scholarly journals Optical vortices with an infinite number of screw dislocations

2021 ◽  
Vol 45 (4) ◽  
pp. 497-505
Author(s):  
A.A. Kovalev
Keyword(s):  
Gaussian Beam ◽  
Intensity Distribution ◽  
Topological Charge ◽  
Complex Amplitude ◽  
Cosine Function ◽  
Optical Data ◽  
Optical Vortices ◽  
Screw Dislocations ◽  
Arbitrary Power ◽  
Straight Line

In optical data transmission with using vortex laser beams, data can be encoded by the topological charge, which is theoretically unlimited. However, the topological charge of a single separate vortex (screw dislocation) is limited by possibilities of its generating. Therefore, we investigate here three examples of multivortex Gaussian light fields (two beams are form-invariant and one beam is astigmatic) with an unbounded (countable) set of screw dislocations. As a result, such fields have an infinite topological charge. The first beam has the complex amplitude of the Gaussian beam, but multiplied by the cosine function with a squared vortex argument. Phase singularity points of such a beam reside in the waist plane on the Cartesian axes and their density grows with increasing distance from the optical axis. The transverse intensity distribution of such a beam has a shape of a four-pointed star. All the optical vortices in this beam has the same topological charge of +1. The second beam also has the complex amplitude of the Gaussian beam, multiplied by the vortex-argument cosine function, but the cosine is raised to an arbitrary power. This beam has a countable number of the optical vortices, which reside in the waist plane uniformly on one Cartesian axis and the topological charge of each vortex equals to power, to which the cosine function is raised. The transverse intensity distribution of such beam consists of two light spots residing on a straight line, orthogonal to a straight line with the optical vortices. Finally, the third beam is similar to the first one in many properties, but it is generated with a tilted cylindrical lens from a 1D parabolic-argument cosine grating.

scholarly journals Optical vortices with an infinite number of screw dislocations

2021 ◽  
Vol 45 (4) ◽  
pp. 497-505
Author(s):  
A.A. Kovalev
Keyword(s):  
Gaussian Beam ◽  
Intensity Distribution ◽  
Topological Charge ◽  
Complex Amplitude ◽  
Cosine Function ◽  
Optical Data ◽  
Optical Vortices ◽  
Screw Dislocations ◽  
Arbitrary Power ◽  
Straight Line

In optical data transmission with using vortex laser beams, data can be encoded by the topological charge, which is theoretically unlimited. However, the topological charge of a single separate vortex (screw dislocation) is limited by possibilities of its generating. Therefore, we investigate here three examples of multivortex Gaussian light fields (two beams are form-invariant and one beam is astigmatic) with an unbounded (countable) set of screw dislocations. As a result, such fields have an infinite topological charge. The first beam has the complex amplitude of the Gaussian beam, but multiplied by the cosine function with a squared vortex argument. Phase singularity points of such a beam reside in the waist plane on the Cartesian axes and their density grows with increasing distance from the optical axis. The transverse intensity distribution of such a beam has a shape of a four-pointed star. All the optical vortices in this beam has the same topological charge of +1. The second beam also has the complex amplitude of the Gaussian beam, multiplied by the vortex-argument cosine function, but the cosine is raised to an arbitrary power. This beam has a countable number of the optical vortices, which reside in the waist plane uniformly on one Cartesian axis and the topological charge of each vortex equals to power, to which the cosine function is raised. The transverse intensity distribution of such beam consists of two light spots residing on a straight line, orthogonal to a straight line with the optical vortices. Finally, the third beam is similar to the first one in many properties, but it is generated with a tilted cylindrical lens from a 1D parabolic-argument cosine grating.

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 Topological stability of optical vortices diffracted by a random phase screen

2019 ◽  
Vol 43 (6) ◽  
pp. 917-925 ◽  
Author(s):  
V.V. Kotlyar ◽  
A.A. Kovalev ◽  
A.P. Porfirev
Keyword(s):  
Intensity Distribution ◽  
Topological Charge ◽  
Random Phase ◽  
Optical Vortex ◽  
Phase Screen ◽  
Optical Vortices ◽  
Average Intensity ◽  
Vortex Identification ◽  
Topological Stability ◽  
Random Phase Screen

Here, we theoretically demonstrate that if a Gaussian optical vortex is distorted by a random phase screen (diffuser) then the average intensity distribution in the focus of a spherical lens has a form of a ring with a nonzero value on the optical axis. The radius of the average-intensity ring depends on both the topological charge of an optical vortex and on the diffusing power of the diffuser. Therefore, the value of the topological charge cannot be unambiguously determined from the radius of the average intensity ring. However, the value of the topological charge of the optical vortex can be obtained from the number of points of phase singularity that can be determined using a Shack-Hartmann wavefront sensor. It is also shown that if we use a linear combination of two optical vortices, then the average intensity distribution has local maxima, the number of which is equal to the difference of the topological charges of the two original vortices. The number of these maxima no longer depends on the scattering force of the diffuser and can serve as an indicator for optical vortex identification. Modeling and experiments confirm the theoretical conclusions.

