Orbitalization ellipse via singular value decomposition

Area of Science:

• Optics and Photonics
• Quantum Optics
• Optical Engineering

Background:

• The geometric structure of light beam oscillations in Orbital Angular Momentum (OAM) space is defined by the orbitalization ellipse.
• Understanding this ellipse is crucial for applications utilizing OAM-carrying beams.

Purpose of the Study:

• To introduce a numerical framework for identifying the orbitalization ellipse's shape and orientation.
• To leverage singular value decomposition (SVD) for analyzing OAM beam properties.

Main Methods:

• Constructing a matrix from the beam's OAM components.
• Applying singular value decomposition (SVD) to this matrix.
• Analyzing the singular values and vectors to determine ellipse parameters.

Main Results:

• Demonstrated that SVD provides an effective numerical method for characterizing the orbitalization ellipse.
• Successfully determined the shape and orientation of the ellipse from OAM components.
• The framework offers insights into the geometric structure of OAM beams.

Conclusions:

• Singular value decomposition offers a powerful tool for analyzing the orbitalization ellipse in OAM space.
• This method facilitates the optimization of optical systems employing high-dimensional OAM beams.
• The findings contribute to a deeper understanding of light beam structures and their manipulation.