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Porfirev A, Khonina S, Ustinov A, Ivliev N, Golub I. Vectorial spin-orbital Hall effect of light upon tight focusing and its experimental observation in azopolymer films. Opto-Electron Sci 2, 230014 (2023). doi: 10.29026/oes.2023.230014
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Vectorial spin-orbital Hall effect of light upon tight focusing and its experimental observation in azopolymer films
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Abstract
Hall effect of light is a result of symmetry breaking in spin and/or orbital angular momentum (OAM) possessing optical system and is caused by e.g. refractive index gradient/interface between media or focusing of a spatially asymmetrical beam, similar to the electric field breaking the symmetry in spin Hall effect for electrons. The angular momentum (AM) conservation law in the ensuing asymmetric system dictates redistribution of spin and orbital angular momentum, and is manifested in spin-orbit, orbit-orbit, and orbit-spin conversions and reorganization, i.e. spin-orbit and orbit-orbit interaction. This AM restructuring in turn requires shifts of the barycenter of the electric field of light. In the present study we show, both analytically and by numerical simulation, how different electric field components are displaced upon tight focusing of an asymmetric light beam having OAM and spin. The relation between field components shifts and the AM components shifts/redistribution is presented too. Moreover, we experimentally demonstrate, for the first time, to the best of our knowledge, the spin-orbit Hall effect of light upon tight focusing in free space. This is achieved using azopolymers as a media detecting longitudinal or z component of the electrical field of light. These findings elucidate the Hall effect of light and may broaden the spectrum of its applications. -
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References
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Porfirev A, Khonina S, Ustinov A, Ivliev N, Golub I. Vectorial spin-orbital Hall effect of light upon tight focusing and its experimental observation in azopolymer films. Opto-Electron Sci 2, 230014 (2023). doi: 10.29026/oes.2023.230014
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Figure 1.
Numerical investigation of vectorial spin-orbital Hall effect of light upon tight focusing: (a) spatial frequency domain in Cartesian coordinates, (b–d) on- and off-axis propagation of a circularly polarized first-order optical vortex beam. The symmetry breaking in the longitudinal component and extrinsic OAM
$L_z^{{\rm{ext}}}$ -
Figure 2.
Comparison of asymmetry in focusing a shifted vortex beam with m=±1 order for x-linear polarization.
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Figure 3.
Comparison of asymmetry in focusing a shifted vortex beam with m=±2 order for x-linear polarization.
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Figure 4.
Comparison of asymmetry in focusing a shifted vortex beam with m=±1 order for y-linear polarization.
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Figure 5.
Comparison of asymmetry in focusing a shifted vortex beam with m=±2 order for y-linear polarization.
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Figure 6.
Comparison of asymmetry in focusing a shifted vortex beam with m=+1 order for “±” -circular polarization.
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Figure 7.
Comparison of asymmetry in focusing a shifted vortex beam with m=+2 order for “±”-circular polarization.
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Figure 8.
The experimental setup for laser printing. Laser is a solid-state laser (λ=532 nm); L1, L2, L3, L4, L5, and L6 are spherical lenses (f1=25 mm, f2=150 mm, f3=500 mm, f4=400 mm, f5=150 mm, and f6=50 mm); M1, M2, M3, M4, M5, and M6 are mirrors, SLM is a reflective spatial light modulator (HOLOEYE PLUTO VIS); D is a circular diaphragm, BS is a beam splitter, PE is a polarizing element (a half wave or a quarter wave plate), MO1 and MO2 are microobjectives (NA=0.65 and 0.1); S is a glass substrate with a thin azopolymer film; xyz is a three-axis (XYZ) translation stage, IB is a light bulb, F is a neutral density filter, CAM is a ToupCam UCMOS08000KPB video camera. The inset shows an example of a phase mask realized with the SLM and used for the generation of a first-order OV beam.
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Figure 9.
Laser patterning of an azopolymer thin film with x-linearly polarized on- and off-axis OV beams of ±1 order. The right part of the figure shows the experimentally generated intensity distribution, numerically calculated distribution of
$ {\nabla } $ -
Figure 11.
Laser patterning of an azopolymer thin film with right- and left handed circularly polarized on- and off-axis OV beams of ±1 order. The right part of the figure shows the experimentally generated intensity distribution, numerically calculated distribution of
$ {\nabla }$ -
Figure 10.
Laser patterning of an azopolymer thin film with y-linearly polarized on- and off-axis OV beams of ±1 order. The right part of the figure shows the experimentally generated intensity distribution, numerically calculated distribution of
$ {\nabla }$
