optics - electric field of unpolarized light after reflect?

Reflection and transmission (Fresnel equation) of polarized light are treated in many optics or electromagnetism books.

If $E_s$ and $E_p$ is incident electric field with s-polarization and p-polarization, respectively, reflected electric field would be $E'_s = r_s E_s$ or $E'_p = r_p E_p$, where $r$ is reflection coefficient and $'$ means reflected field.

Then electric field of any polarized light can be calculated by decomposition.

For instance, since $E_{45^{\circ}} = \frac 1 {\sqrt{2}} ({ E_p + E_s })$, $E'_{45}$ would be $\frac{1}{\sqrt 2} (E'_p + E'_s )$

However, how can I express electric field of reflected unpolarized light?