# Lossy electromagnetic wave and reactive power

Consider an electromagnetic wave in a lossy medium. This medium has a complex permittivity $$\varepsilon_r=\varepsilon_r' +j \varepsilon_r''$$ and a wave impedance given by $$Z=\frac{E}{H}=\sqrt{\frac{\mu_0}{\varepsilon_0 \varepsilon_r}}$$ where we assumed $$\mu_r=1$$. Hence, the complex permittivity results in a complex impedance and thus in a phase difference between $$E$$ and $$H$$.

The Poynting vector is given by $$\mathbf{S}=\frac{1}{2} \left( \mathbf{E}\times\mathbf{H}^* \right)$$ where the real part gives the net active power and the imaginary part gives the reactive power. So, when there is a phase difference between $$E$$ and $$H$$, there is also reactive power associated with the wave.

From this, we could conclude: every propagating electromagnetic wave in a lossy medium has also reactive power associated with it.

However, this conclusions sounds strange to me and I am not sure of it... Do I miss something or is there a mistake is the reasoning?