Diffraction regimes of phase gradient metasurfaces in background media with symmetry breaking

We theoretically investigate the far-field diffraction patterns of phase gradient metagratings (PGMs) in symmetry-breaking background media. We will show that the breaking of spatial symmetry induces breaking of the corresponding diffraction momentum space such that wave diffraction exhibits more complex behavior in the symmetry-broken case than in the symmetric case. Three different diffraction regimes are identified for different asymmetry ratios γ=n₂/n₁ (where n₂/n₁ is the refractive index of the transmission/reflection medium). Specifically, a wave momentum gap emerges in the local diffraction region of γ < 0.5, providing physics to control the diffraction transition from the transmission side to the reflection side or vice versa; wave momentum overlap can be observed in the multiple diffraction region of γ > 1.5, resulting in simultaneous coupling of light to multiple diffraction orders in transmission or reflection space channels, thereby providing a way to realize multiple-beam-steering or splitting effects. Our work provides a theory for using PGMs to manipulate the transport of light or sound waves across interfaces between different media.