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I'm having some issues with plane waves propagating through a medium which is:

- linear

- spatially and temporally homogeneous

- spatially non-dispersive

- isotropic

- temporally dispersive

- passive

I know that permittivity, permeability and the k-vector are complex in temporally dispersive media.

There are different notations of the above-mentioned quantities, so I'm going to briefly introduce those which I'm used to:

[tex]\epsilon (\omega) = \epsilon ' (\omega) - j \epsilon''(\omega)[/tex][tex]\mu (\omega) = \mu ' (\omega) - j \mu''(\omega)[/tex][tex]\underline{k} = \underline{\beta} - j \underline{\alpha}[/tex][tex]\underline{k} \cdot \underline{k} = \omega^2 \epsilon \mu[/tex]Where[tex]\epsilon'' , \mu'' \geq 0[/tex] in a passive medium and [tex]\alpha>0[/tex].

During class, my professor stated that, in the medium in question, the so-called "attenuation angle" (the angle between the attenuation vector alpha and the phase vector beta) is 90° or lower, because:[tex]\underline{\alpha} \cdot \underline{\beta} \geq0[/tex]

The statement was derived from the following equation:

[tex](\underline{\beta} - j \underline{\alpha}) (\underline{\beta} - j \underline{\alpha}) = \omega^2 \epsilon \mu [/tex]

(Tearing Re[] and Im[] apart we have:)

[PLAIN]http://img834.imageshack.us/img834/706/immagine1iz.png [Broken]

My professor said [tex]Im[\epsilon \mu] < 0[/tex] and my issue is right here.

I carried out the product:

[tex]\epsilon \mu = (\epsilon ' - j \epsilon'' ) (\mu' - j \mu'') = \epsilon' \mu' - j \epsilon' \mu'' - j \epsilon'' \mu' - \epsilon'' \mu''[/tex][tex]Im[\epsilon \mu] = - \epsilon' \mu'' - \epsilon'' \mu' [/tex]

Mu'' and epsilon'' are non-negative, but what about mu' and epsilon' ?

Are they both positive in a passive medium?

Thanks in advance.

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# Plane waves: sign of Re(ε), Re(μ) in passive media, attenuation angle

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