Synthesis of fractional-order non-uniformly correlated beams with controllable parameters

A class of random, stationary, scalar beams with spatially varying correlations called Fractional-order non-uniformly correlated (FNUC) beams is introduced as an extended version of conventional non-uniformly correlated (NUC) beams. The evolution behavior of the coherence and average intensity distribution of the beams during free-space propagation is numerically analyzed in detail by means of the pseudo-mode decomposition and fast Fourier transform algorithm. We demonstrate that the FNUC beams exhibit the peculiar self-focusing properties during propagation and allow control of their focusing ability and focal depth through the newly introduced parameter (fractional-order number) and the radial phase. Furthermore, an experiment involving a programmable spatial light modulator is carried out to generate the FNUC beams with a controllable fractional-order number. The intensity evolution and self-healing properties of the beams are experimentally studied when blocked by an obstacle. The experimental results agree well with the theoretical predictions. The FNUC beams may find potential applications in optical manipulation and beam shaping, offering a new paradigm for designing customizable random sources with tailored propagation dynamics.