Modelization theory for vectorial structured light

Area of Science:

• Optics and Photonics
• Quantum Information Science
• Mathematical Physics

Background:

• Vectorial light beams possess complex polarization and spatial properties.
• Orbital Angular Momentum (OAM) is a key property for advanced optical applications.
• Characterizing structured light beams, especially vectorial ones, is crucial for their manipulation and application.

Purpose of the Study:

• To develop a comprehensive method for characterizing vectorial random light beams carrying OAM.
• To introduce a novel mathematical framework, the Modelization Matrix (MM), for beam analysis.
• To establish a unique geometrical signature for these structured light beams.

Main Methods:

• Defined a 2L-dimensional polar Fourier space for the light beam.
• Introduced the Modelization Matrix (MM) based on scalar radial field correlations.
• Filtered MM elements based on orbital angular momentum (OAM) and polarization components.

Main Results:

• Achieved complete characterization of vectorial, random light beams with OAM.
• Demonstrated that the Modelization Matrix (MM) uniquely encodes the beam's structured state as an ellipse.
• Introduced measures for quantifying modal weight distribution and inter-modal coupling within the beam.

Conclusions:

• The Modelization Matrix (MM) offers a powerful tool for analyzing complex light beams.
• The elliptical signature derived from the MM provides a geometrical insight into beam structure.
• The developed framework facilitates a deeper understanding of modal properties in structured light.