Measuring the topological charge of optical vortices: from the orbital angular momentum of individual photons to the angular uncertainty principle

2004 ◽  
Author(s):  
J. Courtial ◽  
M. Padgett ◽  
J. Leach ◽  
E. Yao ◽  
S. Barnett ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Uncertainty Principle ◽  
Topological Charge ◽  
Optical Vortices

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 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 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 High-Efficiency Spin-Related Vortex Metalenses

Nanomaterials ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1485
Author(s):  
Wei Wang ◽  
Ruikang Zhao ◽  
Shilong Chang ◽  
Jing Li ◽  
Yan Shi ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Topological Charge ◽  
High Efficiency ◽  
Infrared Band ◽  
Mid Infrared ◽  
Integrated Devices ◽  
Vortex Beams ◽  
Topological Charges

In this paper, one spin-selected vortex metalens composed of silicon nanobricks is designed and numerically investigated at the mid-infrared band, which can produce vortex beams with different topological charges and achieve different spin lights simultaneously. Another type of spin-independent vortex metalens is also designed, which can focus the vortex beams with the same topological charge at the same position for different spin lights, respectively. Both of the two vortex metalenses can achieve high-efficiency focusing for different spin lights. In addition, the spin-to-orbital angular momentum conversion through the vortex metalens is also discussed in detail. Our work facilitates the establishment of high-efficiency spin-related integrated devices, which is significant for the development of vortex optics and spin optics.

scholarly journals Sectorial perturbation of vortex beams: Shannon entropy, orbital angular momentum and topological charge

2019 ◽  
Vol 43 (5) ◽  
pp. 723-734 ◽  
Author(s):  
A.V. Volyar ◽  
M.V. Bretsko ◽  
Ya.E. Akimova ◽  
Yu.A. Egorov ◽  
V.V. Milyukov
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Shannon Entropy ◽  
Topological Charge ◽  
External Perturbation ◽  
Informational Entropy ◽  
Large Perturbation ◽  
Wide Range ◽  
Vortex Beams ◽  
Computing Measuring

Transformations of the vortex beams structure subjected to sectorial perturbation were theoretically and experimentally studied. The analysis was based on computing (measuring) the vortex spectrum that enables us to find the orbital angular momentum (OAM) and Shannon entropy (informational entropy). We have revealed that, in the general case, the number of vortices caused by an external perturbation is not related to the topological charge. For arbitrary perturbation, the topological charge remains equal to the initial topological charge of the unperturbed vortex beam. Growth of the vortex number induced by perturbations is associated with the optical uncertainty principle between the sectorial angle and the OAM. The computer simulation has shown that OAM does not depend on the number of vortices induced by perturbations. Moreover, two maxima are formed both in the positive and negative regions of the vortex spectrum. As a result, the OAM does not practically change in a wide range of perturbation angles from 0 to 90 °. However, at large perturbation angles, when the energy is almost equally redistributed between the vortex modes with opposite signs of the topological charge, the OAM rapidly decreases. At the same time, the Shannon entropy monotonically increases with growing perturbation angle. This is due to the fact that the entropy depends only on the number of vortex states caused by external perturbations.

scholarly journals Topological charge and angular momentum of light beams carrying optical vortices

2004 ◽  
Author(s):  
M S Soskin ◽  
V N Gorshkov ◽  
M V Vasnctsov ◽  
J T Malos ◽  
N R Heckenberg
Keyword(s):  
Angular Momentum ◽  
Topological Charge ◽  
Optical Vortices ◽  
Light Beams
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