Strategy for designing broadband epsilon-near-zero metamaterials

A strategy is proposed to design a certain kind of metamaterial with near-zero electric permittivity over a broad frequency band, i.e., the broadband epsilon-near-zero (ENZ) metamaterials. Based on the Bergman–Milton spectral representation of the effective permittivity, the design is first carried out in the dimensionless spectral space, where the effective permittivity of the ENZ metamaterials is mathematically determined by a series of zeros and poles (singularities), which can be easily arranged as required by the operating band. Then, through a fast inverse algorithm, the mathematical structures of the ENZ metamaterials can be transformed back to their physical structures, which can be put into practical applications. The effective permittivity of the designed ENZ metamaterials is examined, and the distribution of the electric field inside the designed ENZ metamaterials is also explored, in order to reveal the physical reason behind the broadband ENZ phenomenon.