Auto-focusing and self-healing of symmetric odd-Pearcey Gauss beams

In this study, a new, to the best of our knowledge, form of odd-Pearcey Gauss beams with peculiar characteristics is presented. Compared with the Pearcey beam, the odd-Pearcey Gauss beam is symmetrical about the origin. At the initial stages, the odd-Pearcey Gauss beam propagates with a main central lobe and some residual spots that autofocus to the center, and then splits into two off-axis parabolic lobes after the autofocus finishes. Furthermore, we also introduce the soft well function to investigate the propagation profiles of the odd-Pearcey Gauss beams passing through it with different calibers and discuss the influence of the Gaussian waist width towards the focal distance and the propagation form of the odd-Pearcey Gauss beam. We also enumerate some potential and possible applications based on its peculiar characteristics.