspond to stable and unstable array states.

Phase vortices from a Young's three-pinhole interferometer

An analysis is presented of the phase vortices generated in the far field by an arbitrary arrangement of three monochromatic point sources of complex spherical waves. In contrast with the case of three interfering plane waves, in which an infinitely extended vortex lattice is generated, the spherical sources generate a finite number of phase vortices. Analytical expressions for the vortex core locations are developed and shown to have a convenient representation in a discrete parameter space. Our far-field analysis may be mapped onto the case of a coherently illuminated Young's interferometer, in which the screen is punctured by three rather than two pinholes.

Influence of surface termination on negative reflection by photonic crystals

When a wave impinges obliquely to the interface of a Photonic Crystal (PhC), the wave can be completely reflected in counter-propagating direction instead of the usually expected specular direction. However the beam is totally specularly reflected with a simple modification of the surface termination. The analysis of the time average Poynting vector evidences that PhC termination modifies the energy flow and determines the reflection properties.

Interferometric optical vortex array generator

Two new interferometric configurations for optical vortex array generation are presented. These interferometers are different from the conventional interferometers in that they are capable of producing a large number of isolated zeros of intensity, and all of them contain optical vortices. Simulation and theory for optical vortex array generation using three-plane-wave interference is presented. The vortex dipole array produced this way is noninteracting, as there are no attraction or repulsion forces between them, leading to annihilation or creation of vortex pairs.

Generation of vortex-type markers in a one-wave setup

What we believe to be a new arrangement of an optical vortex interferometer (OVI) is presented. In the proposed configuration the optical vortex lattice is generated in a one-wave setup by use of birefringent elements--Wollaston compensators. The obtained vortex lattice is regular and stable, which is necessary for predicted applications. The new OVI configuration allows the measurement of waves and optical media properties.

Dislocation lines in the swallowtail diffraction catastrophe

The three-dimensional distribution of amplitude and phase represented by the swallowtail catastrophe diffraction integral is based on a network of null lines for amplitude (wave dislocations or optical vortices), where the phase is singular. In the tail region there is four-wave interference, which results in an approximately repeating pattern of amplitude based on the monoclinic space group C 2/ m and also an approximately repeating pattern of wave dislocations based on the black–white monoclinic space group C 2/ m ′. Helical dislocations spring from the plane of symmetry and gradually straighten out to be parallel to the two riblines of the caustic; eventually they become the straight dislocations of the Pearcey pattern for the cusp catastrophe. In the front region, where there are zero or two points of stationary phase, each dark Airy fringe surface associated with the fold surface condenses into a single dislocation in the plane of symmetry.