acoustotreams.AcousticTMatrix.xs

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

Scattering and extinction cross section (m^2).

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

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

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 wavenumber in the background medium. All repeated indices are summed over. The incoming flux is \(I\).

Parameters:

  • inc (array_like) – Incident wave or its expansion coefficients.

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

Returns:

tuple[float]