Non-Hermitian doping of epsilon-near-zero media

The recently introduced concept of photonic doping in epsilon-near-zero media enables the tailoring and control of the effective magnetic response over broad regions of the parameter space, by resorting to a limited number of arbitrarily placed, nonmagnetic doping particles. Here, we theoretically extend this idea to non-Hermitian scenarios with either doping particles or host media characterized by tailored distributions of gain and loss. This considerably enlarges the attainable effective permeability parameter space, granting access to the entire complex plane. In this extended vision, losses are not considered as second-order, detrimental effects, and their interplay with gain is instrumental to enabling several intriguing effects of potential interest in reconfigurable nanophotonics and optical sensing, whose practical implementation is deferred to future studies.