# What happens to σ (conductivity) when the permitivity is negative?

## Homework Statement:

In my textbooks derivation of I don't understand what happend to jβ or σ when ε = -ε.

## Relevant Equations:

$$γ = sqrt{jωμ( jωε +σ ) = α + jβ [\tex] We are using the textbook by Jin, "Theory and Comutation of Electromagnetic Fields". In the section on metamaterialshe derives the dispersion relationship. He shows that when ε'= -ε & μ' = μ then the dispersion equation [tex] γ =\sqrt{jωμ( jωε +σ )} = α + jβ$$ goes to
$$γ = α = ω \sqrt{μ'ε'}$$
causing the plane wave to only attenuate in this medium.
I don't see what happens to the term $$jωμσ$$.
How does it go to zero?
Maybe we assume σ = 0, but I don't see it stated explicately, and in the next paragraph when he derives the dispersion relationship for double negative materials, the he gets $$γ = β = ω \sqrt{μ'ε'}$$
with no real explanation of what is happening.
I'm sure I'm missing something, but not sure what it is.

Delta2

## Answers and Replies

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Twigg
Gold Member
In this section the author assumes no losses in the material. That means the resistivity ##\sigma## is set to zero, as a simplifying assumption. Here's a quote: "However, let us ignore these losses and examine how a plane wave propagates in this type of medium."