A New Strategy for Designing Broadband Epsilon-Near-Zero Metamaterials*

We have developed a new strategy for designing metamaterials in multi-layered film with permittivity being closed to zero over a broad frequency range, which is as known as broadband epsilon-near-zero (ENZ) materials. Milton representation, Bergman-Milton representation and electromagnetic representation of the effective permittivity ($\epsilon_{eff}$) are used, and the strategy consist of the following 3 parts: choosing the operation frequency range, properly placing the poles and zeros into the range, and solving the inverse problem by equating different representations of $\epsilon_{eff}$. Demonstration of the strategy is carried out by zeroth and first order design with several examples. The distribution of electric field inside the designed materials is investigated to reveal the physical principles of the broadband ENZ phenomenon. The study would be further extended to other geometries (e.g. multi-shell cylinder) through conformal transformation. The results obtained are useful for designing ENZ metamaterials.