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I'm wondering whether there are materials for which an incident EM wave would behave as $\vec E(z,t)=\vec E_0 e^{\kappa z}e^{i(kz-\omega t)}$ where z describes how far from the surface the fields are and $\kappa>0$. Non perfect conductors for example, would have a similar dependency except for the sign in front of $\kappa$, which makes evanescent waves. While in the case I'm looking for, we'd have "enhanced waves".

I also wonder the same thing for waveguides. For example if we consider a rectangular waveguide as well as a TM mode whose frequency is lower than the cutoff frequency, then that TM mode cannot propagage inside the waveguide, the dependency of that mode with respect to "z" (direction alongside the waveguide) is a decaying exponential which is exactly the same than an EM field in a metal, I believe. So I wonder whether there are materials which would make up the waveguide such that the EM fields would get enhanced, at least on a "small distance" (say over a few wavelengths). If so, what kind of materials are they?

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We know from the basic electromagnetic theory that the energy stored in an electric field goes like the volume integral of the mod-square of the electric field. If we have an electric field undergo exponential decay within a medium, such as an electric field propagating in a material with a non-zero skin depth, then we notice that there is definite loss of energy in the field. We can acquit this loss to the thermo-kinetic energy gained by the charged particles in the material. In other words, the material is being heated by the electric field. In order to have growth in the electric field, we would need the opposite scenario. The electrons in the material must forfeit their thermo-kinetic energy to support the wave's intensity. This is the idea behind laser cooling. The electric field resonates with the electrons in a material causing the photons to be absorbed. The electrons undergo excitations and emit photons with greater energy that of the incoming photons. The loss of energy of the atoms in the materials is acquitted to nuclear recoil. Hence the material is cooled and the electric field intensity is increased.

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Gain medium of lasers, but you need to pump it.

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  • $\begingroup$ By pumping it, do you mean that I'd have to spend energy for the enhancing of the fields to happen? $\endgroup$ – thermomagnetic condensed boson Nov 1 '15 at 14:57
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    $\begingroup$ @no_choice99: If the medium is to provide gain for a long time, then yes, you'll need to spend energy (to maintain population inversion). $\endgroup$ – akhmeteli Nov 1 '15 at 15:45

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