acoustotreams.AcousticTMatrix.xs

AcousticTMatrix.xs(inc, flux=0.5)[source]

Scattering and extinction cross section.

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

\[\begin{split}\sigma_\mathrm{sca} = \frac{1}{2 I} b_{lm}^\ast T_{l'm',lm}^\ast k^{-2} C_{l'm',l''m''}^{(1)} T_{l''m'',l'''m'''} b_{l'''m'''} \\ \sigma_\mathrm{ext} = \frac{1}{2 I} b_{lm}^\ast k^{-2} T_{lm,l'm'} b_{l'm'}\end{split}\]

where \(b_{lm}\) are the expansion coefficients of the incident wave, \(T\) is the T-matrix, \(C^{(1)}\) is the (regular) translation matrix and \(k\) is the wave number in the medium. All repeated indices are summed over. The incoming flux is \(I\).

Parameters:

  • inc (complex, array) – Incident wave or its expansion coefficients

  • flux (optional) – Ingoing flux corresponding to the incident wave. Used for the result’s normalization. A plane wave has the flux 0.5 in this normalization, which is used as default.

Returns:

tuple[float]