Quantized Orbital Angular Momentum from Discrete Chaotic Phase Surfaces

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.