Efficient Beam Manipulation with Phase Symmetry Operations on Modulated Metasurfaces

Beam manipulation is of paramount importance in wave engineering, enabling diverse beam shapes like pencil beams, flat-top beams, and isoflux beams to cater to various application missions. Among the beams, shaping flat-top and isoflux beams remains challenging with the traditional synthesis approaches that mainly rely on optimization algorithms. Here, we develop modulated metasurfaces to efficiently generate flat-top and isoflux beams from the first principle of field superposition with negligible optimizations, by performing phase symmetry operations. The theoretical analysis not only facilitates the shaping of 1D and 2D flat-top and isoflux beams but also exhibits controllable beamwidths. Experimental validation confirms the efficacy of the phase symmetry operations in generating flat-top beams with adjustable beamwidths. The concept of phase symmetry operations can be extended to other vectorial components, offering potential applications for the manipulation of various wave types such as acoustic waves, water surface waves, and beyond, thereby advancing related applications.