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Beam manipulation is of paramount importance in wave engineering, enablingdiverse beam shapes like pencil beams, flat-top beams, and isoflux beams tocater to various application missions. Among the beams, shaping flat-top andisoflux beams remains challenging with the traditional synthesis approachesthat mainly rely on optimization algorithms. Here, we develop modulatedmetasurfaces to efficiently generate flat-top and isoflux beams from the firstprinciple of field superposition with negligible optimizations, by performingphase symmetry operations. The theoretical analysis not only facilitates theshaping of 1D and 2D flat-top and isoflux beams but also exhibits controllablebeamwidths. Experimental validation confirms the efficacy of the phase symmetryoperations in generating flat-top beams with adjustable beamwidths. The conceptof phase symmetry operations can be extended to other vectorial components,offering potential applications for the manipulation of various wave types suchas acoustic waves, water surface waves, and beyond, thereby advancing relatedapplications.

Efficient Beam Manipulation with Phase Symmetry Operations on Modulated Metasurfaces