Question

Physical significance of negative dielectric constant

Answer 1

First of all negative dielectric constant means is related to the non-resistance of the material to the electric field.
Apart from metals (which have their negative permittivity at optical frequencies) there are some natural materials (such as ferroelctrics) display negative permittivity.
The negative permittivity (with positive permeability) means that refractive index becomes complex,with a lot of consequence from this complexity.