Topological reactions of optical correlation vortices

This paper outlines a new research project (CREST) for structure health monitoring. The purpose is to develop a networked sensor for static, full-axis deformation of large and long structures such as bridges, roads, and railways. We propose a novel technique based on the combined use of an optical vortex (OV) beam and correlation image sensors (CIS). Since the beam profile of OV involves definitive features known as zeros or phase singularities and they are invariant through propagation, we can encode and transmit information to determine geometrical relations between the sender and receiver nodes. By demodulating an amplitude and phase profile of OV using the CIS, all (three lateral and three rotational) displacement components can be determined. The basic optical setup is presented and the results of the fundamental experiments are shown.

This work presents an investigation of tight focusing of optical vortices, which produce regions where the Poynting vector is directed opposite to the beam's propagation direction-known as areas of reverse energy flow. We study both phase optical vortices and polarization optical vortices (cylindrical vector beams). For phase optical vortices, it is shown that the emergence of reverse energy flow as well as splitting of the initial optical vortex depends on the handedness of the circular polarization and the phase of the initial optical vortex. An optical vortex with an initial topological charge of $m\; \le \; - {3}$ splits into three optical vortices with topological charges $m + {2}$, ${-}{1}$, and ${-}{1}$ when the polarization is right circular. In contrast, under left-hand circular polarization, a vortex with the topological charge $m$ is preserved at the focus. The reverse-flow regions are located between the centers of phase singularities (screw dislocation points). As the topological charge of the phase vortex increases, the region of reverse flow along the radial coordinate widens, and the distance from the vortex center to the optical axis also increases. In the focusing of cylindrical vector beams (polarization optical vortices), the reverse energy flow region is also observed, but screw dislocations are absent.

Internal conical diffraction produces a superposition of orthogonally polarised zero- and first-order Bessel like beams from an incident circularly polarised Gaussian beam. For right-circularly polarised light, the first-order beam has an optical vortex of charge -1. Upon propagation of the first-order beam through a second biaxial crystal, a process which is termed cascade conical refraction, the generated beam is a superposition of orthogonally polarised fields of charge 0 and -1 or 0 and -2. This spin to orbital angular momentum conversion provides a new method for the generation and annihilation of optical vortices in an all-optical arrangement that is solely dependent on the incident polarisation and vortex handedness.

The behavior of an axial optical vortex (OV), which is generated with the use of a Gaussian beam and two ramps implemented by a phase-only spatial light modulator (SLM), is studied as a function of the parameters of two ramps. The analytic solution of a wave equation is obtained in the Fresnel approximation for the diffraction of a Gaussian beam on the two-ramp structure. Nonlinear dependences of the ellipticity gamma of the intensity distribution in the OV core, as well as the angle (phi between the x-axis and the major ellipse axis of the vortex core, on the ramp phase gradient K, are analyzed. The values of given parameters obtained in optical and numerical experiments are in good agreement. It is shown that, as the gradients of the phases of two ramps vary in the limits of 3pi rad/cm, the ellipticity and the slope angle of the major axis ellipse are changed, respectively, by 0.3 and 56 degrees. This gives possibility to efficiently control the parameters of OVs.

Linear and nonlinear processes of generation and transformation of optical vortices in crystals were investigated. New universal methods for production of Bessel light beams with optical vortices of the first, second and higher order by means of uniaxial and biaxial crystals were proposed. Light beams with optical vortices of topological charge +/- 1 and +/- 2 are experimentally obtained using KTP and HIO3 (iodic acid) biaxial crystals. We studied type II second harmonic generation by Bessel beams with optical vortices in nonlinear crystals. Results of investigation of the processes of Bessel light vortex order doubling, transfer of vortex to the second harmonic radiation, and annihilation of optical vortices with the opposite signa are presented.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In the present presentation, we report the experimentally and theoretically investigated spatial wavefront conversion properties of an optical vortex (OV) generation system including azo-dye doped liquid crystal (ADDLC) polymer composite and vector beam illuminator, focusing on the abilities of flexibility and achromaticity. Threedimensional anisotropic structure was induced by recording vector beam in ADDLC and it can convert a polarized Gaussian beam into polarized OVs whose topological charge is depending on the structure of anisotropy. The photo-induced anisotropic structure can be re-initialized by turning it off and changing the illuminating polarization pattern of vector beam. Numerical simulations and experimental results showed that our anisotropic structure can generate OV with broadband spectrum.

A full comparative analysis of the chain of phase singularities generated when a quasi-plane wave and a Gaussian beam pass a double-phase-ramp (DPR) converter is presented based on the theoretical and experimental data. The overall output beam structure includes a system of interrelated optical vortices (OVs) whose linear trajectories form a threedimensional singular skeleton which can be applied for the trapping and guiding of microparticles. An internal structure of each individual phase singularity is characterized by the OV topological charge and by the morphology parameters of the equal intensity ellipses in the OV-core area. The rectilinear equidistant OV trajectories form a chain in the transverse cross section, and their identical morphology parameters can be useful for the applications to metrology and micromanipulation. As a separate result, we consider the DPR-induced transformations of the incident Laguerre-Gaussian beams of the lowest orders and show that the incident multicharged OVs are transformed into small sub-chains of the OVs located in the near-axial region.

