QPMS
/
qpms
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity
qpms/lepaper/arrayscat.lyx

1041 lines
18 KiB
Plaintext
Raw Blame History

#LyX 2.4 created this file. For more info see https://www.lyx.org/
\lyxformat 584
\begin_document
\begin_header
\save_transient_properties true
\origin unavailable
\textclass article
\begin_preamble
\DeclareUnicodeCharacter{0428}{Ш }
\usepackage{tikz}
\end_preamble
\use_default_options true
\maintain_unincluded_children false
\language english
\language_package default
\inputencoding utf8
\fontencoding auto
\font_roman "default" "TeX Gyre Pagella"
\font_sans "default" "default"
\font_typewriter "default" "default"
\font_math "auto" "auto"
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_roman_osf true
\font_sans_osf false
\font_typewriter_osf false
\font_sf_scale 100 100
\font_tt_scale 100 100
\use_microtype false
\use_dash_ligatures true
\graphics default
\default_output_format default
\output_sync 0
\bibtex_command default
\index_command default
\float_placement class
\float_alignment class
\paperfontsize default
\spacing single
\use_hyperref true
\pdf_title "Multiple-scattering T-matrix approach in nanophotonics"
\pdf_author "Marek Nečada"
\pdf_bookmarks true
\pdf_bookmarksnumbered false
\pdf_bookmarksopen false
\pdf_bookmarksopenlevel 1
\pdf_breaklinks false
\pdf_pdfborder false
\pdf_colorlinks false
\pdf_backref false
\pdf_pdfusetitle true
\papersize a4paper
\use_geometry false
\use_package amsmath 2
\use_package amssymb 1
\use_package cancel 1
\use_package esint 1
\use_package mathdots 1
\use_package mathtools 1
\use_package mhchem 1
\use_package stackrel 1
\use_package stmaryrd 1
\use_package undertilde 1
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 1
\use_minted 0
\use_lineno 0
\index Index
\shortcut idx
\color #008000
\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
\is_math_indent 0
\math_numbering_side default
\quotes_style english
\dynamic_quotes 0
\papercolumns 1
\papersides 1
\paperpagestyle default
\tablestyle default
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header
\begin_body
\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\SI}[2]{}
{#1\,\mathrm{#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\uoft}[1]{\mathfrak{F}#1}
\end_inset
\begin_inset FormulaMacro
\newcommand{\uaft}[1]{\mathfrak{\mathbb{F}}#1}
\end_inset
\begin_inset FormulaMacro
\newcommand{\usht}[2]{\mathbb{S}_{#1}#2}
\end_inset
\begin_inset FormulaMacro
\newcommand{\bsht}[2]{\mathrm{S}_{#1}#2}
\end_inset
\begin_inset FormulaMacro
\newcommand{\sgn}{\operatorname{sgn}}
{\mathrm{sgn}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\pht}[2]{\mathfrak{\mathbb{H}}_{#1}#2}
\end_inset
\begin_inset FormulaMacro
\newcommand{\vect}[1]{\mathbf{#1}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\uvec}[1]{\mathbf{\hat{#1}}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\ud}{\mathrm{d}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\basis}[1]{\mathfrak{#1}}
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\begin_inset FormulaMacro
\newcommand{\dc}[1]{Ш_{#1}}
\end_inset
\end_layout
\end_inset
\begin_inset FormulaMacro
\newcommand{\dc}[1]{\mathrm{III}_{#1}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\rec}[1]{#1^{-1}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\recb}[1]{#1^{\widehat{-1}}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\ints}{\mathbb{Z}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\nats}{\mathbb{N}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\reals}{\mathbb{R}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\ush}[2]{Y_{#1,#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\ushD}[2]{Y'_{#1,#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\vsh}[3]{\vect A_{#1,#2,#3}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\vshD}[3]{\vect A'_{#1,#2,#3}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\hgfr}{\mathbf{F}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\hgf}{F}
\end_inset
\begin_inset FormulaMacro
\newcommand{\ghgf}[2]{\mbox{}_{#1}F_{#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\ghgfr}[2]{\mbox{}_{#1}\mathbf{F}_{#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\ph}{\mathrm{ph}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\kor}[1]{\underline{#1}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\koru}[1]{\utilde{#1}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\swv}{\mathscr{H}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\expint}{\mathrm{E}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\thespace}{\reals^{3}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\medium}{\Theta}
\end_inset
\begin_inset FormulaMacro
