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Update first part of the intro 

Former-commit-id: 0066137ef7c695fbf1fbbb92a47164b7a3e8671c
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Marek Nečada 2019-08-06 12:52:06 +03:00
parent 2a890c56ac
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1 changed files with 29 additions and 14 deletions
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lepaper/intro.lyx
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@ -1,5 +1,5 @@
#LyX 2.4 created this file. For more info see https://www.lyx.org/
\lyxformat 583
\lyxformat 584
\begin_document
\begin_header
\save_transient_properties true
@ -105,26 +105,32 @@ name "sec:Introduction"
\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 problem of electromagnetic response of a system consisting of many relativel
y small, 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.
are often unsuitable for simulating systems with larger number of scatterers
due to their computational complexity: differential methods such as the
finite difference time domain (FDTD) method or the finite element method
(FEM) include the field degrees of freedom (DoF) of the background medium
(which can have very large volumes), whereas integral approaches such as
the boundary element method (BEM) need much less DoF but require working
with dense matrices containing couplings between each pair of DoF.
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.
dipole approximation (CDA) where drastic reduction of the number of DoF
is achieved by approximating individual scatterers to electric dipoles
(characterised by a polarisability tensor) 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.
CDA is easy to implement and demands relatively little computational resources
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.
with diameter larger than a small fraction of the wavelength, which results
to quantitative errors.
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
@ -154,7 +160,16 @@ multiple-scattering
-matrix method
\emph default
(MSTMM) (TODO a.k.a something??), and it has been implemented previously for
(MSTMM), a.k.a.
\emph on
superposition
\begin_inset Formula $T$
\end_inset
-matrix method
\emph default
(TODO a.k.a something; refs??), and it has been implemented previously for
a limited subset of problems (TODO refs and list the limitations of the
available).