Topological encryption enabled by longitudinal component of structured light field

Three-dimensional (3D) vectorial distribution of electromagnetic field of light is a crucial characteristic in modern optics, providing increasing degrees of freedom for light–matter interaction, optical communication, encryption, and so on. However, the longitudinal polarization component of light is often neglected under the paraxial approximation as it is much weaker compared with the transverse component. We aim to demonstrate that even under the paraxial condition, the longitudinal component of a structured light field can still be customized and effectively utilized. We proposed a theoretical approach to customize the longitudinal field under the paraxial condition, enabling the generation of the longitudinal field with various topological structures. Furthermore, the topological encoding and encryption enabled by the longitudinal field are achieved by each knotted/linked topological structure as an information carrier, showing that although the longitudinal field is weak under the paraxial condition, its topological structure can still be recovered through the related transverse field. Our work emphasizes the possibility of fully utilizing the longitudinal field under the paraxial condition, which has long been overlooked. It provides a new vitality to the longitudinal field and highlights its potential in information encryption, optical communication, and light–matter interaction.