# Physical interpretation of conductivity with electromagnetic waves?

 P: 23 Hi all, I'm trying to understand exactly what the physical meaning of conductivity/current is in relation to waves. if we have a wave traveling through a conductor, we find that it decays exponentially, i.e. $e^{-\alpha z}$ where $\alpha=imag(k)=\omega\sqrt{\frac{\epsilon\mu}{2}} \left[\sqrt{1+(\frac{\sigma}{\epsilon\omega})^2}+1 \right]^{1/2}$ and $k^2=\mu\epsilon\omega^2+i\mu\sigma\omega$ My question is, what is the physical interpretation of the conductivity(σ) with respect to currents? How does it cause an exponential decay of the field strength as the wave travels through the material? Does it absorb the electric field by creating a current since $J=\sigma E$ ? Thanks!
 Sci Advisor Thanks P: 2,552 In my opinion, the most clear treatment of these issues is given in the Feynman Lectures vol. II. There Feynman explains in very simple terms the classical theory of electromagnetic waves in media. A insulating homogeneous and isotropic dielectric's properties can be described in a simplified model as a rigid lattice of ions (atomic nuclei) surrounded by electrons harmonically bound to this positive background, including a friction term. Fourier decomposition in time leads to the complex valued dielectric function, $\epsilon(\omega)$, with the usual analyticity constraints for causality (use of the retarded propagator for the response to an external perturbation like an incoming electromagnetic wave). If you have a conductor, you have in addition (quasi-)free electrons which have no harmonic binding force but only a friction force, which leads to a pole of the dielectric function at $\omega=0$. That's the only formal difference between an insulator and a conductor. Superconductivity must be treated as a special case, leading to the London or the Ginzburg-Landau phenomenological theories (the latter is particularly interesting since it can be understood as the Abelian Higgs Mechanism applied to the classical electromagnetic field; see Weinberg, Quantum Theory of Fields, Vol. II).