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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
 
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(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
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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.
 
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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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Authors are encouraged to indicate which category best fits their SISC submissio
n.
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 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

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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.
 
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Should I mention also the cross sections formulae in abstract / intro?
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\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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\end_layout

\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

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

old-fashioned
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 (FEM, FDTD)
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my implementation
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Finite systems:
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motivation (classes of problems that this can solve: response to external
 radiation, resonances, ...)
\end_layout

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theory
\begin_inset Separator latexpar
\end_inset


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T-matrix definition, basics
\begin_inset Separator latexpar
\end_inset


\end_layout

\begin_deeper
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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
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Example results (or maybe rather in the end)
\end_layout

\end_deeper
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Infinite lattices:
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\begin_deeper
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motivation (dispersion relations / modes, ...?)
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theory
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Ewald sum of translation operators (again, we shall see how explicit expressions
 it will take to not make it too repulsive) 
\end_layout

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singularities and convergence (TODO)
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applications: mode problem with SVD, transmision/reflection
\end_layout

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space group symmetries (again, maybe all the symmetry-related stuff separately?)
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\end_deeper
\begin_layout Itemize
Example results (or maybe all in the end)
\end_layout

\end_deeper
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Topology related stuff (TODO)?
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My implementation.
\end_layout

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

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\end_layout

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TODO
\end_layout

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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

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Truncation notation.
\end_layout

\begin_layout Itemize
Example results and benchmarks with BEM; figures!
\end_layout

\begin_layout Itemize
Carefully check the transformation directions in sec.
 
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Check whether everything written is correct also for non-symmorphic space
 groups.
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The text about symmetries is pretty dense.
 Make it more explanatory and human-readable.
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