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\begin_layout Standard

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\newcommand{\bra}[1]{\left\langle #1\right|}
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\begin_layout Title
Technical notes on quantum electromagnetic multiple scattering
\end_layout

\begin_layout Author
Marek Nečada
\end_layout

\begin_layout Affiliation
COMP Centre of Excellence, Department of Applied Physics, Aalto University,
 P.O.
 Box 15100, Fi-00076 Aalto, Finland
\end_layout

\begin_layout Date
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
today
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\end_layout

\begin_layout Abstract
...
 
\end_layout

\begin_layout Section
Theory of quantum electromagnetic multiple scattering
\end_layout

\begin_layout Subsection
Incoherent pumping
\end_layout

\begin_layout Standard
Cf.
 Wubs 
\begin_inset CommandInset citation
LatexCommand cite
key "wubs_multiple-scattering_2004"

\end_inset

, Delga 
\begin_inset CommandInset citation
LatexCommand cite
key "delga_quantum_2014,delga_theory_2014"

\end_inset

.
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\begin_layout Subsection
General initial states
\end_layout

\begin_layout Standard
Look at 
\begin_inset CommandInset citation
LatexCommand cite
key "landau_computational_2015"

\end_inset

 for an inspiration for solving the LS equation with an arbitrary initial
 state.
\end_layout

\begin_layout Section
Computing classical Green's functions
\end_layout

\begin_layout Subsection
Boundary element method
\end_layout

\begin_layout Subsection
T-Matrix method
\end_layout

\begin_layout Subsection
T-Matrix resummation (multiple scatterers)
\end_layout

\begin_layout Subsection
BEM→TM
\end_layout

\begin_layout Standard
Cf.
 SCUFF-TMATRIX (
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LatexCommand ref
reference "sub:SCUFF-TMATRIX"

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)
\end_layout

\begin_layout Section
Available software
\end_layout

\begin_layout Subsection
SCUFF-EM 
\begin_inset CommandInset citation
LatexCommand cite
key "reid_scuff-em_2015"

\end_inset


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SCUFF-TMATRIX
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name "sub:SCUFF-TMATRIX"

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\begin_layout Subsubsection

\family typewriter
SCUFF-SCATTER
\family default

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LatexCommand label
name "sub:SCUFF-SCATTER"

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\end_layout

\begin_layout Subsubsection
Caveats
\end_layout

\begin_layout Description
Units.
 
\family typewriter
SCUFF-SCATTER
\family default
's Angular frequencies specified using the 
\family typewriter
--Omega
\family default
 or 
\family typewriter
--OmegaFile
\family default
 arguments are interpreted in units of 
\begin_inset Formula $c/1\,\mathrm{μm}=3\cdot10^{14}\,\mathrm{rad/s}$
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\begin_inset Foot
status open

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\family typewriter
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LatexCommand href
name "http://homerreid.dyndns.org/scuff-EM/scuff-scatter/scuffScatterExamples.shtml"
target "http://homerreid.dyndns.org/scuff-EM/scuff-scatter/scuffScatterExamples.shtml"

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\end_inset

.
 
\emph on
TODO what are the output units?
\end_layout

\begin_layout Subsection
MSTM 
\begin_inset CommandInset citation
LatexCommand cite
key "mackowski_mstm_2013"

\end_inset


\end_layout

\begin_layout Itemize
The incident field is a gaussian beam or a plane wave in the vanilla code
 (no multipole radiation as input!).
\end_layout

\begin_layout Itemize
The bulk of the useful code is in the 
\family typewriter
mstm-modules-v3.0.f90
\family default
 file.
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For solving the interaction equations 
\begin_inset CommandInset citation
LatexCommand cite
after "(14)"
key "mackowski_mstm_2013"

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, the BCGM (biconjugate gradient method) is used.
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According to the manual 
\begin_inset CommandInset citation
LatexCommand cite
after "2.3"
key "mackowski_mstm_2013"

\end_inset

, they use some method (rotational-axial translation decomposition of the
 translation operation), which 
\begin_inset Quotes eld
\end_inset

reduces the operation from an 
\begin_inset Formula $L_{S}^{4}$
\end_inset

 process to 
\begin_inset Formula $L_{S}^{3}$
\end_inset

 process where 
\begin_inset Formula $L_{S}$
\end_inset

 is the truncation order of the expansion
\begin_inset Quotes erd
\end_inset

 (more details can probably be found at 
\begin_inset CommandInset citation
LatexCommand cite
after "around (68)"
key "mackowski_calculation_1996"

\end_inset

.
 
\end_layout

\begin_deeper
\begin_layout Itemize

\emph on
Not sure if this holds also for nonspherical particles, I should either
 read carefully 
\emph default

\begin_inset CommandInset citation
LatexCommand cite
key "mackowski_calculation_1996"

\end_inset


\emph on
 or look into 
\begin_inset CommandInset citation
LatexCommand cite
key "mishchenko_electromagnetic_2003"

\end_inset

 which is also cited in the manual.
\end_layout

\end_deeper
\begin_layout Itemize
By default spheres, it is possible to add own T-Matrix coefficients instead.
 
\end_layout

\begin_deeper
\begin_layout Itemize

\emph on
Is it then possible to insert a T-Matrix of an arbitrary shape, or is it
 somehow limited to 
\begin_inset Quotes eld
\end_inset

spherical-like
\begin_inset Quotes erd
\end_inset

 particles?
\end_layout

\end_deeper
\begin_layout Itemize
Why the heck are the T-matrix options listed in the 
\begin_inset Quotes eld
\end_inset

Options for random orientation calculations
\begin_inset Quotes erd
\end_inset

?
\end_layout

\begin_layout Section
Code integration
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LatexCommand bibtex
bibfiles "dipdip"
options "apsrev"

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