The ability to engineer the distribution of light with high precision is the key to many applications in optics, ranging from microscopy and material manipulation to optical metrology and telecommunication. Instead of traditional manipulation of light based on using diffractive optical elements such as binary phase or amplitude masks, we demonstrate a promising approach in which a light beam with custom coherence has the capacity of forming specified intensity distribution without additional optical elements. By devising a nontrivial cosine pseudo-Schell-model correlated source, we show theoretically that a controllable donut-shaped beam has almost no vortex phase dependence. Interestingly, a remarkable anomalous self-focusing phenomenon is experimentally observed during propagation, which is irrespective of the phase and the coherence parameter. In particular, tunable intensity distributions with high precision (e.g., Gaussian beam, flat-topped beam, and donut beams) are derived only by simple control of the coherence parameter. The result presents a bright prospect for manipulating light using source coherence and promotes a wide range of applications.

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