A Systematic Approach to Photonic Crystal Based Metamaterial Design

Photonic crystal design procedure for negative refraction has so far been based on trial and error. In this paper, for the first time, a novel and systematic design procedure based on physical and mathematical properties of photonic crystals is proposed to design crystal equi-frequency contours (EFCs) to produce negative refraction. The EFC design is performed by the help of rectangular stair-case (RSC) photonic crystals. The RSC crystal is then converted to more common structures like pillar crystals by matching Fourier coefficients of periodic electric permittivity. Methods to design common crystals which have approximately equal Fourier components to the RSC crystal are also discussed. The proposed procedure can be used to design metamaterials without the difficulties of large trial and error. The devised procedure can also be applied in designing other structures involving photonic crystals.