## Appendix A  
### Polarization of Light  
Polarization of light defines the geometrical orientation of the oscillations of electromagnetic waves. In a transverse wave, the oscillation is in the perpendicular direction respect to the direction of propagation of the beam. When the field vector components along the x and y directions generates a linear trajectory over the time, polarization is called linear, whereas when the tip of the field vector describes a circle or an ellipse in any fixed plane intersecting, and normal to, the direction of propagation, the polarization is classified as circular or elliptical, respectively. The rotation can occur in two possible directions: right circular polarization if the fields rotate in a right-hand sense with respect to the propagation direction, or left circular polarization if the fields rotate in a left-hand sense. Polarization of light can be described with the following two different formalisms [77]:  
* Jones vector, evaluated by means of the Jones calculus, only applicable to light that is already fully polarized;
* Stokes parameters, evaluated by means of the Mueller calculus, for a light that is randomly polarized, partially polarized, or incoherent. Basically, in the Jones formalism, considering propagation along the z axis, the electric field can be written as \(E=E_{x}+E_{y}\), where  
\[\left( \begin{array}{c}E_{x}(z,t)\\ E_{y}(z,t)\end{array} \right)\,=\,\left( \begin{array}{c}A_{x}\cos(\omega t-kz+ \delta_{x})\\ A_{y}\cos(\omega t-kz+\delta_{y})\end{array} \right)\,=\,\left( \begin{array}{c} A_{x}e^{i\beta_{x}}\\ A_{y}e^{i\beta_{y}}\end{array} \right)e^{i(\omega t-kz)} \tag{1}\]  
Here \(i\) is the imaginary unit. The components can be writing as a column vector, which is called Jones vector. \[J\,=\,\left( \begin{array}{c}A_{x}e^{i\beta_{x}}\\ A_{y}e^{i\beta_{y}}\end{array} \right) \tag{2}\]  
The state of polarization of an optical wave can be expressed in terms of the amplitudes \((A_{x},A_{y})\) and the phase variations \((\delta_{x},\delta_{y})\) of the x and y components of the electric field vector. Hence, the polarization state of a light beam is completely described by the complex amplitudes in Equation (2). When a polarized wave with field vector \(E\) is incident on a polarization-changing object, the emerging wave has another polarization state \(E_{1}\) given by  
\[\left( \begin{array}{c}E_{1x}\\ E_{1y}\end{array} \right)\,=\,\left( \begin{array}{cc}j_{11}&j_{12}\\ j_{21}&j_{22}\end{array} \right)\left( \begin{array}{c}E_{x}\\ E_{y}\end{array} \right) \tag{3}\]  
where the \(2\times 2\) transformation matrix is called the Jones matrix. If the optical wave travels through different optical components, the resulting Jones vector can be evaluated by multiplying a cascade of Jones matrices to the input vector, \(J_{N}J_{N\cdot 1}\dots\ J_{2}J_{1}E\), where \(J_{i}\) represents the polarization properties of \(i\)-th element [78]. In the case of Stokes formalism, the polarization of light is described by four factors related to intensity and polarization ellipse parameters as described in Figure A1 and in the following equations:  
\[ \begin{array}{rcl}&S_{0}\ =\ I\\ S_{1}\ =\ Ip\cos 2\psi\cos 2\chi\\ S_{2}\ =\ Ip\cos 2\chi\\ S_{3}\ =\ Ip\sin 2\chi\end{array}  \tag{10}\]  
where \(\ Ip\), \(2\psi\) and \(2\chi\) are the spherical coordinates of the polarization state in the three-dimensional space for the \(S_{1}\), \(S_{2}\) and \(S_{3}\) parameters, \(I\) is the total intensity of the beam, and \(p\) is the degree of polarization given by \(\frac{\sqrt{S_{1}^{2}+S_{2}^{2}+S_{3}^{2}}}{S_{0}}\), constrained by \(0\leq p\leq 1\). Generally, normalized Stokes vector, obtained by normalizing to the total intensity \(S_{0}\), is used and the three significant Stokes parameters are plotted on a spherical region.