Complex Wave Vector in Partial Reflection at a Conductor Interface

[_Andreas]

Homework Statement

I'm writing a school paper on the behavior of electromagnetic waves when they hit the interface between a non-conductor and a conductor. My question is if, in the case of partial reflection, it is correct to allow for both components of the wave vector (the wave is confined to a plane) of the transmitted wave to be complex (in the conductor, there is attenuation in both* directions, isn't it)?

* Of course, if the transmitted wave is orthogonal to the interface there is only one direction to consider.

 

[_Andreas]

If it is of any help, this is how I imagine the electric field vector of the transmitted wave (in the metal) should look: $$\textbf{E}_{0t}\exp i(k'_{xt}x+k'_{zt}z-\omega_t t)\exp(-k''_{xt}x)\exp(-k''_{zt}z),\label{17b}$$. The ' and '' denote the real and the imaginary parts of the wave vector components, respectively. (Ignore the direction signs. What I wonder is if he basic idea is correct).

 

[_Andreas]

No one? Please?