A theoretical study on the conversion efficiencies of gradient meta-surfaces

It was shown in a recent work (Sun S. et al., Nat. Mater., 11 (2012) 426) that an ideal gradient meta-surface (GM) can convert an incident propagating wave (PW) to an obliquely outgoing PW or even a surface wave (SW) with nearly 100% efficiency. Here, based on non-ideal GM systems, we systematically studied the factors that influence the efficiencies of such conversion processes (both PW-PW and PW-SW). We found that while intra-supercell impedance-mismatch can hardly affect the conversion efficiencies, the scatterings caused by inter-supercell discontinuities can have non-negligible effects on the PW-SW conversion efficiency. We proposed a new GM model that can reduce the scatterings so as to improve the PW-SW conversion efficiency. Finally, we demonstrated that a GM containing only 2 supercells can convert a PW to a SW with very high efficiency, while a grating coupler of the same size does not work at all.