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\pdf_title "Multiple-scattering T-matrix approach in nanophotonics"
\pdf_author "Marek Nečada"
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\begin_layout Title
\begin_inset Formula $T$
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-matrix simulations in finite and infinite systems of electromagnetic scatterers
 (TODO better title)
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Excerpt from the SIAM Journal of Scientific Computing Editorial Policy:
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The purpose of SIAM Journal on Scientific Computing (SISC) is to advance
 computational methods for solving scientific and engineering problems.
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SISC papers are classified into three categories:
\begin_inset Separator latexpar
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\begin_deeper
\begin_layout Itemize
Methods and Algorithms for Scientific Computing: Papers in this category
 may include theoretical analysis, provided that the relevance to applications
 in science and engineering is demonstrated.
 They should contain meaningful computational results and theoretical results
 or strong heuristics supporting the performance of new algorithms.
 
\end_layout

\begin_layout Itemize
Computational Methods in Science and Engineering: Papers in this section
 will typically describe novel methodologies for solving a specific problem
 in computational science or engineering.
 They should contain enough information about the application to orient
 other computational scientists but should omit details of interest mainly
 to the applications specialist.
 
\end_layout

\begin_layout Itemize
Software and High-Performance Computing: Papers in this category should
 concern the novel design and development of computational methods and high-qual
ity software, parallel algorithms, high-performance computing issues, new
 architectures, data analysis, or visualization.
 The primary focus should be on computational methods that have potentially
 large impact for an important class of scientific or engineering problems.
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\begin_layout Quotation
Authors are encouraged to indicate which category best fits their SISC submissio
n.
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All submissions to SISC must be well written and accessible to a wide variety
 of readers, and should represent a clear advance in the state of the art.
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Due to space limitations, articles are normally limited to 20 journal pages.
 Exceptions can be made in special cases only with the concurrence of the
 referees, the associate editor, and the editor-in-chief.
 
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Category: Methods and Algorithms for Scientific Computing?
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\begin_layout Abstract
The (somewhat underrated) T-matrix multiple scattering method (TMMSM) can
 be used to solve the electromagnetic response of systems consisting of
 many compact scatterers, retaining a good level of accuracy while using
 relatively few of degrees of freedom, largely surpassing other methods
 in the number of scatterers it can deal with.
\end_layout

\begin_layout Abstract
Here we extend the method to infinite periodic structures using Ewald-type
 lattice summation, and we exploit the possible symmetries of the structure
 to further improve its efficiency.
 (SHOULD I MENTION ALSO THE CROSS SECTION FORMULAS IN THE ABSTRACT?)
\end_layout

\begin_layout Abstract
We release a modern implementation of the method, including the theoretical
 improvements presented here, under GNU General Public Licence.
\end_layout

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Outline
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Intro: 
\begin_inset Separator latexpar
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\begin_deeper
\begin_layout Itemize
problem of optical response of nanoparticle arrays
\end_layout

\begin_layout Itemize
application domain of my method, computational complexity
\end_layout

\begin_layout Itemize
brief comparison of complexities with the 
\begin_inset Quotes eld
\end_inset

old-fashioned
\begin_inset Quotes erd
\end_inset

 (FEM, FDTD)
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my implementation
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Finite systems:
\begin_inset Separator latexpar
\end_inset


\end_layout

\begin_deeper
\begin_layout Itemize
motivation (classes of problems that this can solve: response to external
 radiation, resonances, ...)
\end_layout

\begin_layout Itemize
theory
\begin_inset Separator latexpar
\end_inset


\end_layout

\begin_deeper
\begin_layout Itemize
T-matrix definition, basics
\begin_inset Separator latexpar
\end_inset


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\begin_deeper
\begin_layout Itemize
How to get it?
\end_layout

\end_deeper
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translation operators (TODO think about how explicit this should be, but
 I guess it might be useful to write them to write them explicitly (but
 in the shortest possible form) in the normalisation used in my program)
\end_layout

\begin_layout Itemize
employing point group symmetries and decomposing the problem to decrease
 the computational complexity (maybe separately)
\end_layout

\end_deeper
\begin_layout Itemize
Example results (or maybe rather in the end)
\end_layout

\end_deeper
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Infinite lattices:
\begin_inset Separator latexpar
\end_inset


\end_layout

\begin_deeper
\begin_layout Itemize
motivation (dispersion relations / modes, ...?)
\end_layout

\begin_layout Itemize
theory
\begin_inset Separator latexpar
\end_inset


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\begin_deeper
\begin_layout Itemize
Ewald sum of translation operators (again, we shall see how explicit expressions
 it will take to not make it too repulsive) 
\end_layout

\begin_layout Itemize
singularities and convergence (TODO)
\end_layout

\begin_layout Itemize
applications: mode problem with SVD, transmision/reflection
\end_layout

\begin_layout Itemize
space group symmetries (again, maybe all the symmetry-related stuff separately?)
\end_layout

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\begin_layout Itemize
Example results (or maybe all in the end)
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\end_deeper
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Topology related stuff (TODO)?
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\begin_layout Itemize
My implementation.
\end_layout

\begin_layout Itemize
Maybe put the numerical results separately in the end.
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\end_layout

\begin_layout Section
TODOs
\end_layout

\begin_layout Itemize
Consistent notation of balls.
 How is the difference between two cocentric balls called?
\end_layout

\begin_layout Itemize
It could be nice to include some illustration (example array) to the introductio
n.
 Put a specific example of how large system are we able to simulate?
\end_layout

\begin_layout Itemize
Maybe mention that in infinite systems, it can be also much faster than
 other methods.
\end_layout

\begin_layout Itemize
Translation operators: rewrite in sph.
 harm.
 convention independent form.
\end_layout

\begin_layout Itemize
Truncation notation.
\end_layout

\begin_layout Itemize
Example results!
\end_layout

\begin_layout Itemize
Figures.
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Concrete comparison with other methods.
\end_layout

\begin_layout Itemize
Fix and unify notation (mainly indices) in infinite lattices section.
\end_layout

\begin_layout Itemize
Carefully check the transformation directions in sec.
 
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\end_layout

\begin_layout Itemize
The text about symmetries is pretty dense.
 Make it more explanatory and human-readable.
\end_layout

\begin_layout Itemize
Check whether everything written is correct also for non-symmorphic space
 groups.
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