Often, light can be represented, approximately or exactly, by a complex scalar wave (psi) , smoothly varying in space and/or time. The field (psi) could be a cartesian component of the electromagnetic field or of the vector potential, or one of several scalar potentials appropriate to different circumstances. This meeting has been concerned with the line singularities of the phase of (psi) . Here, I wish to make some general remarks about these lines. Except where stated, all the remarks are independent of the particular wave equation that (psi) satisfies.

A simple derivation is given for the known result that the component of total angular momentum along the propagation direction of a general paraxial beam can be separated into orbital and spin parts. Comments are made about orbital angular momentum and wave dislocations, and about how the orbital and spin angular momentum can be changed by propagation in a refracting medium.

Geometro-optical (GO) models were used to describe the properties of light fields having helical wave front structure inside the resonant cavity. The quantization rules of the ray packs dimensions of screw modes in cavity were defined. To describe helical fields with nonuniform azimuthal rotation of the phase a method combining the potentialities of the ray approach with those of composition of Gaussian rays method was used.

It is known that Laguerre-Gauss beams with indices n equals 0 and nonzero m have a single phase singularity of order m and the intensity shaped as a circumference. In this work a generalization of these beams is proposed, namely, for any closed curve on the plane there exists a family of singular beams depending on a pair of integer-valued parameters, any member of which is structurally stable under propagation and focusing. In particular, when the curve is a circumference Laguerre-Gauss modes and parameters n,m are obtained.

We show how to synthesize a wave with monochromatic mixed screw-edge dislocation. We obtained theoretically and experimentally that a mixed screw-edge dislocation embedded in a monochromatic Gaussian beam does not propagate as a self- similar stable object, but transforms into several pairs of opposite-sign optical vortices in near field, and produces single-charge optical vortices in far field.

We show directly that a light beam carrying optical vortex rotates in space around the axis of propagation. The spatial rotation and related angular momentum result from the helical wavefront with axial phase singularity. Using Gaussian envelope of a 'singular' beam, we calculate the angular velocity of rotation. Experimental observation of light beam rotation is performed at the first time to our knowledge and confirms the theoretical predictions.

Optical Vortex (OV), or wavefront screw dislocation represents a wavefront phase defect, where the wavefront attains a helicoidal shape. The wave possessing axial OV is one of the possible solutions of scalar wave equation. It means the expression for OV has in the simplest case a form E(r,(phi) ) varies direct as rexp(i(phi) ), where r, (phi) are cylindrical coordinates. Therefore OV is a discontinuity of the phase such that the phase circulation around its axes is an integral multiple of 2(pi) . The phase change for circulation around the axis may have different signs. It determines the topological sign of screw dislocation and correspondingly the helicoidal form of dislocation: with right twirl (positive) or left twirl (negative). Moreover, in a general case a wavefront around vortex axis may have a form of multistart helicoid, with a pitch m(lambda) , when (lambda) is the wavelength, and m is integer. The objective of this paper is to present experimental reversal of screw dislocation by four-wave mixing and to investigate the sign of dislocation within phase- conjugated beam with respect to the incident signal beam.

The hydrodynamic description of light propagation through the randomly inhomogeneous medium is developed based on the analogy of the vortex phase dislocations with the potential circular flow of liquid caused by the isolated point vortexes. It is shown that the determining factor in forming of the wave fronts structure of optical speckle-fields is a spatial dynamics of the phase gradient rotor. The singular equations for description of the rotor are derived and methods to regularize these equations are proposed.

It has been shown previously that it is possible to two- dimensionally trap a microscopic absorbing particle against a substrate using a focused doughnut beam. Beam angular momentum associated with the phase singularity is transferred to the particle, causing it to rotate. A detailed consideration of the optical forces acting on a particle shows the importance of wavefront curvature for stable trapping and lead to a quantitative description of the motion of the particle in single and multiple beam traps.

