qpms/lepaper/arrayscat.lyx

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\pdf_title "Multiple-scattering T-matrix approach in nanophotonics"
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QPMS Photonic Multiple Scattering suite (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:
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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.
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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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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.
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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.
It largely surpasses other methods in the number of scatterers it can deal
with, while retaining very good accuracy.
\end_layout
\begin_layout Abstract
TODO REWRITE: We release a modern implementation of the method under GNU
General Public Licence, with several theoretical advancements presented
here, such as exploiting the system symmetries to further improve the efficienc
y of the method, or extending it on infinite periodic systems.
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Outline
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Intro:
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problem of optical response of nanoparticle arrays
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application domain of my method, computational complexity
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brief comparison of complexities with the
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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, ...)
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theory
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T-matrix definition, basics
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\end_inset
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How to get it?
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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)
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employing point group symmetries and decomposing the problem to decrease
the computational complexity (maybe separately)
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Example results (or maybe rather in the end)
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Infinite lattices:
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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)
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singularities and convergence (TODO)
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applications: mode problem with SVD, transmision/reflection
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space group symmetries (again, maybe all the symmetry-related stuff separately?)
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Example results (or maybe all in the end)
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Topology related stuff (TODO)?
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My implementation.
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Maybe put the numerical results separately in the end.
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TODOs
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Consistent notation of balls.
How is the difference between two cocentric balls called?
\end_layout
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Abstract.
\end_layout
\begin_layout Itemize
Translation operators: rewrite in sph.
harm.
convention independent form.
\end_layout
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Truncation notation.
\end_layout
\begin_layout Itemize
Example results!
\end_layout
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Figures.
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Concrete comparison with other methods.
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Fix and unify notation (mainly indices) in infinite lattices section.
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Carefully check the transformation directions in sec.
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The text about symmetries is pretty dense.
Make it more explanatory and human-readable.
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