We investigate the dynamics of partially coherent Pearcey–Gauss beams propagating in free space, theoretically and experimentally. They are produced by introducing the degree of coherence (DOC) function with Gaussian Schell-model correlation into the light source in the frequency domain. Under a nearly incoherent state, the oscillation of the sidelobe turns smooth, and the intensity distribution concentrates on the mainlobe. Particularly, partially coherent Pearcey–Gauss beams would maintain the inherent properties of autofocusing performance and inversion effect without diminishing the autofocusing distance and form-invariable propagation. Moreover, the opening angle and the shift of peak intensity of the beams can be controlled by the binary parabola in the spectrum distribution of the Pearcey function. Our experimental results are in great agreement with the theoretical analysis.

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The propagation dynamics of a chirped Airy vortex (CAiV) beam with x-polarization in uniaxial crystals orthogonal to the optical axis is studied analytically and numerically. The effect of the ratio of extraordinary and ordinary refractive indices, the chirp parameter, as well as the propagation distance is analyzed, which shows that the focused position of the CAiV beams can be controlled through changing the ratio of the extraordinary and ordinary refractive indices. In addition, with the propagation distance increasing, the asymmetry of the intensity and the angular momentum of the CAiV beam during propagation becomes much more visible. The variation of the chirp parameters can change the attenuation velocity of the vortex as well.

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In this paper, generalized ring Pearcey beams are proposed theoretically and their corresponding generation is demonstrated experimentally by use of the double‐phase method. Generalized ring Pearcey beams evolve into circular or elliptical ring Pearcey beams, depending on the elliptical parameter. It is shown that the autofocusing properties of such beams can be effectively controlled by adjusting the elliptical parameter and the spatial distribution factor. To perform a more comprehensive investigation, the radially polarized forms of the beams are also realized in experiments. It is found that for both cases of vector and scalar, the peak intensity of the beams at the autofocusing plane undergo a dramatic increase as compared with that at the initial plane. Finally, by taking optical trapping as an example, it is proved that generalized ring Pearcey beams could be a productive instrument for industrial applications.