# Interpretation of real and imaginary parts of the Poynting vector in a vacuum

It is known that the flux of the Poynting Vector through a certain surface represents the total electromagnetic power flowing through it.

Then, its real part is the active power, while its imaginary part is the reactive power. Now let's consider an EM wave in vacuum: what do active power and reactive power mean?

From a circuit point of view, I'd say that the active power is that is dissipated in resistances, while reactive power is that is stored in inductances and/or capacitances. But in vacuum there are not materials with those properties. So what is their physical meaning?

Also, how do you end up with imaginary Poynting vector ($$\mathbf{S}$$) in free-space? Whenever I see Poynting vector in time-harmonic treatment you get something like:
$$\mathbf{S} = \frac{1}{2} \Re\left(\mathbf{E}^\dagger\times\mathbf{H}\right)$$
For complex-valued electric ($$\mathbf{E}$$) and magnetic ($$\mathbf{H}$$) fields. In frees-space electric and magnetic fields are in phase, so even $$\mathbf{E}^\dagger\times\mathbf{H}$$ will be real-valued (i.e. $$\Re$$ is superfluous).
• For quantitites quadratic in time-harmonic fields, you have to be very careful. In fact it is better to take a step back to real valued fields (i.e. if $\mathbf{\tilde{E}}$ is complex time-harmonic, then $\mathbf{E}=\mathbf{\tilde{E}}\exp\left(i\omega t\right) + \mathbf{\tilde{E}}^\dagger\exp\left(-i\omega t\right)$ is real-valued; $\omega$ is the angular frequency), and clarify what you intend to seek. – Cryo Oct 8 '19 at 11:14