Quantized Orbital Angular Momentum from Discrete Chaotic Phase Surfaces

TL;DR

This paper introduces a new theory for generating orbital angular momentum (OAM) using chaotic phase surfaces with discrete biases, establishing selection rules and universal scaling laws validated by simulations.

Contribution

It develops a theoretical framework for OAM generation from chaotic surfaces with discrete biases, revealing selection rules and universal scaling behavior.

Findings

Ensemble-averaged OAM exists only at integer bias values.

Monte Carlo simulations confirm the selection rules with high suppression of forbidden levels.

Analytical expressions accurately predict the OAM power spectrum and scaling behavior.

Abstract

We present a new theory for orbital angular momentum (OAM) generation by chaotic phase surfaces with discrete integer bias distributions. We derive fundamental selection rules that determine which OAM modes can be coherently generated. Our analysis shows that ensemble-averaged OAM exists only when the bias parameter takes integer values that match the discrete OAM eigenspace, creating "allowed" and "forbidden" OAM levels. We derive analytical expressions for the OAM power spectrum and demonstrate universal caling behavior within the allowed manifold. These theoretical predictions are validated by comprehensive Monte Carlo simulations, which confirm the selection rules with a forbidden-level suppression factor exceeding 10^4 and demonstrate the universal scaling with exceptional accuracy.