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

Abstract

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.

A Rotationally Symmetric Multifocal Pearcey Beam with a Polygonal Profile

“…Subsequently the auto‐focusing circle Pearcey beams with circularly symmetric distribution is presented. [ 3 ] In addition by modulating the Pearcey beam, some new kinds of auto‐focusing beams have been generated successively, such as the canonical vortex‐modulated chirped circular Pearcey Gaussian beam, [ 4 ] the odd Pearcey Gaussian beam, [ 5 ] and the partially coherent Pearcey beam. [ 6 ] Moreover, it is worth mentioning that the chirped circular Pearcey Gaussian beam (CCPGB) has the same circularly symmetric transverse distribution, which can auto‐focus abruptly during propagation and rotate abruptly and quickly in the focal point.…”

Dynamic Optical Vortex Trajectory Guided by the Symmetric Pearcey Gaussian Vortex Beam in the Uniformly Moving Parabolic Potential

“…[6] Subsequently, many types of new light fields based on the Pearcey beam have been studied extensively, including dual Pearcey, [7] circle Pearcey beam, [8] odd-symmetric DOI: 10.1002/andp. 202300167 Pearcey beams, [9] symmetric Pearcey Gaussian beams, [10] and so on. Therefore, these remarkable properties from different types of new light fields drive the application in the field of optics, such as optical imaging [11] and optical trapping.…”

“…[ 3 ] After that, the Pearcey beam received a great deal of attention because it possesses some exciting propagation properties similar to the self‐healing of the Airy beam, [ 4 ] the autofocusing of the abruptly autofocusing beam, [ 5 ] the form‐invariant of the Bessel beam. [ 6 ] Subsequently, many types of new light fields based on the Pearcey beam have been studied extensively, including dual Pearcey, [ 7 ] circle Pearcey beam, [ 8 ] odd‐symmetric Pearcey beams, [ 9 ] symmetric Pearcey Gaussian beams, [ 10 ] and so on. Therefore, these remarkable properties from different types of new light fields drive the application in the field of optics, such as optical imaging [ 11 ] and optical trapping.…”

Paraxial Propagation Properties of Radially Polarized Odd‐Pearcey Gaussian Beams in Free Space

“…As Pearcey beams have been intensively investigated recently, their paraxial and non-paraxial propagation properties are increasingly reported. Exactly, circular Pearcey beams (CPBs), [29] radially polarized circle Pearcey vortex beams (RPCPVs), [30] odd-Pearcey Gaussian beams (OPGBs) [31] have been proposed and studied successively. Despite the importance of Pearcey beams, there remains a paucity of survey on the paraxial propagation of radially polarized odd-Pearcey Gaussian beams (RPOPGBs).…”

“…The radially polarized beams are essential for a wide range of technologies, and OPGBs are observed for excellent auto-focusing and self-healing properties during propagation. [31] Therefore, further studies on the propagation of the RPOPGBs in free space are valuable. Generated on the extended Pearcey function, the RPOPGBs can be analyzed within catastrophe theory.…”