Fig. 1

Schematic and electric field distribution of zero-index materials. a Schematic diagram of the ZIM with a high out-of-plane radiation directivity under TM excitation. The pitch, radius and height of the metamaterial are a, r and h, respectively. Electric field phase distributions over the cross sections of b a conventional 5a × 5a 2D ZIM with an inclusion relative permittivity equal to 13.8; c a bulk zero-index material based on the Lorentz model; d the same ZIM as in b whose size is approximately one operating wavelength; and e a 2D ZIM whose inclusion and background matrix permittivities are 294 and 25, respectively