Angular momentum redirection phase of vector beams in a non-planar geometry.

Area of Science:

• Optics and Photonics
• Quantum Optics

Background:

• Geometric phases are acquired by electric fields propagating along non-planar paths.
• Previously, geometric phases were linked to spin redirection and spatial mode transformation independently.
• These transformations resulted in separate rotations of polarization and intensity profiles.

Purpose of the Study:

• To investigate the non-planar propagation of scalar and vector light fields.
• To demonstrate the simultaneous rotation of polarization and intensity profiles.
• To analyze the relationship between geometric phase and beam properties.

Main Methods:

• Studying the non-planar propagation of light fields.
• Analyzing scalar and vector light fields.
• Deriving the geometric phase based on topological charge and helicity.

Main Results:

• Polarization and intensity profiles rotate by the same angle during non-planar propagation.
• The acquired geometric phase is proportional to j = ℓ + σ, where ℓ is topological charge and σ is helicity.
• Radial and azimuthally polarized beams with j = 0 are identified as system eigenmodes unaffected by the geometric path.

Conclusions:

• Non-planar propagation induces a unified rotation of polarization and intensity profiles.
• The geometric phase offers a new parameter (j = ℓ + σ) for controlling light.
• Findings are relevant for photonic spin Hall effects, vector microscopy, and topological optical communication systems.