${\displaystyle n_{1}=1.44}$

${\displaystyle n_{2}=1.0}$

Reflection coefficients, and polarization vector components for the incident and reflected fields are shown for incident angle 0-90 degrees.

Incident field is 45 degrees linearly polarized wave i.e. ${\displaystyle {E}_{0}^{\mathrm {TE} }={E}_{0}^{\mathrm {TM} }=1,\Delta \phi _{i}=0}$

To take into account the polarization we can divide the incident field in TE- and TM- polarized components. In this case we define the orthogonal polarizations as ${\displaystyle {\textbf {E}}({\textbf {r}},t)=\left({\textbf {E}}_{0}^{\mathrm {TE} }+e^{-j\Delta \phi _{i}}{\textbf {E}}_{0}^{\mathrm {TM} }\right)e^{-j{\textbf {k}}_{i}\cdot {\textbf {r}}},\quad \mathrm {where} \quad \Delta \phi _{i}=\phi _{\mathrm {TE} }-\phi _{\mathrm {TM} },}$ i.e. phase difference of the orthogonal TE and TM components.

The state-of-polarization (SOP) of the wave is now defined on plane perpendicular to wave vector i.e. ${\displaystyle {\textbf {k}}_{i}\cdot ({\textbf {r}}-{\textbf {r}}_{0})=0}$. SOP is analyzed by polarization vector ${\displaystyle {\textbf {p}}={\frac {\textbf {E}}{{|}{\textbf {E}}{|}}}=[p_{\mathrm {TE} }\;p_{\mathrm {TM} }].}$

Each component has a polarization dependent reflection coefficient ${\displaystyle r_{\mathrm {TE} }\;\mathrm {and} \;r_{\mathrm {TM} }}$.

The field after the reflection is then

${\displaystyle {\textbf {E}}({\textbf {r}},t)=\left(r_{\mathrm {TE} }{\textbf {E}}_{0}^{\mathrm {TE} }+r_{\mathrm {TM} }{\textbf {E}}_{0}^{\mathrm {TM} }\right)e^{-j{\textbf {k}}_{r}\cdot {\textbf {r}}}.}$