- #1

- 138

- 4

## 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.

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.