Titlebook: Optical Hall Effect in the Sharp Focus of Laser Light; Victor V. Kotlyar,Alexey A. Kovalev,Anton G. Nalim Book 2024 The Editor(s) (if appl

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Cylindrical Fractional-Order and Double-Index Vector Laser Beams,Cylindrical vector beams (CVBs) (Zhan in Adv. Opt. Photon. 1:1–57, 2009) are now widely used because of the unique properties they exhibit in tight focusing.

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Hall Effect in Paraxial Laser Beams,In micromachines, elements can be driven by light and optical vortex beams are widely adopted in optical tweezers. One of the natural generalizations of optical vortex beams are light fields with multiple vortices.

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Spin Hall Effect at the Focus for Light with Linear Polarization,lect the vector nature of the light wave. In this case, to calculate the light field at the focus, it is necessary to take into account all the components of the strength of the electric and magnetic field of the light wave.

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Spin Hall Effect at the Focus for Light with Circular Polarization,ett. A 333:181–186, 2004; Bliokh and Bliokh in Phys. Rev. Lett. 96:073903, 2006) the theory of the Hall effect for light was developed. In (Kavokin et al. in Phys. Rev. Lett. 95:136601, 2005; Hosten and Kwiat in Science 319:787–790, 2008) the Hall effect in optics was experimentally discovered.

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Focusing of Cylindrical Vector Beams and Their Modifications,arch In this section, we derive the Poincare-Hopf and Stokes indices . and σ for .th-order cylindrical vector beams. We show that in the source plane of the beams (where the on-axis field component is zero),

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Sharp Focusing of Modified Cylindrical Vector Laser Beams, R Soc Lond A 253:358–379, 1959). Numerous follow-up publications relied on the Richards-Wolf formalism to look into the behavior of more general electromagnetic fields with various polarization states.