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

  • #1
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Homework Statement:

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

Relevant Equations:

[tex] 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 [/tex] goes to
[tex] γ = α = ω \sqrt{μ'ε'} [/tex]
causing the plane wave to only attenuate in this medium.
I don't see what happens to the term [tex] jωμσ [/tex].
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 [tex] γ = β = ω \sqrt{μ'ε'} [/tex]
with no real explanation of what is happening.
I'm sure I'm missing something, but not sure what it is.
 
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Answers and Replies

  • #2
Twigg
Gold Member
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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."
 

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