Fig. 1

Concept of studied metagratings. a Schematic diagram of the proposed PGM consisting of periodically repeated supercells. b Geometric topology of the supercell composed of m groups of unit cells. The regions in gray are sound-hard materials and the regions with blue colors are gradient index materials for generating gradient phase shift along +x-direction. c Trajectories of rays propagating in two adjacent unit cells. d Sketch map of diffraction mechanism and multiple reflections effect in the jth unit cell in (c). Each unit cell can be regarded as a Fabry–Perot (FP) resonator, inside which the wave oscillates back and forth L times before reaching a resonance condition that determines the reflection or transmission. The higher order diffraction depends on the propagation number L and the number m of unit cells in a supercell