Orbital angular momentum and topological charge of a multi-vortex Gaussian beam

2020 ◽  
Vol 37 (11) ◽  
pp. 1740
Author(s):  
Alexey A. Kovalev ◽  
Victor V. Kotlyar ◽  
Alexey P. Porfirev
Keyword(s):  
Angular Momentum ◽  
Gaussian Beam ◽  
Orbital Angular Momentum ◽  
Topological Charge

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 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 Optimization of the probability of orbital angular momentum for Laguerre-Gaussian beam in Kolmogorov and non-Kolmogorov turbulence

2018 ◽  
Vol 26 (17) ◽  
pp. 21861 ◽  
Author(s):  
Yangsheng Yuan ◽  
Dong Liu ◽  
Zhengxian Zhou ◽  
Huafeng Xu ◽  
Jun Qu ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Gaussian Beam ◽  
Orbital Angular Momentum ◽  
Kolmogorov Turbulence

scholarly journals Measuring the Topological Charge of Orbital Angular Momentum Beams by Utilizing Weak Measurement Principle

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Jing Zhu ◽  
Pei Zhang ◽  
Qichang Li ◽  
Feiran Wang ◽  
Chenhui Wang ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Topological Charge ◽  
Weak Measurement ◽  
Measurement Principle

scholarly journals Effects of the Coupling between the Orbital Angular Momentum and the Temporal Degrees of Freedom in the Most Intense Ring of Ultrafast Vortices

2020 ◽  
Vol 10 (6) ◽  
pp. 1957 ◽  
Author(s):  
Miguel A. Porras
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Pulse Energy ◽  
Topological Charge ◽  
Degrees Of Freedom ◽  
Maximum Energy ◽  
Laser Source ◽  
Source Spectrum ◽  
Vortex Center ◽  
Peak Intensity

It has recently been shown that the temporal and the orbital angular momentum (OAM) degrees of freedom in ultrafast (few-cycle) vortices are coupled. This coupling manifests itself with different effects in different parts of the vortex, as has been shown for the ring surrounding the vortex where the pulse energy is maximum, and also in the immediate vicinity of the vortex center. However, in many applications, the ring of maximum energy is not of primary interest, but the one where the peak intensity of the pulse is maximum, which is particularly true in nonlinear optics applications such as experiments with ultrafast vortices that excite high harmonics and attosecond pulses that also carry OAM. In this paper, the effects of the OAM-temporal coupling on the ring of maximum pulse peak intensity, which do not always coincide with the ring of maximum pulse energy, are described. We find that there is an upper limit to the magnitude of the topological charge that an ultrafast vortex with a prescribed pulse shape in its most intense ring can carry, and vice versa, a lower limit to the pulse duration in the most intense ring for a given magnitude of the topological charge. These limits imply that, with a given laser source spectrum, the duration of the synthesized ultrafast vortex increases with the magnitude of the topological charge. Explicit analytical expressions are given for the ultrafast vortices that contain these OAM-temporal couplings effects, which may be of interest in various applications, in particular in the study of their propagation and interaction with matter.

Topological charge transfer in frequency doubling of fractional orbital angular momentum state

2016 ◽  
Vol 109 (15) ◽  
pp. 151103 ◽  
Author(s):  
R. Ni ◽  
Y. F. Niu ◽  
L. Du ◽  
X. P. Hu ◽  
Y. Zhang ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Charge Transfer ◽  
Orbital Angular Momentum ◽  
Topological Charge ◽  
Frequency Doubling ◽  
Momentum State ◽  
Angular Momentum State
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