Light in Conductors

$\tilde{E}(z,t)={\tilde{E}}_0{e}^{i(\tilde{k}z-\omega t)}$

• Electric field inside conductors

$\tilde{B}(z,t)={\tilde{B}}_0{e}^{i(\tilde{k}z-\omega t)}$

$\tilde{k}=k+i\kappa$

$k\equiv \omega \sqrt{\frac{\epsilon \mu }{2}}\sqrt{\sqrt{1+{\left(\frac{\sigma }{\epsilon \omega }\right)}^2}+1}$

• $\epsilon$ is the permittivity of the material
• $\mu$ is the permeability of the material

$\kappa \equiv \omega \sqrt{\frac{\epsilon \mu }{2}}\sqrt{\sqrt{1+{\left(\frac{\sigma }{\epsilon \omega }\right)}^2}-1}$

$d=\frac{1}{\kappa }$

• Skin depth of a material. The distance it takes for the amplitude of a wave to decrease by a factor of $\frac{1}{e}$