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.

Note

The solver will enforce the following input bounds on the given source sampling matrix entries: $I_{0, \mathrm{scaled}}>=0$ , $\mathrm{DoP}\in [0,1]$ ,:math:psiin [0,1] and $e \in [0,1]$

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 $\boldsymbol \sigma$ .