Autofocusing properties of partially coherent caustic beams

Partially coherent caustic (autofocusing) beams are critical for many optical applications in complex environments, such as materials processing within scattering media, where precise light control is essential. These beams offer significant advantages as their coherence can be adjusted to enhance performance in adverse environments. However, a key limitation is that reducing coherence typically increases the optical diffraction, weakening the beam's focusing ability and limiting its effectiveness. In this work, we address this issue by generating a circular swallowtail beam on an incoherent background (CSBIB) through the incoherent superposition of weighted cosine modes. Our results demonstrate that the truncated CSBIB exhibits enhanced autofocusing properties under low coherence. A decrease in coherence improves autofocusing by shortening the focal length and increasing the maximum intensity, outperforming traditional partially coherent caustic beams. These findings introduce a new avenue for combining catastrophe optics with coherence engineering, enabling high-order caustic beams optimized for environments where partial coherence is either unavoidable or intentionally engineered.