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 A minimal subwavelength focal spot for the energy flux

2021 ◽  
Vol 5 (45) ◽  
pp. 685-691
Author(s):  
S.S. Stafeev ◽  
V.D. Zaicev
Keyword(s):  
Energy Flux ◽  
Topological Charge ◽  
Focal Spot ◽  
Polarized Light ◽  
Spot Size ◽  
Optical Vortices ◽  
Matter Interaction ◽  
Linearly Polarized ◽  
Light Matter Interaction ◽  
Tight Focus

It is shown theoretically and numerically that circularly and linearly polarized incident beams produce at the tight focus identical circularly symmetric distributions of an on-axis energy flux. It is also shown that the on-axis energy fluxes from radially and azimuthally polarized optical vortices with unit topological charge are equal to each other. An optical vortex with azimuthal polarization is found to generate the minimum focal spot measured for the intensity (all other parameters being equal). Slightly larger (by a fraction of a percent) is the spot size calculated for the energy flux for the circularly and linearly polarized light. The spot size in terms of intensity is of importance in light-matter interaction, whereas the spot size in terms of energy flux affects the resolution in optical microscopy.

scholarly journals Sharp Focusing of a Hybrid Vector Beam with a Polarization Singularity

Photonics ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 227
Author(s):  
Victor V. Kotlyar ◽  
Sergey S. Stafeev ◽  
Anton G. Nalimov
Keyword(s):  
Focal Plane ◽  
Topological Charge ◽  
Light Field ◽  
Stokes Vector ◽  
Elliptical Polarization ◽  
Intensity Pattern ◽  
Singularity Index ◽  
Sharp Focusing ◽  
New Type ◽  
Local Polarization

The key result of this work is the use of the global characteristics of the polarization singularities of the entire beam as a whole, rather than the analysis of local polarization, Stokes and Poincare–Hopf indices. We extend Berry’s concept of the topological charge of scalar beams to hybrid vector beams. We discuss tightly focusing a new type of nth-order hybrid vector light field comprising n C-lines (circular polarization lines). Using a complex Stokes field, it is shown that the field polarization singularity index equals n/2 and does not preserve in the focal plane. The intensity and Stokes vector components in the focal plane are expressed analytically. It is theoretically and numerically demonstrated that at an even n, the intensity pattern at the focus is symmetrical, and instead of C-lines, there occur C-points around which axes of polarization ellipses are rotated. At n = 4, C-points characterized by singularity indices 1/2 and ‘lemon’-type topology are found at the focus. For an odd source field order n, the intensity pattern at the focus has no symmetry, and the field becomes purely vectorial (with no elliptical polarization) and has n V-points, around which linear polarization vectors are rotating.

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).

Two tailorable two-arms-cross patterns with equal intensity generated by a composite square zone plate

2020 ◽  
Vol 34 (05) ◽  
pp. 2050072
Author(s):  
Tian Xia ◽  
Shubo Cheng ◽  
Shaohua Tao
Keyword(s):  
Topological Charge ◽  
Construction Method ◽  
Zone Plate ◽  
Optical Vortices ◽  
Laser Alignment ◽  
Zone Plates ◽  
Potential Applications ◽  
Hollow Beams ◽  
Spiral Phase

A composite square zone plate (CSZP) is proposed to generate two two-arms-cross patterns with equal intensity and arbitrarily designed axial positions. Moreover, the CSZP with the spiral phase has two square optical vortices located at the arbitrary positions. In addition, we find that the same topological charge of twin square optical vortices for the CSZP follows a modulo-4 transmutation rule. The construction method of proposed zone plates is illustrated in detail. We prove numerically and experimentally that the CSZP and spiral-phase CSZP produce two tailorable two-arms-cross patterns with equal intensity and square optical vortices, respectively. The proposed zone plate can be used to generate hollow beams and have potential applications in infrared antennas and laser alignment systems.

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 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 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.

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