There are materials with negative effective permittivity and permeability. However, there can be materials where only one of them is negative. Solving the wave equation results in a purely imaginary wave number. Does this mean this results in complete attenuation of wave ?
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Nonmagnetic materials have a relative permeability $\mu_r$ close or equal to 1. Relative permittivity $\varepsilon_r$, in any case, is usually taken to be a complex quantity.
Silver is an example of a material where one is negative and the other positive; according to refractiveindex.info (taken from Johnson & Christy, 1972), $\varepsilon_r = -18.295+0.48085i$ at 633 nm, and I assume $\mu_r\approx 1$ since silver is not magnetic.
If you have a purely imaginary wave number, that is called an evanescent wave, and its amplitude falls off exponentially over a distance often called the skin depth when in the context of a conductor.
However, in practice, e.g. when reflecting a light wave from a silver surface, there will be a small amount of leakage into the silver, because the wave number is not purely imaginary, because $\varepsilon_r$ is not purely real.
