Intensity

In wave physics (especially wave optics), the intensity (or irradiance) is the power incident on an area, i.e.,

$$I=\frac{P}{A}$$

We define it as the time average of the Poynting vector $\vec{S}$.

$$I=⟨|\vec{S}|{⟩}_T=⟨|\vec{E}\times \vec{H}|{⟩}_T=\frac{1}{2}{E}_0{H}_0=\frac{1}{2}\sqrt{\frac{ϵ}{\mu }}{E}_0^2$$

i.e., for a plane harmonic wave, $I\propto E_0^2$. This formula is only valid for linear polarisations. For a circularly or elliptically polarised light, we can express the irradiance as the sum of the two linear irradiances with the orthogonal components.

$$I=\frac{1}{2}{ϵ}_{0}cn\left(E_{uo}^2+E_{vo}^2\right)$$