On the Possibilities to Create a Negative Permittivity Metamaterial with Zero Imaginary Part of the Permittivity at a Specific Frequency-Electrical Network Theory Approach

A permittivity function suggested in the literature describing a material that exhibits negative permittivity and no loss at a specific frequency (and losses at other frequencies) is analyzed using electrical network theory. An equivalent circuit of the polarization admittance consisting of RLC components is derived. Further, a proof is given showing that if the admittance is lossless at a specific frequency, then all components with losses (resistances) in the circuit have to be short circuited or blocked or virtually disconnected at this frequency by the use of ideal lossless resonant LC circuits. However, in the literature, inductors in metamaterials are associated with inherently lossy metal nanoparticles, hence invalidating the suggested permittivity function unless a lossless inductor at optical frequencies is found or proved possible.