Not yet reviewed by Pith; the record is open.

Beam shaping techniques enable tailored beam trajectories, offering unprecedented connectivity opportunities in wireless communications. Current approaches rely on flat apertures, which limit trajectory flexibility due to inherent geometric constraints. To overcome such restrictions, we propose adopting curved apertures as a more versatile alternative for beam shaping. We introduce a novel formulation for wave trajectory engineering compatible with arbitrarily shaped apertures. Theoretical and numerical analyses demonstrate that curved apertures offer improved control over wave propagation, are more resilient to phase control constraints, and achieve higher power density across a wider portion of the desired beam trajectory than flat apertures.