treams.TMatrix.xs

TMatrix.xs(illu, flux=0.5)

Scattering and extinction cross section.

Possible for all T-matrices (global and local) in non-absorbing embedding. The values are calculated by

\[\begin{split}\sigma_\mathrm{sca} = \frac{1}{2 I} a_{slm}^\ast T_{s'l'm',slm}^\ast k_{s'}^{-2} C_{s'l'm',s''l''m''}^{(1)} T_{s''l''m'',s'''l'''m'''} a_{s'''l'''m'''} \\ \sigma_\mathrm{ext} = \frac{1}{2 I} a_{slm}^\ast k_s^{-2} T_{slm,s'l'm'} a_{s'l'm'}\end{split}\]

where \(a_{slm}\) are the expansion coefficients of the illumination, \(T\) is the T-matrix, \(C^{(1)}\) is the (regular) translation matrix and \(k_s\) are the wave numbers in the medium. All repeated indices are summed over. The incoming flux is \(I\).

Parameters:

• illu (complex, array) – Illumination coefficients

• flux (optional) – Ingoing flux corresponding to the illumination. Used for the result’s normalization. The flux is given in units of \(\frac{\text{V}^2}{{l^2}} \frac{1}{Z_0 Z}\) where \(l\) is the unit of length used in the wave number (and positions). A plane wave has the flux 0.5 in this normalization, which is used as default.

Returns:

tuple[float]