In the optical vortex microscopy the focused Gaussian beam with optical vortex scans a sample. An optical vortex can be introduced into a laser beam with the use of a special optical element--a vortex lens. When moving the vortex lens, the optical vortex changes its position inside the spot formed by a focused laser beam. This effect can be used as a new precise scanning technique. In this paper, we study the optical vortex behavior at the sample plane. We also estimate if the new scanning technique results in observable effects that could be used for a phase object detection.

The spatial dynamics of vortex dipole nested in a Gaussian opti cal beam is analyzed with scal ar diffraction theory. It is shown that the generation and annihilation of vortices are accompanied by extrem e wave front distortions. Process of nucleation and annihilation of vortex dipole is considered to confirm the vortex aftereffect in the process of transformation of an aberration wave front into a singular one. After the vortex dipole annihilation the absolute values of the average and Gaussian curvatures increase greatly in the local areas of wave front. The phase reconstruction error increases in these areas in the process of wave front sensing. To investigate the features of the vortex aftereffect for simple field the light rays which take part in the combined translational and rotary motion of energy around the field zero-lines are constructed. The phase is computed as a potential of the optical field using the light rays. Integration of the phase gradient along the ray or energy-stream line allows a uniq ue value of the phase to be connected with a point of the ray. Wave front of the beam is constructed from the computed phase. As in the vicinity of the vortex core the energy-stream line takes a spiral shape the phase incursion along th e line increases. After the vortex annihilation and vanishing of the spiral shape the incursion remains and creates the vortex aftereffect in the form of the extreme wave front distortions. The revealed effect should be taken into accoun t when constructing the systems of adaptive optics aimed at functioning in strong turbulence conditions. Keywords: Singular phase, optical vortex, strong turbulence, phase reconstruction

Light diffraction is studied numerically and experimentally on a double fork‐shaped grating representing a periodic grating containing two spaced dislocations. The spatial dynamics of the phase singularities (optical vortices) has been investigated as a function of dislocation parameters. Produced optical vortices affect each other while propagating in a free space. For dislocations of the same topological charge, the propagation trajectories and their transverse displacement coordinates depend on the dislocation spacing, and the larger the dislocation spacing, the smaller the relative displacement of the optical vortices and the smaller their trajectory curvatures. For oppositely charged dislocations, three types of spatial behavior of optical vortices are found. The numerical results agree well with the experimental data.

Fork-shaped gratings are periodic structures containing a spatial dislocation known to be used for the production of optical vortices in a far field. Spatial overlapping of diffraction orders in a near field results in complex spatial evolution of optical vortices. In this paper, we report the results of near-field diffraction on fork-shaped gratings with different topological charges and analyze the evolution of specific optical vortices during propagation. Optical vortices have been shown to form two-dimensional well-ordered spatial configurations in specific transverse planes. The locus of points of optical singularities has been shown to form two helical lines twisted around the ±1 diffraction order directions. Our results demonstrate that the spatial behaviour of optical vortices is in close connection with the spatial ordering arising from the Talbot effect. The quantity of optical vortices demonstrates complex spatial dynamics, which includes spatial oscillations and decreasing along the propagation direction. These results provide a foundation towards a deeper understanding of near-field singular optics phenomena.

Optical vortex trajectory of the edge-diffracted single-charged Laguerre-Gaussian beam

Optical vortices have a topologically charged phase singularity and zero intensity distribution in the centre. Optical vortex creation is regarded as a significant means for information transmission for applications in quantum computing, encryption, optical communication, etc. In this study, using finite-difference time-domain (FDTD) simulation, we calculated the electric field intensity and phase distribution of 2D lattices of optical vortices generated from various polygonal plasmonic lens structures using surface states of a Weyl semimetal (MoTe2). It was shown that a hexagonal lens is the best performing plasmonic lens. Further, we posited here a unified mathematical formulation for optical electrical field and phase distribution in the near field for any polygonal plasmonic lens. Our theoretical calculation corroborated well with FDTD results, validating the proposed generalized formula. Such plasmonic lens structures demonstrating scaling behavior offer great potential for designing next-generation optical memories.

Nonlinear propagation effects on high-power optical-vortex pulses in anisotropic crystals is reported. Nonlinear effects on optical-vortex pulse generation through the spin-orbit interaction and its propagation in an anisotropic crystal is investigated.The beam of the left-circularly-polarized optical vortex pulse is focused on one of the surfaces of a LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> or rutile crystal (NC) by a convex lens L1. After propagating along the optic axis of the crystal, the beam is collimated by another convex lens L2.

Vortex Stagnation problem in iterative Fourier transform algorithms