Abstract
The geometric structure of light beam oscillations in the Orbital Angular Momentum (OAM) space, i.e., the space spanned by the spiral basis eil phi, l, and phi being the OAM index and azimuthal angle, respectively, is determined by the orbitalization ellipse [ Opt. Lett. 50, 391 (2025) 10.1364/OL.545613]. Here, we show that applying singular value decomposition to a matrix constructed from the beam's OAM components provides an insightful numerical framework for finding the shape and orientation of the ellipse, hence benefiting the optimization of optical systems leveraging OAM-carrying beams of high dimensions. (c) 2025 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.