Quantum-optical photonic analogies as a tool for free-space propagation of a Pearcey beam

The theoretical and experimental generation of the Pearcey–Gaussian beam has inspired the study of a broader family of related beams, such as the circular Pearcey beam and, more recently, the abruptly dual auto-focusing circular Pearcey edge dislocation beam, which exhibits both abrupt dual auto-focusing and enhanced self-healing capabilities, paving the way for various applications such as optical communication, optical metrology, and optical tweezers. In this context, we present the analytical solution for the paraxial propagation of a finite-energy Pearcey beam using the $SU\left(2\right)$ Lie group. This group-theoretical approach provides a robust and general framework for addressing propagation problems in optics and photonics. Although the Pearcey beam is a well-known example, this is, to our knowledge, the first time it has been analytically treated through this method.