qpms/lepaper/arrayscat.lyx

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\pdf_title "Multiple-scattering T-matrix approach in nanophotonics"
\pdf_author "Marek Nečada"
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\begin_layout Standard

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\begin_layout Title
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\begin_inset Formula $T$
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-matrix simulations: symmetries and periodic lattices
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Multiple-scattering 
\begin_inset Formula $T$
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-matrix simulations for nanophotonics: symmetries and periodic lattices
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\begin_layout Author
Marek Nečada
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\begin_layout Address
Department of Applied Physics 
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Aalto University School of Science
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P.O.
 Box 15100
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FI-00076 Aalto
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Finland
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\begin_layout Email
marek@necada.org
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\begin_layout Author
Päivi Törmä
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\begin_layout Address
Department of Applied Physics 
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Aalto University School of Science
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P.O.
 Box 15100
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FI-00076 Aalto
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Finland
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\begin_layout Email
paivi.torma@aalto.fi
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\begin_layout Subjectclass
78-10, 78-04, 78M16, 78A45, 65R20, 35B27
\end_layout

\begin_layout Keywords
T-matrix, multiple scattering, lattice modes, symmetry-adapted basis, metamateri
als, Ewald summation
\end_layout

\begin_layout Abstract
The multiple scattering method T-matrix (MSTMM) 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 degrees of
 freedom, largely surpassing other methods in the number of scatterers it
 can deal with.
 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, so that systems containing tens of thousands
 of particles can be studied with relative ease.
 
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Should I mention also the cross sections formulae in abstract / intro?
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We release a modern implementation of the method, including the theoretical
 improvements presented here, under GNU General Public Licence.
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Outline
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Intro: 
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\begin_deeper
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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 
\begin_inset Quotes eld
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old-fashioned
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 (FEM, FDTD)
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my implementation
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Finite systems:
\begin_inset Separator latexpar
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\begin_deeper
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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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\begin_deeper
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T-matrix definition, basics
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\begin_deeper
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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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\end_deeper
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Example results (or maybe rather in the end)
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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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\begin_deeper
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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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TODO
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URLs from bibtex do not appear in the references.
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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?
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Maybe mention that in infinite systems, it can be also much faster than
 other methods.
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Truncation notation.
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\begin_layout Itemize
Example results and benchmarks with BEM; figures!
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\begin_deeper
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Given up for BEM, SCUFF-EM too unreliable.
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\end_deeper
\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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Given up
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The text about symmetries is pretty dense.
 Make it more explanatory and human-readable.
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Alternative titles:
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\begin_layout Itemize
Many-particle 
\begin_inset Formula $T$
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-matrix simulations for nanophotonics: symmetries, scattering and lattice
 modes
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\begin_layout Itemize
Many-particle 
\begin_inset Formula $T$
\end_inset

-matrix simulations for nanophotonics: symmetries, scattering and lattice
 modes.
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\begin_layout Itemize
\begin_inset Formula $T$
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-matrix simulations in finite and infinite systems of electromagnetic scatterers
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Excerpt from the SIAM Journal of Scientific Computing Editorial Policy:
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\begin_layout Quotation
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.
 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 Section
Summary
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We presented two major enhancements of the electromagnetic multiple-scattering
 
\begin_inset Formula $T$
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-matrix method: 1) Employing Ewald summation techniques enables very efficient
 computation of lattice modes and optical response of infinite periodic
 nanoparticle structures.
 2) Exploiting possible symmetries of the system by transformation into
 symmetry adapted basis reduces the requirements on computational resources
 considerably, enabling simulations of finite systems with tens of thousands
 of scatterers.
 These enhancements are included into the QPMS software suite, which we
 hereby make publicly available under the GNU General Public License.
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\begin_layout Section
Acknowledgments
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\begin_layout Standard
We thank Nicki Källman, Kristian Arjas and Javier Cuerda for useful discussions.
 This work was supported by the Academy of Finland under project numbers
 303351, 307419, 327293, 318987 (QuantERA project RouTe), and by the European
 Research Council (ERC-2013-AdG-340748-CODE).
 We acknowledge the computational resources provided by the Aalto Science-IT
 project.
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LatexCommand bibtex
btprint "btPrintCited"
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options "plain"
encoding "default"

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