Partially coherent persistent hollow beams enabled by cross-phase modulation

We propose and experimentally validate a new class of partially coherent random beams, termed partially coherent persistent hollow (PCPH) beams, generated via cross-phase modulation. These beams possess three notable properties: persistent hollow-core profiles during far-field propagation, tunable focusing characteristics, and enhanced robustness against environmental disturbances. While partial coherence improves propagation stability in complex media, it often erodes structured features such as central intensity nulls. By embedding a tailored cross-phase into the source field, PCPH beams maintain well-defined annular intensity profiles, even under extremely low spatial coherence. We systematically investigate the influence of coherence width and beam order on the hollow-core retention and demonstrate that PCPH beams outperform conventional vortex beams in preserving their hollow structure under thermal turbulence. Experimental results confirm the theoretical predictions and reveal strong potential for PCPH beams in optical manipulation, free-space optical communication, and robust beam shaping in adverse conditions.