scholarly journals Transformation of a high-order edge dislocation to optical vortices (spiral dislocations)

2021 ◽  
Vol 45 (3) ◽  
pp. 319-323
Author(s):  
V.V. Kotlyar ◽  
A.A. Kovalev ◽  
A.G. Nalimov
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Edge Dislocation ◽  
Topological Charge ◽  
Hermite Polynomial ◽  
High Order ◽  
Cylindrical Lens ◽  
Optical Vortices ◽  
Focal Distance ◽  
Straight Line

We theoretically show that an astigmatic transformation of an nth-order edge dislocation (a zero-intensity straight line) produces n optical elliptical vortices (spiral dislocations) with unit topological charge at the double focal distance from the cylindrical lens, located on a straight line perpendicular to the edge dislocation, at points whose coordinates are the roots of an nth-order Hermite polynomial. The orbital angular momentum of the edge dislocation is proportional to the order n.

scholarly journals Measurement of the orbital angular momentum of an astigmatic Hermite–Gaussian beam

2019 ◽  
Vol 43 (3) ◽  
pp. 356-367
Author(s):  
V.V. Kotlyar ◽  
A.A. Kovalev ◽  
A.P. Porfirev
Keyword(s):  
Angular Momentum ◽  
Gaussian Beam ◽  
Orbital Angular Momentum ◽  
Topological Charge ◽  
Optical Axis ◽  
Optical Vortex ◽  
Cylindrical Lens ◽  
Optical Vortices ◽  
Special Choice ◽  
Different Types

Here we study three different types of astigmatic Gaussian beams, whose complex amplitude in the Fresnel diffraction zone is described by the complex argument Hermite polynomial of the order (n, 0). The first type is a circularly symmetric Gaussian optical vortex with and a topological charge n after passing through a cylindrical lens. On propagation, the optical vortex "splits" into n first-order optical vortices. Its orbital angular momentum per photon is equal to n. The second type is an elliptical Gaussian optical vortex with a topological charge n after passing through a cylindrical lens. With a special choice of the ellipticity degree (1: 3), such a beam retains its structure upon propagation and the degenerate intensity null on the optical axis does not “split” into n optical vortices. Such a beam has fractional orbital angular momentum not equal to n. The third type is the astigmatic Hermite-Gaussian beam (HG) of order (n, 0), which is generated when a HG beam passes through a cylindrical lens. The cylindrical lens brings the orbital angular momentum into the original HG beam. The orbital angular momentum of such a beam is the sum of the vortex and astigmatic components, and can reach large values (tens and hundreds of thousands per photon). Under certain conditions, the zero intensity lines of the HG beam "merge" into an n-fold degenerate intensity null on the optical axis, and the orbital angular momentum of such a beam is equal to n. Using intensity distributions of the astigmatic HG beam in foci of two cylindrical lenses, we calculate the normalized orbital angular momentum which differs only by 7 % from its theoretical orbital angular momentum value (experimental orbital angular momentum is –13,62, theoretical OAM is –14.76).

scholarly journals Digital sorting of Hermite-Gauss beams: mode spectra and topological charge of a perturbed Laguerre-Gauss beam

2020 ◽  
Vol 44 (4) ◽  
pp. 501-509
Author(s):  
A.V. Volyar ◽  
E.G. Abramochkin ◽  
Yu. Egorov ◽  
M. Bretsko ◽  
Ya. Akimova
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Topological Charge ◽  
Initial Phase ◽  
Cylindrical Lens ◽  
Theoretical Justification ◽  
Gauss Beam ◽  
Phase Spectra

We developed and implemented an intensity moments technique for measuring amplitude and initial phase spectra, the topological charge (TC) and orbital angular momentum (OAM) of the Laguerre-Gauss (LG) beams decomposed into the basis of Hermite-Gaussian (HG) modes. A rigorous theoretical justification is given for measuring the TC of unperturbed LG beams with different values of radial and azimuthal numbers by means of an astigmatic transformation on a cylindrical lens. We have shown that the measured amplitude and phase spectra of the HG modes make it possible to find the orbital OAM and TC, as well as digitally sorting the HG modes and then restoring the initial singular beam.

scholarly journals Characterization of topological charge and orbital angular momentum of shaped optical vortices

2014 ◽  
Vol 22 (24) ◽  
pp. 30315 ◽  
Author(s):  
Anderson M. Amaral ◽  
Edilson L. Falcão-Filho ◽  
Cid B. de Araújo
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Topological Charge ◽  
Optical Vortices

scholarly journals Optical beams with an infinite number of vortices

2021 ◽  
Vol 45 (4) ◽  
pp. 490-496
Author(s):  
V.V. Kotlyar
Keyword(s):  
Angular Momentum ◽  
Cross Section ◽  
Data Transmission ◽  
Topological Charge ◽  
Laser Beams ◽  
Optical Data ◽  
Optical Vortices ◽  
Straight Line ◽  
Phase Singularities ◽  
Light Beams

In optical data transmission with using vortex laser beams, data can be encoded by the topo-logical charge, which is theoretically unlimited. However, the topological charge of a single sepa-rate vortex is limited by possibilities of its generating. Therefore, in this work, we analyze light beams with an unbounded (countable) set of optical vortices. The summary topological charge of such beams is infinite. Phase singularities (isolated intensity nulls) in such beams typically have a unit topological charge and reside equidistantly (or not equidistantly) on a straight line in the beam cross section. Such beams are form-invariant and, on propagation in space, change only in scale and rotate. Orbital angular momentum of such multivortex beams is finite, since only a finite number of optical vortices fall into the area, where the Gaussian beam has a notable intensity. Other phase singularities are located in the periphery (and at the infinity), where the intensity is almost zero.

scholarly journals Orbital angular momentum and topological charge of a Gaussian beam with multiple optical vortices

2020 ◽  
Vol 44 (1) ◽  
pp. 34-39
Author(s):  
A.A. Kovalev ◽  
V.V. Kotlyar ◽  
D.S. Kalinkina
Keyword(s):  
Numerical Simulation ◽  
Angular Momentum ◽  
Gaussian Beam ◽  
Orbital Angular Momentum ◽  
Topological Charge ◽  
Optical Axis ◽  
Random Phase ◽  
Beam Power ◽  
Optical Vortices ◽  
Local Intensity

Here we study theoretically and numerically a Gaussian beam with multiple optical vortices with unitary topological charge (TC) of the same sign, located uniformly on a circle. Simple expressions are obtained for the Gaussian beam power, its orbital angular momentum (OAM), and TC. We show that the OAM normalized to the beam power cannot exceed the number of vortices in the beam. This OAM decreases with increasing distance from the optical axis to the centers of the vortices. The topological charge, on the contrary, is independent of this distance and equals the number of vortices. The numerical simulation corroborates that after passing through a random phase screen (diffuser) and propagating in free space, the beams of interest can be identified by the number of local intensity minima (shadow spots) and by the OAM.

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