Spin Hall Effect in the Paraxial Light Beams with Multiple Polarization Singularities

Area of Science:

• Optics
• Optical Engineering
• Nanotechnology

Background:

• Micromachines can be controlled using light, particularly structured light featuring polarization singularities.
• Investigating the behavior of light beams with complex polarization is crucial for advancing optical manipulation technologies.

Purpose of the Study:

• To analyze a paraxial vectorial Gaussian beam with multiple polarization singularities.
• To understand the spatial evolution of spin angular momentum (SAM) density and the spin Hall effect in such beams.
• To determine conditions for maximizing SAM density and its relation to beam parameters.

Main Methods:

• Superposition of a cylindrically polarized Laguerre-Gaussian beam and a linearly polarized Gaussian beam.
• Analysis of beam propagation and the generation of alternating SAM density regions.
• Derivation of expressions for maximal SAM magnitude, optimal propagation distance, and singularity circle radius.

Main Results:

• Propagation leads to alternating SAM density areas of opposite signs, demonstrating the spin Hall effect.
• Maximal SAM density occurs on a specific radius circle in each transverse plane.
• An approximate expression for the distance to the plane with maximal SAM density was derived.
• Optimal singularity circle radius for maximal SAM density corresponds to equal energies of the constituent beams.
• Orbital angular momentum density is directly proportional to SAM density, scaled by -m/2.

Conclusions:

• The spin Hall effect arises from the differential divergence of the constituent beams.
• The findings provide a basis for designing micromachines with optically driven elements.
• Understanding SAM dynamics in structured light is key for advanced optical control applications.