Coherent OAM generation from discrete chaotic phase surfaces.

We demonstrate coherent orbital angular momentum (OAM) generation from chaotic phase screens with discrete integer-valued azimuthal bias. Through Fourier analysis, we prove that coherent OAM amplitude is nonzero only when the ensemble-averaged complex phase factor has corresponding integer Fourier coefficients. For discretized Gaussian bias, the coherent power follows a universal exponential profile in scaled coordinates, while continuous bias yields sinc-filtered spectra with algebraic decay. Monte Carlo simulations validate these selection rules, showing forbidden level suppression exceeding four orders of magnitude and correlation with theory above 99.9 percent. The discrete statistical structure enables deterministic control of coherent OAM content, with immediate applications in optical communications and sensing via spatial light modulators or metasurfaces. Beyond static scalar beams, we show that coherent selection extends to spin-orbit coupled vector beams and enables time-multiplexed coherent filters via dynamic discrete bias, both of which elevate practical utility without additional hardware complexity.