Three-dimensional polarization states of monochromatic light fields

Area of Science:

• Optics and Photonics
• Electromagnetism
• Mathematical Physics

Background:

• Describing light polarization in three dimensions (3-D) is crucial for understanding light-matter interactions.
• Existing models often focus on 2-D polarization states, limiting analysis of complex light fields.
• Generalized Jones vectors (GJVs) offer a framework for representing arbitrary 3-D polarization states.

Purpose of the Study:

• To determine 3-D polarization states using generalized Jones vectors (GJVs).
• To analyze the geometrical parameters of 3-D electric field vibrations.
• To introduce a 3-D generalized Jones calculus for characterizing light scattering.

Main Methods:

• Mathematical derivation of 3-D polarization states based on geometrical parameters of the electric field.
• Analysis of polarization states resulting from the superposition of orthogonal field components.
• Introduction of the 3×3 generalized Jones matrix for describing elastic scattering.

Main Results:

• Quantification of distinct linear and circular polarization states in 3-D.
• Identification of contours of equal ellipticity and inclination in 2-D phase space for specific 3-D polarization states.
• Formulation of the generalized Jones calculus for near-field scattering by nano-objects.

Conclusions:

• The study provides a comprehensive framework for describing 3-D light polarization states using GJVs.
• The findings offer new insights into the geometry of polarization in three dimensions.
• The generalized Jones calculus is a powerful tool for analyzing light scattering phenomena.