It is shown that the difference in structure and propagation constants of guided vortices of an optical fiber is connected with a topological phase of the given vortices. The field state of CV and IV vortices is uniquely presented by a pair of numbers: a topological phase (iota) and polarization helicity (sigma) ₂. Symmetry relationships, which are characteristic for the topological phases, extend to this pair of numbers. Thus, a simultaneous change of the sign (iota) and (sigma) ₂ leaves the vortex state unchanged. The sign change of only one of the numbers transforms the vortex from the state CV (or IV) into another state IV (or CV). These symmetry relationships reflect the result of spin-orbital interaction in vortices and determine the eligibility of quantum numbers: topological charge and helicity.

Fundamental properties of eigen vortices of optical fiber with arbitrary refractive index are considered. It is shown that guided vortices are divided into three large groups: CV₊₁⁺ and CV_-1^-; CV₊₁^- and CV_-1⁺; IV₊^- and IV_-⁺. It was obtained that stable CV vortices have different from zero an angular momentum of a motion quantity, when an angular momentum of unstable IV vortices is always equal to zero.

It is experimentally and theoretically shown that as a result of spin-orbital interaction in stable CV and unstable IV vortices of a step low-mode fiber there appears topological birefringence. This type of birefringence depends not only on the polarization basis determined by a vortex helicity (sigma) ₂, but also on the topological charge (iota) . In this presentation the Magnus effect and Rytov-Vladimirsky effect are different aspects of experimental manifestations of topological birefringence of waveguide vortices.

As a rule, the low-mode optical fiber is excited by a linear polarized Gaussian beam. In this case a fundamental HE₁₁ mode and LP₁₁ field combination are propagated through the fiber. The complete field of free space is usually characterized by phase singularities. But in an optical fiber, the fields have complete polarizing structure. In this paper, vector singularities -- dislocations and disinclinations are studied. It is shown that a row edge dislocation of the LP₁₁ mode is splitted into two circular polarized C⁺ and C^- disclinations twisting in the opposite direction and two fixed linear polarizing disclination. The very birth and death events of these dislocations and disclinations determine the light propagation processes along the linearly polarized exciting low-mode fibers.

A set of interference ring patterns is formed by two laser beams after the Mach-Zander interferometer. The first of these beams passes along a short multimode fiber. This fiber is excited by off-axis rays. The second field is a referent Gaussian beam. The reference beam is set near a cusped point of a wave caustics. A conversion of a single ring interference pattern into three ring interference patterns is the result of the displacement of the Gaussian beam near the vicinity of the cusped point. There is only one degenerated ring-interference pattern in an interior caustic region. This optical phenomenon turns out to be a bifurcational process which could be explained by means of the interference between the quasiplane wave having a wavefront with the singularity region in the form of the Whitney's cusp and the Gaussian beam. A model theoretical computation of wave caustics interference and a fundamental Gaussian beam has been done.

We are shown that the using of holographic method for system fibers-hologram forms phase and linear polarized homogeneous beams. The image formed on fiber entrance is reconstructed at definite length of fiber. The rotation of this image corresponds to different azimuts of linear polarization. Observed transformations of fase and polarisation are caused by LV-mode waves and waveguide topological birefringence.

An orbital angular momentum of a circular vortex in a low-mode fiber is studied. An experimental scheme based on a mechanism of a total reflection is proposed. The expression of mechanical torque induced by radiation is obtained.

Experimentally the process of magneto-optical diffraction of light on ferrit-garnet magnetic films with a stripe domain structure with occasional defects in magnetic lattice of a 'fork' type was studied. The analyses of the structure of a magnetic lattice and diffraction field of light shows that the domain lattice with a stripe structure by its action on a laser radiation corresponds to a phase computer-synthesized hologram of a single pure screw dislocation of a wavefront. It is demonstrated that in the result of magneto-optical diffraction on a magnetic hologram it is possible to reconstruct optical vortices with helicoidal wavefronts. The action of a mode convertor which realizes energetically effective conversion of a Hermite-Gaussian beam into a Laguerre-Gaussian beam and vice versa. It is experimentally analyzed is demonstrated that unlike the phase converter studied in reference one the proposed device is less sensitive to matching the astigmatic elements. The application of magnetic holograms in generation of optical vortices enables us to create laser beams with governed parameters. For instance by the action of a gradient field it is possible to shift the position of a singularity in the magnetic lattice, change its sign or eliminate the singularity.

