Starting from the expression for a plane and monochromatic electromagnetic field,
\textbf{E}(\textbf{r},t) = \hat{\textbf{p}}E_p \cos(\omega t - \textbf{k} \cdot \textbf{r} - \phi) + \hat{\textbf{s}}E_s \cos(\omega t - \textbf{k} \cdot \textbf{r}),
Consider some particular cases for values of $\phi$ ($0, \pi/2, ...$) and find the expression
of \textbf{E}(\textbf{r},t) in the cases of linear, circular and elliptical polarization.