Super bursts of the orbital angular momentum in astigmatic-invariant structured LG beams.

A structured Laguerre-Gaussian (sLG) beam in an optical system with an astigmatic element acquires additional degrees of freedom in the form of changing the fine structure of the beam, its orbital angular momentum (OAM), and topological charge. We have theoretically and experimentally revealed that at a certain ratio between the beam waist radius and the focal length of the cylindrical lens, the beam turns into an astigmatic-invariant one, and such a transition does not depend on the beam radial and azimuthal numbers. Moreover, in the vicinity of the OAM zero, its sharp bursts occur, the magnitude of which significantly exceeds the initial beam OAM and grows rapidly as the radial number increases.

Fast oscillations of orbital angular momentum and Shannon entropy caused by radial numbers of structured vortex beams.

We address theoretical and experimental considerations of two-parameter excitation of each Hermite-Gaussian (HG) mode in composition of a structured Laguerre-Gaussian (sLG) beam. The complex amplitude of the sLG beam is shaped in such a way that the radial and azimuthal numbers of eigenmodes are entangled with each other. As a result, variations in the amplitude and phase parameters of mode excitation, although dramatically changing the intensity and phase patterns, do not change the structural stability of the beam.

Control of the orbital angular momentum via radial numbers of structured Laguerre-Gaussian beams.

We found that the internal perturbations of the structured Laguerre-Gaussian beam in the form of two-parametric harmonic excitations of the Hermite-Gaussian (HG) modes in its composition mix up the radial and azimuthal numbers. The harmonic excitation is characterized by two parameters, one of them controls the amplitude of the HG modes, and the second parameter controls the phases of each HG mode. It was revealed that this mixing of the beam quantum numbers leads to the possibility of controlling the orbital angular momentum (OAM) by means of radial numbers.

Structural stability of spiral vortex beams to sector perturbations.

Conditions of breaking down the structural stability of a spiral vortex beam subject to sector perturbations were considered. Employing methods of computer simulation and processing experimental results, we have shown that the spiral vortex beam has a caustic surface, the intersection of which sharply changes a shape of the Poynting vector streamlines and critical points of the spiral beam. Nevertheless, the beam propagation (scaling and rotation) does not change the perturbed streamline's shape and phase pattern.

Fine structure of perturbed Laguerre-Gaussian beams: Hermite-Gaussian mode spectra and topological charge.

We found that small perturbations of the optical vortex core in Laguerre-Gaussian (LG) beams generate a fine structure of the Hermite-Gaussian (HG) mode spectrum in the form of weak variations of amplitudes and phases of the HG modes. We developed and implemented the intensity moments technique for measuring the HG mode spectra. We also theoretically justified and experimentally implemented a technique for measuring the topological charge of the LG beams with an arbitrary number of ring dislocations.

Digital sorting perturbed Laguerre-Gaussian beams by radial numbers.

We developed a new alterative technique of the digital sorting of Laguerre-Gaussian beams (LG) by radial numbers resorting to algebra of the high-order intensity moments. The term "digital mode sorting" involves sorting the main mode characteristics (in the form of a mode spectrum) by the computer cells. If necessary, the spatial mode spectrum can be reproduced, for example, by means of a spatial light modulator.

Topological charge of a linear combination of optical vortices: topological competition.

We theoretically show that optical vortices conserve the integer topological charge (TC) when passing through an arbitrary aperture or shifted from the optical axis of an arbitrary axisymmetric carrier beam. If the beam contains a finite number of off-axis optical vortices with same-sign different TC, the resulting TC of the beam is shown to equal the sum of all constituent TCs. If the beam is composed of an on-axis superposition of Laguerre-Gauss modes (n, 0), the resulting TC equals that of the mode with the highest TC.

Orbital angular momentum and informational entropy in perturbed vortex beams.

We theoretically and experimentally investigated transformations of vortex beams subjected to sector perturbations in the form of a hard-edged aperture. The transformations of the vortex spectra, the orbital angular momentum (OAM), and the informational entropy of the perturbed beam were measured. We found that relatively small angular sector perturbations have almost no effect on the OAM, although the informational entropy is rapidly increasing due to the birth of new optical vortices caused by diffraction at the diaphragm edges.

Measurement of the vortex and orbital angular momentum spectra with a single cylindrical lens.

A new technique for measuring the degenerate spectra of optical vortices and orbital angular momentum (OAM) of singular beams is theoretically studied and experimentally verified. The technique is based on measuring the intensity moments of higher orders of a beam containing vortices with both positive and negative topological charges. The appropriate choice of the vortex mode amplitudes of the combined beam forms anomalous regions in the form of resonant dips and bursts in the OAM spectrum.

Vortex avalanche in the perturbed singular beams.

We have theoretically and experimentally considered transforming a single optical vortex beam into the vortex avalanche caused by weak local perturbations of the holographic grating responsible for the beam shaping. The vortex avalanche is accompanied by a sharp change of the orbital angular momentum (OAM) so that its dependence on the holographic grating perturbations forms the OAM spectrum. We revealed that the restored vortex beam has anomalous regions of the OAM spectrum in a form of sharp dips and bursts (resonances) that occur when the integer perturbation parameter coincides with a topological charge of one of the vortex modes.

Measurement of the vortex spectrum in a vortex-beam array without cuts and gluing of the wavefront.

We present a new technique for measuring the squares of the amplitudes and phases of partial vortex-beams in a complex beam array in real time. The technique is based on measuring the high-order intensity moments and analyzing the solutions of a system of linear equations. Calibration measurements have shown that the measurement error at least for a beam array of 10-15 beams does not exceed 4%.

Super pulses of orbital angular momentum in fractional-order spiroid vortex beams.

