Strategy for designing broadband epsilon-near-zero metamaterial with loss compensation by gain media

A strategy is proposed to design the broadband gain-doped epsilon-near-zero (GENZ) metamaterial. Based on the Milton representation of effective permittivity, the strategy starts in a dimensionless spectral space, where the effective permittivity of GENZ metamaterial is simply determined by a pole-zero structure corresponding to the operating frequency range. The physical structure of GENZ metamaterial is retrieved from the pole-zero structure via a tractable inverse problem. The strategy is of great advantage in practical applications and also theoretically reveals the cancellation mechanism dominating the broadband near-zero permittivity phenomenon in the spectral space.