This demonstration presents the representation of the arbitrary fully polarized electromagnetic wave in the polarization basis $(\theta, \tau)$:
\begin{eqnarray} {\bf{\dot E}} = {\dot E}_1 {\dot {\bf{e}}}_1(\theta,\tau) + {\dot E}_2 {\dot {\bf{e}}}_2(\theta+\pi/2, -\tau) \end{eqnarray} where $\bf{\dot E}$ is the wave with arbitrary polarization (blue), $\dot E_1$ - complex amplitude of the ortihogonal polarization basis component's ${\dot {\bf{e}}}_1(\theta,\tau)$ (red), ${\dot E}_2$ - complex amplitude of the ortihogonal polarization basis orthogonal component's ${\dot {\bf{e}}}_2(\theta+\pi/2, -\tau)$ (magenta). Here $\theta$ is the angle of orientation of the first elliptical component of polarization basis, which has the ellipticity angle $\tau$. In the polarization basis $(\theta, \tau)$, the Jones vector of the wave can be written: $ {\bf{\dot E}} = \left[ {\begin{array}{*{20}{c}} {{E_1}{e^{j{\phi _1}}}}\\ {{E_2}{e^{j{\phi _2}}}} \end{array}} \right] $

Polarization basis parameters:

 Orientation angle $\theta$, degrees:   

 Ellipticity angle $\tau$, degrees:   

Polarization components parameters:

 Amplitude of $\dot E_1$:     

 Amplitude of $\dot E_2$:     

 Phase difference (ϕ₁-ϕ₂):    deg