Answer to Question #127815 in Electricity and Magnetism for christopher seebaran

Question

Show that the wave number of an electromagnetic wave plane wave is complex in a material with conductivity

Answer 1

The equation of a plane wave has the form $\overline E = \overline E_{0}(exp(i(\omega t-kz))$, if the medium has a conductivity, then the wave energy decreases as it propagates, i.e. the modulus of the vector E decreases as well. For this to happen, i.e. a negative real value arises from the product of i and k, the wave number k must be a complex quantity.