High-Order Orbital and Spin Hall Effects at the Tight Focus of Laser Beams

Kotlyar, V. V.; Stafeev, Sergey S.; Козлова, Е. С.; Butt, Muhammad Ali

doi:10.3390/photonics9120970

Cited by 8 publications

(5 citation statements)

References 19 publications

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“…The red ellipses denote a positive longitudinal SAM, and the blue ellipses mark negative longitudinal SAM. Because of this, at the focus of both light fields in Equations ( 4) and ( 15), a longitudinal optical spin Hall effect occurs, according to which regions with different-signed longitudinal spins are spatially separated [17,18].…”

Section: Discussion Of the Resultsmentioning

confidence: 99%

Polarization Strips in the Focus of a Generalized Poincaré Beam

Kotlyar,

Kovalev,

Telegin

et al. 2024

Photonics

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We analyze the tight focusing of a generalized Poincaré beam using a Richards–Wolf formalism. Conventional Poincaré beams are superpositions of two Laguerre–Gaussian beams with orthogonal polarization, while the generalized Poincaré beams are composed of two arbitrary optical vortices with rotationally symmetric amplitudes. Analytical relationships for projections of the electric field in the focal plane are derived. Using the superposition of a right-handed circularly polarized plane wave and an optical vortex with a topological charge of −1 as an example, relationships for the intensity distribution and the longitudinal projection of the spin angular momentum vector are deduced. It is theoretically and numerically shown that the original beam has a topological charge of –1/2 and a C-point of circular polarization, and it is generated at the focal plane center, producing an on-axis C-line with a singularity index of –1/2 (a star). Furthermore, when making a full circle of some radius around the optical axis, the major axis vector of polarization ellipse is theoretically and numerically shown to form a one-sided polarization (Möbius) strip of order −3/2, which has three half-twists and a single ‘patching’ in which two oppositely directed vectors of the major axis of polarization ellipse occur close to each other.

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Section: Discussion Of the Resultsmentioning

confidence: 99%

Polarization Strips in the Focus of a Generalized Poincaré Beam

Kotlyar,

Kovalev,

Telegin

et al. 2024

Photonics

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“…These characteristics are SAM and AM, which are not related to each other. We start with the definition of the AM (18) and explicitly write out the quantities included in it:…”

Section: Physical Meaning Of the Third Term In The Equation For The Ammentioning

confidence: 99%

“…The tight focusing of high-order Poincare beams was considered in [16]. In our recent works, we investigated the Hall effect in the tight focus of high-order cylindrical vector beams [17], beams with hybrid inhomogeneous polarization [18], Poincaré beams [19], and optical vortices with circular polarization [20]. Another version of the Hall effect in a sharp focus appears when the center of a vortex laser beam gravity is shifted in the case of its limitation by a diaphragm [21].…”

Section: Introductionmentioning

confidence: 99%

Hall Effect at the Focus of an Optical Vortex with Linear Polarization

et al. 2023

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The tight focusing of an optical vortex with an integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components of the spin angular momentum (SAM) (it was equal to zero) and orbital angular momentum (OAM) (it was equal to the product of the beam power and the TC) vectors averaged over the beam cross-section were separately preserved during the beam propagation. This conservation led to the spin and orbital Hall effects. The spin Hall effect was expressed in the fact that the areas with different signs of the SAM longitudinal component were separated from each other. The orbital Hall effect was marked by the separation of the regions with different rotation directions of the transverse energy flow (clockwise and counterclockwise). There were only four such local regions near the optical axis for any TC. We showed that the total energy flux crossing the focus plane was less than the total beam power since part of the power propagated along the focus surface, while the other part crossed the focus plane in the opposite direction. We also showed that the longitudinal component of the angular momentum (AM) vector was not equal to the sum of the SAM and the OAM. Moreover, there was no summand SAM in the expression for the density of the AM. These quantities were independent of each other. The distributions of the AM and the SAM longitudinal components characterized the orbital and spin Hall effects at the focus, respectively.

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“…На рис. 1 показаны распределения интенсивности I (4), а также продольных составляющих СУМ S z (10), ОУМ L z (14), второго слагаемого в (29) и полного УМ J z (12) в остром фокусе вихревого поля с правой круговой поляризацией и с однородной единичной начальной амплитудой A(θ) = 1 (1) при n = 0, -1, -2 и при следующих параметрах: длина волны λ = 532 нм, фокусное расстояние линзы f = 10 мкм, числовая апертура NA = sin θ 0 = 0,95, область расчета -2 × 2 мкм. Распределения СУМ, ОУМ, второго слагаемого в (29) и полного УМ нормированы на максимальную интенсивность, и соответствующие максимальные значения каждой величины показаны рядом с цветовой шкалой под каждым рисунком.…”

Section: моделированиеunclassified

Focusing a vortex beam with circular polarization: angular momentum

Kotlyar,

Kovalev,

Telegin

2023

Computer Optics

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Based on the Richards-Wolf formalism, we obtain two different exact expressions for the angular momentum (AM) density in the focus of a vortex beam with the topological charge n and with right circular polarization. One expression for the AM density is derived as the cross product of the position vector and the Poynting vector and has a nonzero value at the focus for an arbitrary integer number n. The other expression for the AM density is deduced as a sum of the orbital angular momentum (OAM) and the spin angular momentum (SAM). We reveal that at the focus of the light field under analysis, the latter turns zero at n = –1. While both these expressions are not equal to each other at each point of space, 3D integrals thereof are equal. Thus, exact expressions are obtained for densities of AM, SAM and OAM at the focus of a vortex beam with right-hand circular polarization and the identity for the densities AM = SAM + OAM is shown to be violated. Besides, it is shown that the expressions for the strength vectors of the electric and magnetic fields near the sharp focus, obtained by adopting the Richards-Wolf formalism, are exact solutions of the Maxwell's equations. Thus, Richards–Wolf theory exactly describes the behavior of light near the sharp focus in free space.

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High-Order Orbital and Spin Hall Effects at the Tight Focus of Laser Beams

Cited by 8 publications

References 19 publications

Polarization Strips in the Focus of a Generalized Poincaré Beam

Polarization Strips in the Focus of a Generalized Poincaré Beam

Hall Effect at the Focus of an Optical Vortex with Linear Polarization

Focusing a vortex beam with circular polarization: angular momentum

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