  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.