We consider optical properties of hypergeometric-Gaussian beam compositions with spiral-like intensity and phase distributions called spiroid beams. Their orbital angular momentum as a function of a fractional-order topological charge has a chain of super-pulses (bursts and dips). The form of the super-pulses can be controlled by the spiral parameters.

Transmission of fractional topological charges via circular arrays of anisotropic fibers.

We demonstrate that in circular arrays of anisotropic fibers at certain distribution of anisotropy directors robust transmission of optical fields with half-integer topological charges is possible. We show that this is possible because the supermodes of such arrays may contain in their circularly polarized components half-integer topological charges of opposite values. We also study the structure of singularities in these supermodes.

Helical-core fiber analog of a quarter-wave plate for orbital angular momentum.

We have studied the effect of a twist defect on the conversion of the fundamental mode (FM) into an optical vortex (OV) in a helical-core fiber (HCF). We have shown that if such a twist defect is situated in the middle of the HCF, which converts the FM into an OV, such a fiber system can continuously change the orbital angular momentum (OAM) of the output field from 0 to 1 (in a.u.

Vector erf-Gaussian beams: fractional optical vortices and asymmetric TE and TM modes.

We have considered the paraxial vector erf-Gaussian beams with field distribution in the form of the error function that are shaped by the cone of plane waves with a fractional step of the azimuthal phase distribution modulated by the Gaussian envelope. We have revealed that the initial distributions of the transverse electric and transverse magnetic fields have a far from standard form but at the far diffraction field the field distributions recover nearly the symmetric form.

Emerging correlation optics.

This feature issue of Applied Optics contains a series of selected papers reflecting the state-of-the-art of correlation optics and showing synergetics between the theoretical background and experimental techniques.

Rotational spin Hall effect in a uniaxial crystal.

We have considered the propagation process of the phase-matched array of singular beams through a uniaxial crystal. We have revealed that local beams in the array are rotated when propagating. However the right and left rotations are unequal.

Engineering of the space-variant linear polarization of vortex-beams in biaxially induced crystals.

We considered the propagation of Bessel beams through the biaxially induced birefringent crystal implemented by the mechanical torsion of the uniaxial crystal around its optical axis. Analyzing the solutions to the wave equation in the form of eigenmodes, we found that the system enables us to convert the beams with a uniform distribution of the linear polarization at the beam cross section into radially, azimuthally, and spirally polarized beams. Moreover, we revealed that the above system permits us to convert the beams with the space-variant linear polarization in accordance with the rule -s⇄s+1, where s is the topological index of the centered polarization singularity.

Subwave spikes of the orbital angular momentum of the vortex beams in a uniaxial crystal.

We have theoretically predicted gigantic spikes of orbital angular momentum caused by conversion processes of the centered optical vortex in the circularly polarized components of an elliptic vortex beam propagating perpendicularly to the crystal optical axis. We have experimentally observed the conversion process inside subwave deviations of the crystal length. We have found that the total orbital angular momentum of the wave beam is conserved.

Natural shaping of the cylindrically polarized beams.

We have experimentally and theoretically shown that the circularly polarized beam bearing a singly charged optical vortex propagating through a uniaxial crystal can be split after focusing into the radially and azimuthally polarized beams in the vicinity of the focal area provided that the polarization handedness and the vortex topological charge have opposite signs.

Spatially engineered polarization states and optical vortices in uniaxial crystals.

We describe how the propagation of light through uniaxial crystals can be used as a versatile tool towards the spatial engineering of polarization and phase, thereby providing an all-optical technique for vectorial and scalar singular beam shaping in optics. Besides the prominent role played by the linear birefringence, the influence of circular birefringence (the optical activity) is discussed as well and both the monochromatic and polychromatic singular beam shaping strategies are addressed. Under cylindrically symmetric light-matter interaction, the radially, azimuthally, and spirally polarized eigen-modes for the light field are revealed to be of a fundamental interest to describe the physical mechanisms at work when dealing with scalar and vectorial optical singularities.

Extreme spin-orbit coupling in crystal-traveling paraxial beams.

The dynamics of the spin-orbit coupling in elegant and standard Hermite-Gaussian (HG), Laguerre-Gaussian (LG), and Bessel-Gaussian (BG) beams propagating through a uniaxial crystal are analyzed. We consider the structure of the electric fields of the paraxial beams and show that the extreme values of the spin and orbital angular momenta are inherent in the elegant HG and LG of high orders. The spin-orbit coupling in the BG beam of the lowest order can result in nearly 100% energy transport from a vortex-free beam to the vortex-bearing beam at a relatively small crystal length.

Determination of topological charges of polychromatic optical vortices.

We introduce a simple, single beam method for determination of the topological charge of polychromatic optical vortices. It is based on astigmatic transformation of singular optical beams, where the intensity pattern of a vortex beam acquires a form of dark stripes in the focal plane of a cylindrical lens. The number of the dark stripes is equal to the modulus of the vortex topological charge, while the stripe tilt indicates the charge sign.

Nondiffracting vortex-beams in a birefringent chiral crystal.

A vector-wave analysis of nondiffracting beams propagating along a birefringent chiral crystal for the case of tensor character of both the optical activity and linear birefringence is presented. We have written characteristic equations and found propagation constants and amplitude parameters of the eigenmodes. The characteristic curves have anomalous zones described by an isotropic point or a gap-point, provided that the elements of an optical activity tensor obey the requirement g(11)g(33)<0, |g(33)|>|g(11)|.

Quadrefringence of optical vortices in a uniaxial crystal.

The splitting of a single optical vortex into four separate ones in a singular beam is theoretically and experimentally described for the propagation of obliquely incident light in a uniaxial crystal. We also find the condition under which the generated vortices in each of the four individual beams propagate independently without changing their structure and have different locations in all beams for any crystal lengths.