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Box 15100 \begin_inset Newline newline \end_inset FI-00076 Aalto \begin_inset Newline newline \end_inset Finland \end_layout \begin_layout Email marek@necada.org \end_layout \begin_layout Author Päivi Törmä \end_layout \begin_layout Address Department of Applied Physics \begin_inset Newline newline \end_inset Aalto University School of Science \begin_inset Newline newline \end_inset P.O. Box 15100 \begin_inset Newline newline \end_inset FI-00076 Aalto \begin_inset Newline newline \end_inset Finland \end_layout \begin_layout Email paivi.torma@aalto.fi \end_layout \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. \begin_inset Note Note status open \begin_layout Plain Layout \begin_inset Marginal status open \begin_layout Plain Layout Should I mention also the cross sections formulae in abstract / intro? \end_layout \end_inset \end_layout \end_inset We release a modern implementation of the method, including the theoretical improvements presented here, under GNU General Public Licence. \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Section Outline \end_layout \begin_layout Itemize Intro: \begin_inset Separator latexpar \end_inset \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 \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) \end_layout \begin_layout Itemize my implementation \end_layout \end_deeper \begin_layout Itemize 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 \end_layout \begin_deeper \begin_layout Itemize How to get it? \end_layout \end_deeper \begin_layout Itemize 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 \begin_layout Itemize 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 \end_layout \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 \end_deeper \begin_layout Itemize Example results (or maybe all in the end) \end_layout \end_deeper \begin_layout Itemize Topology related stuff (TODO)? \end_layout \begin_layout Itemize My implementation. \end_layout \begin_layout Itemize Maybe put the numerical results separately in the end. \end_layout \end_inset \end_layout \begin_layout Section* \begin_inset Note Note status open \begin_layout Section* TODO \end_layout \begin_layout Itemize URLs from bibtex do not appear in the references. \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 Truncation notation. \end_layout \begin_layout Itemize Example results and benchmarks with BEM; figures! \end_layout \begin_deeper \begin_layout Itemize Given up for BEM, SCUFF-EM too unreliable. \end_layout \end_deeper \begin_layout Itemize Carefully check the transformation directions in sec. \begin_inset CommandInset ref LatexCommand ref reference "sec:Symmetries" plural "false" caps "false" noprefix "false" \end_inset \end_layout \begin_layout Itemize Check whether everything written is correct also for non-symmorphic space groups. \end_layout \begin_deeper \begin_layout Itemize Given up \end_layout \end_deeper \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout The text about symmetries is pretty dense. Make it more explanatory and human-readable. \end_layout \end_inset \begin_inset Note Note status open \begin_layout Plain Layout Alternative titles: \end_layout \begin_layout Itemize Many-particle \begin_inset Formula $T$ \end_inset -matrix simulations for nanophotonics: symmetries, scattering and lattice modes \end_layout \begin_layout Itemize Many-particle \begin_inset Formula $T$ \end_inset -matrix simulations for nanophotonics: symmetries, scattering and lattice modes. \end_layout \begin_layout Itemize \begin_inset Formula $T$ \end_inset -matrix simulations in finite and infinite systems of electromagnetic scatterers \end_layout \end_inset \begin_inset Note Note status open \begin_layout Plain Layout Excerpt from the SIAM Journal of Scientific Computing Editorial Policy: \end_layout \begin_layout Quotation The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems. \end_layout \begin_layout Quotation SISC papers are classified into three categories: \begin_inset Separator latexpar \end_inset \end_layout \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. \end_layout \end_deeper \begin_layout Quotation Authors are encouraged to indicate which category best fits their SISC submissio n. \end_layout \begin_layout Quotation 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. \end_layout \begin_layout Quotation 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. \end_layout \begin_layout Plain Layout Category: Methods and Algorithms for Scientific Computing? \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset CommandInset include LatexCommand include filename "intro.lyx" literal "true" \end_inset \begin_inset CommandInset include LatexCommand include filename "finite.lyx" literal "true" \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout \begin_inset CommandInset include LatexCommand include filename "finite-old.lyx" literal "true" \end_inset \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset CommandInset include LatexCommand include filename "infinite.lyx" literal "true" \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout \begin_inset CommandInset include LatexCommand include filename "infinite-old.lyx" literal "true" \end_inset \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset CommandInset include LatexCommand include filename "symmetries.lyx" literal "true" \end_inset \end_layout \begin_layout Standard \begin_inset CommandInset include LatexCommand include filename "examples.lyx" literal "true" \end_inset \end_layout \begin_layout Section Summary \end_layout \begin_layout Standard We presented two major enhancements of the electromagnetic multiple-scattering \begin_inset Formula $T$ \end_inset -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 dozens 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. \end_layout \begin_layout Section Acknowledgments \end_layout \begin_layout Standard We thank 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 318937 (PROFI), by Centre for Quantum Engineering (CQE) at Aalto University, and by the European Research Council (ERC-2013-AdG-340748-CODE). We acknowledge the computational resources provided by the Aalto Science-IT project. \end_layout \begin_layout Standard \begin_inset CommandInset bibtex LatexCommand bibtex btprint "btPrintCited" bibfiles "Tmatrix" options "plain" encoding "default" \end_inset \end_layout \end_body \end_document