In this work, we present a novel method for designing non-Hermitian zero-index photonic crystals using dielectric materials with tunable parameters. By adding non-Hermitian elements, either gain or loss, Dirac dispersion in the complex frequency domain can be achieved onto the original double-zero-index photonic crystals with accidental degeneracy. Our effective medium theory shows that the composite structure can maintain the near-zero value of the real parts of the effective permittivity ε and permeability μ while their imaginary parts can be designed. Multiple geometrical parameters in the added components can provide a large range of tunability of the imaginary parts of our proposal of non-Hermitian zero-index photonic crystals, which makes it a perfect platform for future non-Hermitian optics applications. With the adjustability of the imaginary part of the effective parameters, we achieve a wide tunability of the surface impedance of the non-Hermitian zero-index photonic crystals designed, and two applications are thus demonstrated. An arbitrary impedance matching is realized by both numerical simulations and microwave experiments so that the impedance mismatch between any two materials can be mitigated by our design. The emergence of a Zak phase will induce interface states between two non-Hermitian zero-index photonic crystals with different surface impedances, which also verifies our successful strategy to engineer material surface impedance. The research offers a general approach to constructing non-Hermitian zero-index materials, paving the road for material realization of non-Hermitian optics devices.
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