From 9e03e819a95e58ac22f83e28e4fbe4d5068ee722 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= <marek@necada.org>
Date: Sun, 13 May 2018 14:55:44 +0300
Subject: [PATCH] Some notes about scuff-tmatrix interoperability

Former-commit-id: c9af5492c190f2012b5592d4434fec776a646de7
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+#LyX 2.1 created this file. For more info see http://www.lyx.org/
+\lyxformat 474
+\begin_document
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+\use_hyperref true
+\pdf_title "Sähköpajan päiväkirja"
+\pdf_author "Marek Nečada"
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+
+\begin_body
+
+\begin_layout Title
+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).
+\end_layout
+
+\end_body
+\end_document