\newcommand{\mezikuli}[3]{\Theta_{#1,#2}\left(#3\right)}
\end_inset
\begin_inset FormulaMacro
\newcommand{\epsbg}{\mathrm{\epsilon_{b}}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\mubg}{\mathrm{\mu_{b}}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\rcoeffp}[1]{a_{#1}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\rcoeffincp}[1]{\tilde{a}_{#1}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\rcoeff}{a}
\end_inset
\begin_inset FormulaMacro
\newcommand{\rcoeffinc}{\tilde{a}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\rcoeffptlm}[4]{\rcoeffp{#1,#2#3#4}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\rcoefftlm}[3]{\rcoeffp{#1#2#3}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\rcoeffincptlm}[4]{\rcoeffincp{#1,#2#3#4}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\vswfrtlm}[3]{\vect v_{#1#2#3}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\sswfoutlm}[2]{\psi_{#1,#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\outcoeff}{f}
\end_inset
\begin_inset FormulaMacro
\newcommand{\outcoeffp}[1]{f_{#1}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\outcoeffptlm}[4]{\outcoeffp{#1,#2#3#4}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\outcoefftlm}[3]{\outcoeffp{#1#2#3}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\vswfouttlm}[3]{\vect u_{#1#2#3}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\Tp}[1]{T_{#1}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\openball}[2]{B_{#1}\left(#2\right)}
\end_inset
\begin_inset FormulaMacro
\newcommand{\closedball}[2]{\overline{B_{#1}\left(#2\right)}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\tropr}{\mathcal{R}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\troprp}[2]{\mathcal{\tropr}_{#1\leftarrow#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\trops}{\mathcal{S}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\tropsp}[2]{\mathcal{\trops}_{#1\leftarrow#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\tropcoeff}{C}
\end_inset
\begin_inset FormulaMacro
\newcommand{\truncated}[2]{\left[#1\right]_{l\le#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\truncate}[2]{\left[#1\right]_{#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\dlmfFer}[2]{\mathsf{P}_{#1}^{#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\antidelta}{\gamma}
\end_inset
\begin_inset FormulaMacro
\newcommand{\groupop}[1]{\hat{P}_{#1}}
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
These are compatibility macros for the (...)-old files:
\end_layout
\end_inset
\begin_inset FormulaMacro
\newcommand{\vswfr}[3]{\vswfrtlm{#3}{#1}{#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\vswfs}[3]{\vswfouttlm{#3}{#1}{#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\svwfs}[3]{\vswfouttlm{#3}{#1}{#2}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\coeffrip}[4]{\rcoeffptlm{#1}{#4}{#2}{#3}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\coeffsip}[4]{\outcoeffptlm{#1}{#4}{#2}{#3}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\coeffr}{\rcoeffp{}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\coeffs}{\outcoeffp{}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\transop}{\trops}
\end_inset
\begin_inset FormulaMacro
\newcommand{\coeffripext}[4]{\rcoeffincptlm{#1}{#4}{#2}{#3}}
\end_inset
\begin_inset FormulaMacro
\newcommand{\Kp}{K}
\end_inset
\end_layout
\begin_layout Title
Multiple-scattering
\begin_inset Formula $T$
\end_inset
-matrix simulations for nanophotonics: symmetries and periodic lattices
\end_layout
\begin_layout Author
Marek Nečada
\begin_inset Foot
status open
\begin_layout Plain Layout
\begin_inset CommandInset href
LatexCommand href
target "marek@necada.org"
type "mailto:"
literal "false"
\end_inset
\end_layout
\end_inset
, Päivi Törmä
\begin_inset Foot
status open
\begin_layout Plain Layout
\begin_inset CommandInset href
LatexCommand href
target "paivi.torma@aalto.fi"
type "mailto:"
literal "false"
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Address
Department of Applied Physics, Aalto University School of Science, P.O.
Box 15100, FI-00076 Aalto, Finland
\end_layout
\begin_layout Standard
\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
\end_layout
\begin_layout Standard
\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 Abstract
The 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 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
\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 Standard
\begin_inset CommandInset bibtex
LatexCommand bibtex
btprint "btPrintCited"
bibfiles "Tmatrix"
options "plain"
encoding "default"
\end_inset
\end_layout
\end_body
\end_document
Reference in New Issue View Git Blame Copy Permalink