Electromagnetic wave propagating in a metal
Hi. I've been having trouble with this question for a few days. The question is as follows;
"Consider a plane electromagnetic wave with angular frequency ω propagating in a large good metal with electric conductivity s (assume that sigma/omega*epsilon_0 ≫ 1), the wave electric field may be written as E=E_0 exp[omega*tkz]. The electric field only has an x component. If we assume that the wave number k is real and known, find the expression for the angular frequency (its real and imaginary part) by assuming that the metal has both relative permittivity and relative permeability equal to 1."
Using Maxwell's, Ampere's and Ohm's Laws, we find that
k^2 = epsilon_0*mu_0*omega^2 + j*mu_0*sigma*omega
My notes show the logical conclusion of such a question if k is complex and omega is real, but I'm not really sure of how to do the reverse.
If sigma/omega*epsilon_0≫1, then the first part of the RHS disappears so that
k^2=j*mu_0*sigma*omega
which can be rearranged to get
omega = (k^2/(mu_0*sigma))*j
I then let omega be complex, so that omega = beta  alpha*j... but I have no idea where to go from here (or if this is even correct). Any help would be appreciated!
