# Electromagnetic Field Intensity: Square law power = Poynting vector?

Consider an arbitrary polychromatic wave in vacuum (an actual wave, not evanescent!), assuming real waves.

In scalar wave theory, optical intensity is defined as (Saleh & Teich, p.68):

$$I = \langle u^2(\mathbf{r}, t) \rangle_{\text{time}}$$

Where $$u$$ is the real wavefunction.

In electromagnetic wave theory,

$$I = \langle S(\mathbf{r}, t) \rangle_{\text{time}} = \langle \frac{1}{\mu_0} \mathbf{E} \times \mathbf{B} \rangle_{\text{time}}$$

How does one prove that they are equivalent?

P.S. Also see wikipedia (link to highlight)

It appears that both formulas(definitions) are NOT equivalent, as 'optical intensity' is operationally defined as what you would measure based on square-law detectors that only respond to the electric field! (check out any quantum optics text that deals with photoelectric theory of photon detection), right?

The units are not equivalent to begin with, differing by an uninteresting constant.