From 94a4d59cfbc04609cfd595e8f0be65c02f77d3d5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= Date: Sun, 28 Jul 2019 16:29:37 +0300 Subject: [PATCH] Restoring accidentally deleted intro Former-commit-id: f485907e47efb727e1e26f34aa8ca93b810bd103 --- lepaper/intro.lyx | 197 +++++++++++++++++++++++++++++++++++++++------- 1 file changed, 168 insertions(+), 29 deletions(-) diff --git a/lepaper/intro.lyx b/lepaper/intro.lyx index f802303..30c98c7 100644 --- a/lepaper/intro.lyx +++ b/lepaper/intro.lyx @@ -1,37 +1,29 @@ -#LyX 2.4 created this file. For more info see https://www.lyx.org/ -\lyxformat 583 +#LyX 2.1 created this file. For more info see http://www.lyx.org/ +\lyxformat 474 \begin_document \begin_header -\save_transient_properties true -\origin unavailable \textclass article \use_default_options true \maintain_unincluded_children false -\language english +\language finnish \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" +\inputencoding auto +\fontencoding global +\font_roman TeX Gyre Pagella +\font_sans default +\font_typewriter default +\font_math auto \font_default_family default -\use_non_tex_fonts false +\use_non_tex_fonts true \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 +\font_osf true +\font_sf_scale 100 +\font_tt_scale 100 \graphics default -\default_output_format default +\default_output_format pdf4 \output_sync 0 \bibtex_command default \index_command default -\float_placement class -\float_alignment class \paperfontsize default \spacing single \use_hyperref true @@ -66,8 +58,6 @@ \suppress_date false \justification true \use_refstyle 1 -\use_minted 0 -\use_lineno 0 \index Index \shortcut idx \color #008000 @@ -76,14 +66,10 @@ \tocdepth 3 \paragraph_separation indent \paragraph_indentation default -\is_math_indent 0 -\math_numbering_side default -\quotes_style english -\dynamic_quotes 0 +\quotes_language swedish \papercolumns 1 \papersides 1 \paperpagestyle default -\tablestyle default \tracking_changes false \output_changes false \html_math_output 0 @@ -95,6 +81,159 @@ \begin_layout Section Introduction +\begin_inset CommandInset label +LatexCommand label +name "sec:Introduction" + +\end_inset + + +\end_layout + +\begin_layout Standard +The problem of electromagnetic response of a system consisting of many compact + scatterers in various geometries, and its numerical solution, is relevant + to many branches of nanophotonics (TODO refs). + The most commonly used general approaches used in computational electrodynamics +, such as the finite difference time domain (FDTD) method or the finite + element method (FEM), are very often unsuitable for simulating systems + with larger number of scatterers due to their computational complexity. + Therefore, a common (frequency-domain) approach to get an approximate solution + of the scattering problem for many small particles has been the coupled + dipole approximation (CDA) where individual scatterers are reduced to electric + dipoles (characterised by a polarisability tensor) and coupled to each + other through Green's functions. + +\end_layout + +\begin_layout Standard +CDA is easy to implement and has favorable computational complexity but + suffers from at least two fundamental drawbacks. + The obvious one is that the dipole approximation is too rough for particles + with diameter larger than a small fraction of the wavelength. + The other one, more subtle, manifests itself in photonic crystal-like structure +s used in nanophotonics: there are modes in which the particles' electric + dipole moments completely vanish due to symmetry, regardless of how small + the particles are, and the excitations have quadrupolar or higher-degree + multipolar character. + These modes typically appear at the band edges where interesting phenomena + such as lasing or Bose-Einstein condensation have been observed – and CDA + by definition fails to capture such modes. +\end_layout + +\begin_layout Standard +The natural way to overcome both limitations of CDA mentioned above is to + include higher multipoles into account. + Instead of polarisability tensor, the scattering properties of an individual + particle are then described a more general +\begin_inset Formula $T$ +\end_inset + +-matrix, and different particles' multipole excitations are coupled together + via translation operators, a generalisation of the Green's functions in + CDA. + This is the idea behind the +\emph on +multiple-scattering +\begin_inset Formula $T$ +\end_inset + +-matrix method +\emph default +(MSTMM) (TODO a.k.a something??), and it has been implemented previously for + a limited subset of problems (TODO refs and list the limitations of the + available). + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +TODO přestože blablaba, moc se to nepoužívalo, protože je težké udělat to + správně. +\end_layout + +\end_inset + + Due to the limitations of the existing available codes, we have been developing + our own implementation of MSTMM, which we have used in several previous + works studying various physical phenomena in plasmonic nanoarrays (TODO + examples with refs). + +\end_layout + +\begin_layout Standard +Hereby we release our MSTMM implementation, the +\emph on +QPMS Photonic Multiple Scattering +\emph default + suite, as an open source software under the GNU General Public License + version 3. + (TODO refs to the code repositories.) QPMS allows for linear optics simulations + of arbitrary sets of compact scatterers in isotropic media. + The features include computations of electromagnetic response to external + driving, the related cross sections, and finding resonances of finite structure +s. + Moreover, in QPMS we extensively employ group theory to exploit the physical + symmetries of the system to further reduce the demands on computational + resources, enabling to simulate even larger systems. + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +(TODO put a specific example here of how large system we are able to simulate?) +\end_layout + +\end_inset + + Although systems of large +\emph on +finite +\emph default + number of scatterers are the area where MSTMM excels the most—simply because + other methods fail due to their computational complexity—we also extended + the method onto infinite periodic systems (photonic crystals); this can + be used for quickly evaluating dispersions of such structures and also + their topological invariants (TODO). + The QPMS suite contains a core C library, Python bindings and several utilities + for routine computations, such as TODO. + It includes extensive Doxygen documentation, together with description + of the API, making extending and customising the code easy. +\end_layout + +\begin_layout Standard +The current paper is organised as follows: Section +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Finite" + +\end_inset + + is devoted to MSTMM theory for finite systems, in Section +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Infinite" + +\end_inset + + we develop the theory for infinite periodic structures. + Section +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Applications" + +\end_inset + + demonstrates some basic practical results that can be obtained using QPMS. + Finally, in Section +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Comparison" + +\end_inset + + we comment on the computational complexity of MSTMM in comparison to other + methods. \end_layout \end_body