A review and comparison are given of localized (soliton-like) structures with nonzero topological index in the two types of nonlinear optical systems: (1) homogeneous medium with nonlinearity of refractive index (conservative system), and (2) wide-aperture laser with saturable absorption (dissipative system).

Feasibility of noninterferometric methods to measure the phase distribution in laser beam cross-section for visualization of the vortex dislocations of optical speckle-field wavefront is analyzed. Peculiarities of the phase retrieval from the measured intensity distribution (the phase problem in optics) and from the wave front slopes measured by the Hartman sensor are discussed. A concept of the vortex and potential parts of the phase is introduced. An analytic formula to retrieve the potential phase from the measured intensity distribution of optical speckle-field has been obtained. We show that the considered ways of measurements allow the positions of the dislocations centers to be sensed and spatial configuration of the intensity zero-lines to be reconstructed.

In reference 1 it was shown that beams containing phase singularities have enough various intensity distributions, in particular, the distribution looked like an arbitrary planar curve. In this work we present a method of synthesis of these beams by means of one-dimensional phase elements. The basis of the method is the result stated in reference 1 that Fourier transform with an additional astigmatic phase converts such beams into light fields with one-dimensional structure. Thus, the synthesis of a singular beam can be reduced to formation of one-dimensional light fields with subsequent astigmatic Fourier transform of them. One-dimensional light field synthesis is carried out by means of two one-dimensional phase elements located at some distances along the beam propagation. One-dimensional phase masks were realized experimentally on dichromated gelatin layers which were made by sensibilization of standard holographic photoplates. The masks were recorded through an exposure of layers by an argon ion laser operating at the wavelength of 0.488 mkm. The laser beam was transformed into a narrow line of 10 mkm width. The recording was made by moving a layer in its own plane step-by-step with the help of an electric motor controlled by a computer. (The step size was 5 mkm.) After the exposure these layers were developed by water vapors according to a technique described in reference 2. Experimental results of synthesis of a beam whose intensity looks like a boundary of a regular triangle are presented.

We report on single optical beam splitting into several beams in a slab waveguide made of poly(methyl methacrylate) (PMMA) doped with dye 4-(Dicyanomethylene)-2-methyl-6-(p- dimethylaminostyryl)4H-pyran known as DCM. The effect is associated with permanent refractive index decrease caused by upconverted dye photobleaching. The effect takes place at much lower power than nonlinear propagation effects in Kerr media (less than 1 kW/cm²). The proposed model of splitting uses soliton-like solutions of Shrodinger-type nonlinear propagation equation complemented by the rate equation for the refractive index change. Computer simulations based on the model demonstrate all the effects observed experimentally such as beam splitting into two primary side branches followed by their collapse into multiple secondary branches. Simulations also show that the beam sent through a (pi) -step phase mask has behavior similar to that of a spatial dark soliton.

It is known that one-dimensional phase problem in optics can be reduced to a search of zero positions of the analytic continuation of a light field complex amplitude. Usually this procedure is executed by means of numerical methods based on the measurement of the field intensity on several planes. In this work it is shown that the analytic continuation can be realized by optical way. Namely, two-dimensional Fourier transform with an additional astigmatic phase converts a one- dimensional object field into a singular wavefield. The field zeros are the same as that of the analytic continuation of one-dimensional Fourier transform of the initial field. Thus, it is possible to restore the object field through one measurement. Results of computer simulations are presented.

Conditions of occurrence of phase helical dislocations inside laser cavities and in the turbulent media are established. Statistical characteristics of radiation having dislocational structure of wave front are investigated. It is shown that such dislocations are formed when a size of correlation zone of intensity fluctuations becomes much smaller than the beam size.