Managing focal fields of vector beams with multiple polarization singularities

Area of Science:

• Optics and Photonics
• Electromagnetism
• Light-Matter Interactions

Background:

• Vector beams possess complex polarization structures.
• Polarization singularities are key features influencing beam propagation.
• Understanding tight focusing is crucial for optical applications.

Purpose of the Study:

• To investigate the tight focusing of vector beams with multiple polarization singularities.
• To analyze how singularity characteristics (number, position, topological charge) affect focal fields.
• To demonstrate control over focal field polarization by manipulating singularity distributions.

Main Methods:

• Theoretical analysis of vector beam focusing.
• Numerical simulations of light propagation and focal field formation.
• Examination of polarization states (ellipticity, linear, hybrid) at the focal plane.

Main Results:

• Focal field ellipticity is determined by the spatial distribution of polarization singularities.
• Even-fold rotation symmetry in singularity location and topological charge leads to locally linearly polarized transverse fields.
• Absence of such symmetry results in locally hybrid polarization states.
• Intensity at the focal plane remains unchanged despite alterations in polarization distribution.

Conclusions:

• The spatial arrangement and topological charge of polarization singularities in vector beams precisely control the polarization states of the resulting focal fields.
• This provides a method to engineer focal field polarization without affecting intensity.
• Potential applications in optical trapping, microscopy, and information processing.