SourceSampling

Type:Matrix<float>, or section
Range:[v_11, …, v_1j; …; v_i1, …; v_ij], j<=6
Default:-/-
Appearance:simple

Defines the source sampling of the illumination pupil in normalized \boldsymbol \sigma_\perp coordinates. For the notation see the parent section Illumination.

Each row in the matrix corresponds to a source point. The columns of the table must contain the following quantities: \sigma_x, \sigma_y, I_{0, \mathrm{scaled}}, \mathrm{DoP}, \psi, and e. The quantities \sigma_x, \sigma_y and \mathrm{DoP} were introduced in the parent section Illumination. Instead of the intensity I_0 as introduced in the parent section Illumination a scaled intensity I_{0, \mathrm{scaled}} is passed. Details are given below.

Together with the total intensity I_0, the additional parameters \psi and e are used to fix the Jones vector components E_{\mathrm{pol}, x} and E_{\mathrm{pol}, y} of the completely polarized state \TField{P}_{\mathrm{pol}}:

In general the completely polarized state exhibit a elliptical polarization with ellipticity given by e and orientation \psi, so that

\begin{eqnarray*}
\left (
\begin{array}{c}
E_{\mathrm{pol}, x} \\
E_{\mathrm{pol}, y}
\end{array}
\right ) = \sqrt{\frac{I_\mathrm{pol}}{1+e^2}}
\left (
\begin{array}{cc}
\cos(\psi) & -\sin(\psi) \\
\sin(\psi) & \cos(\psi)
\end{array}
\right )
\left (
\begin{array}{c}
1 \\
ie
\end{array}
\right ),
\end{eqnarray*}

where I_\mathrm{pol}=\mathrm{DoP} \cdot I_0 is the intensity of the completely polarized state.

The completely unpolarized component

\begin{eqnarray*}
\TField{P}_{\mathrm{unpol}} = A\cdot \TField{I}
\end{eqnarray*}

is determined from

\begin{eqnarray*}
2 A = \trace{\TField{P}_\mathrm{unpol}} =
\trace{\TField{P}}-\trace{\TField{P}_{\mathrm{pol}}}=(1-\mathrm{DoP}) \cdot I_0.
\end{eqnarray*}

Warning

The given data, I_0, etc, refer to the effective light source in the pupil plane.

Intensity scaling

It remains to fix the input quantity I_{0, \mathrm{scaled}} for a given source point \boldsymbol\sigma. In the parent section the total intensity I_0 referred to the squared magnitude |\VField{E}|^2 of the electric field vector of a plane wave. However, in many textbooks the intensity of a plane wave is defined as the magnitude of the Poynting vector, that is, as the energy flux through a unit surface perpendicular to the propagation direction. JCMsuite uses the following convention:

The sum over all given scaled intensities I_{0, \mathrm{scaled}}(\boldsymbol \sigma) gives the total energy flux through the pupil plane:

\begin{eqnarray*}
\VField{P}_{z} = \sum_{\boldsymbol\sigma_i} I_{0, \mathrm{scaled}}(\boldsymbol \sigma_i).
\end{eqnarray*}

Hence, the scaled intensities already accounts for the integration of the extended illumination over the source points \boldsymbol \sigma.