Impedance-matched metadevices with a single matrix material

Artificial periodic structures including photonic crystals (PCs) and metamaterials have been widely employed to construct metadevices, whereas their effective refractive indices n_e and relative impedances Z_r are usually coupled together and hard to design separately. Here, we present a method for flexibly tuning the indices n_e and impedances Z_r of PCs. The unit cell of PC consists of a dielectric matrix with multiple air holes symmetrically distributed around the center of the unit cell. We find that the index n_e of the PC mainly depends on the filling ratio of the dielectric, while its impedance Z_r relies on the position of the holes. When the holes have an appropriate distance from the center of the unit cell, matched impedances (Z_r = 1) can be achieved for PCs with different indices n_e. As a result, impedance-matched metadevices, such as generalized Mikaelian lenses with high efficiency (> 96%), can be constructed even with high refractive indices in their matrices.