Suppose you have a plane electromagnetic wave that crosses a medium with index of refraction $n$ with equation:$$e^{i\omega(t-\frac{nx}{c})}$$ Where $c$ is the speed of light.
What's the effect of changing $n$ by $n-ik$,$i=\sqrt{-1}$.
What does k physically represents?
Just do some manipulation:
$$\begin{align} E &\propto e^{i\omega(t - nx/c)}\\ &\propto e^{i\omega(t + ikx/c - nx/c)}\\ &\propto e^{-\omega kx/c}e^{i\omega(t - nx/c)} \end{align}$$
so, you see an exponential decay in the electric field as the wave travels a distance x. Therefore, one can interpret $\omega k$ as giving you information about how much of the field the medium is absorbing.
