Some notes about scuff-tmatrix interoperability

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Marek Nečada 2018-05-13 14:55:44 +03:00
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Important note about the T-matrices obtained by scuff-tmatrix
\end_layout
\begin_layout Standard
From what I managed to dig from the scuff-em documentation (and partially
source code, but with less reliability), the spherical waves used in scuff-em
are (at least in magnitude)
\series bold
power-normalised
\series default
.
\end_layout
\begin_layout Standard
However, the vector spherical harmonics have an additional factor of
\begin_inset Formula $i$
\end_inset
compared to Kristensson and while Kristensson states the interrelations
\begin_inset Formula
\begin{eqnarray*}
\nabla\times v_{1lm}(kr) & = & kv_{2lm}(kr),\\
\nabla\times v_{2lm}(kr) & = & kv_{1lm}(kr),
\end{eqnarray*}
\end_inset
Reid has
\begin_inset Formula
\[
N_{lm}=-\frac{1}{ik}\nabla\times M_{lm},
\]
\end_inset
in other words
\begin_inset Formula $\nabla\times M_{lm}=ikN_{lm}$
\end_inset
.
Therefore, it is quite possible that additional
\begin_inset Formula $i$
\end_inset
-factors will have to be added to the
\begin_inset Formula $B$
\end_inset
coefficients.
Moreover, it is totally unclear whether Reid uses C.-S.
phase or not in his spherical harmonics.
\end_layout
\begin_layout Standard
I will have to try all the possibilities to see how much it affects the
results.
If too much, one way to determine it
\begin_inset Quotes sld
\end_inset
exterimentally
\begin_inset Quotes srd
\end_inset
would be to try a configuration with several spheres and compare it to
the analytical Mie + translation coefficients -based solution.
\end_layout
\begin_layout Standard
According to the documentation, in the output T-matrix files, the outgoing
(singular) spherical wave indices are in the lefter columns, while the
incoming (regular) wave indices are on the right (and then the T-matrix
entry follows).
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