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The epsilon-near-zero (ENZ) condition in natural and artificial plasmas is considered for spatially dispersive materials. In the presence of spatial dispersion the ENZ condition must be judged by vanishing of the electric displacement field in real-space. Unlike the simple case of local materials where ENZ occurs at the plasma frequency, in spatially dispersive materials the matter is more complicated. To consider the spatially dispersive case, we obtain the momentum-dependent permittivity in real-space, and define a characteristic length parameter, in addition to the Debye length, which governs polarization screening. Using this formulation, conditions are investigated under which the electric displacement field (equivalently, the real-space permittivity) can vanish or be strongly diminished, even in the presence of spatial dispersion, implementing an ENZ material.

On the epsilon near zero condition for spatially dispersive materials