Partially coherent Pearcey–Gauss source with hyperbolic sine correlation of the spatial spectrum

By designing the intricate coherence structure, we are able to create a desired beam profile and trajectory. Our research focus lies on the Fourier plane, specifically emphasizing the coherence of spatial frequencies, and we find it can be seen as a constant system response. A theoretical framework is developed, and experimental studies are conducted to generate a light field of the spatial spectrum with a complex correlation using the pseudo-mode superposition method. We successfully produce partially coherent Pearcey-Gauss beams whose spatial spectrum is hyperbolic sine correlational. Interestingly, these beams maintain the distinctive propagation properties of the Pearcey pattern while exhibiting the remarkable ability to split the mainlobe into two separate lobes.