Electron four-petal Lorentz–Gauss vortex beam

Abstract

Inspired by the rapid advancements in structured laser beams, we explore the intriguing characteristics of structured wave packets in electron optics. With potential applications in electron beam lithography and electron beam welding, the ability to generate electron beams with higher tunability and self-healing properties is of great interest. In this paper, we propose a new class of beam, termed the electron four-petal Lorentz–Gauss vortex beams (EFPLGVBs), and numerically study its propagation characteristics in free space and a constant magnetic field, respectively. The EFPLGVB exhibits flexible tunability in its propagation behaviors, with its focusing period, maximum probability density, and evolution dynamics being adjustable via parameters, the magnetic flux density, the four-petal term, and the topological charge. Adjustment of the magnetic flux density yields up to a 62.7-fold increase in the maximum probability density, indicating significantly enhanced focusing strength. In addition, the EFPLGVB shows superior self-healing ability. The self-healing ability is investigated in different contexts, including different media and the presence of a Gaussian absorption obstacle at varying positions. Quantitative assessments indicate an improvement in the self-healing ability, as evidenced by a maximum increase of 68.6% in the similarity index and a maximum decrease of 85.5% in the mean-squared error. Upon encountering an obstacle, the EFPLGVB exhibits a remarkable capacity for self-healing, effectively restoring its original state as if the obstacle had never been encountered. The high tunability and the superior self-healing ability underscore the EFPLGVB’s potential for robust applications in electron optics.