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 Comparison of the focused optical vortices produced by high-aperture phase conventional and spiral zone plates

2021 ◽  
Vol 2103 (1) ◽  
pp. 012175
Author(s):  
A A Savelyeva ◽  
E S Kozlova ◽  
V V Kotlyar
Keyword(s):  
Gaussian Beam ◽  
Focal Plane ◽  
Topological Charge ◽  
Focal Spot ◽  
Zone Plate ◽  
Fdtd Simulation ◽  
Optical Vortices ◽  
Phase Zone ◽  
Linearly Polarized ◽  
Sharp Focusing

Abstract Using the FDTD simulation, sharp focusing of a linearly polarized Gaussian beam with an embedded topological charge m = 3 by a phase zone plate and focusing of a Gaussian beam by a phase spiral zone plate with topological charge m = 3 were studied. The obtained results showed that proposed elements formed different patterns of intensity at a focal plane. The spiral zone plate forms a focal spot with three petals. At a distance of 13.5 μm from the focus, the lobe structure of the intensity (and energy flux) is replaced by an annular distribution.

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.

scholarly journals Astigmatic transformation of a set of edge dislocations embedded in a Gaussian beam

2021 ◽  
Vol 45 (2) ◽  
pp. 190-199
Author(s):  
V.V. Kotlyar ◽  
A.A. Kovalev ◽  
A.G. Nalimov
Keyword(s):  
Angular Momentum ◽  
Gaussian Beam ◽  
Topological Charge ◽  
Focal Length ◽  
Vertical Axis ◽  
Optical Vortices ◽  
Vortex Beam ◽  
Initial Plane ◽  
Parallel Lines ◽  
Edge Dislocations

It is theoretically shown how a Gaussian beam with a finite number of parallel lines of intensity nulls (edge dislocations) is transformed using a cylindrical lens into a vortex beam that carries orbital angular momentum (OAM) and has a topological charge (TC). In the initial plane, this beam already carries OAM, but does not have TC, which appears as the beam propagates further in free space. Using an example of two parallel lines of intensity nulls symmetrically located relative to the origin, we show the dynamics of the formation of two intensity nulls at the double focal length: as the distance between the vertical lines of intensity nulls is being increased, two optical vortices are first formed on the horizontal axis, before converging to the origin and then diverging on the vertical axis. At any distance between the zero-intensity lines, the optical vortex has the topological charge TC=–2, which conserves at any on-axis distance, except the initial plane. When the distance between the zero-intensity lines changes, the OAM that the beam carries also changes. It can be negative, positive, and at a certain distance between the lines of intensity nulls OAM can be equal to zero. It is also shown that for an unlimited number of zero-intensity lines, a beam with finite OAM and an infinite TC is formed.

scholarly journals Topological Charge and Asymptotic Phase Invariants of Vortex Laser Beams

Photonics ◽  
2021 ◽  
Vol 8 (10) ◽  
pp. 445
Author(s):  
Alexey A. Kovalev ◽  
Victor V. Kotlyar ◽  
Anton G. Nalimov
Keyword(s):  
Numerical Simulation ◽  
Data Transmission ◽  
Topological Charge ◽  
Light Field ◽  
Observation Point ◽  
Laser Beams ◽  
Optical Data ◽  
Optical Signals ◽  
Asymptotic Phase ◽  
Ring Approximation

It is well known that the orbital angular momentum (OAM) of a light field is conserved on propagation. In this work, in contrast to the OAM, we analytically study conservation of the topological charge (TC), which is often confused with OAM, but has quite different physical meaning. To this end, we propose a huge-ring approximation of the Huygens–Fresnel principle, when the observation point is located on an infinite-radius ring. Based on this approximation, our proof of TC conservation reveals that there exist other quantities that are also propagation-invariant, and the number of these invariants is theoretically infinite. Numerical simulation confirms the conservation of two such invariants for two light fields. The results of this work can find applications in optical data transmission to identify optical signals.

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