Tailoring 3D propagation-invariant light via generalized non-annular angular spectrum distributions

For propagation-invariant optical fields along a fixed axis, equal longitudinal wavevectors fundamentally dictate an annular angular spectrum. While this physical constraint inherently restricts the design of optical fields, we present a generalized theoretical framework that expands this regime. By deriving the rigorous mathematical mapping between 3D spatial coordinates and 2D angular wavevectors, we enable the flexible generation of non-diffracting light with customized asymmetric transverse profiles along tailored propagation paths. We experimentally demonstrate this capability using phase multiplexing. Our findings provide a foundational approach for 3D structured light design, offering promising applications in robust free-space optical communication.