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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
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1 changed files with 29 additions and 14 deletions
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@ -1,5 +1,5 @@
#LyX 2.4 created this file. For more info see https://www.lyx.org/ #LyX 2.4 created this file. For more info see https://www.lyx.org/
\lyxformat 583 \lyxformat 584
\begin_document \begin_document
\begin_header \begin_header
\save_transient_properties true \save_transient_properties true
@ -105,26 +105,32 @@ name "sec:Introduction"
\end_layout \end_layout
\begin_layout Standard \begin_layout Standard
The problem of electromagnetic response of a system consisting of many compact The problem of electromagnetic response of a system consisting of many relativel
scatterers in various geometries, and its numerical solution, is relevant y small, compact scatterers in various geometries, and its numerical solution,
to many branches of nanophotonics (TODO refs). is relevant to many branches of nanophotonics (TODO refs).
The most commonly used general approaches used in computational electrodynamics The most commonly used general approaches used in computational electrodynamics
, such as the finite difference time domain (FDTD) method or the finite are often unsuitable for simulating systems with larger number of scatterers
element method (FEM), are very often unsuitable for simulating systems due to their computational complexity: differential methods such as the
with larger number of scatterers due to their computational complexity. 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 Therefore, a common (frequency-domain) approach to get an approximate solution
of the scattering problem for many small particles has been the coupled of the scattering problem for many small particles has been the coupled
dipole approximation (CDA) where individual scatterers are reduced to electric dipole approximation (CDA) where drastic reduction of the number of DoF
dipoles (characterised by a polarisability tensor) and coupled to each is achieved by approximating individual scatterers to electric dipoles
other through Green's functions. (characterised by a polarisability tensor) coupled to each other through
Green's functions.
\end_layout \end_layout
\begin_layout Standard \begin_layout Standard
CDA is easy to implement and has favorable computational complexity but CDA is easy to implement and demands relatively little computational resources
suffers from at least two fundamental drawbacks. but suffers from at least two fundamental drawbacks.
The obvious one is that the dipole approximation is too rough for particles 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 The other one, more subtle, manifests itself in photonic crystal-like structure
s used in nanophotonics: there are modes in which the particles' electric s used in nanophotonics: there are modes in which the particles' electric
dipole moments completely vanish due to symmetry, regardless of how small dipole moments completely vanish due to symmetry, regardless of how small
@ -154,7 +160,16 @@ multiple-scattering
-matrix method -matrix method
\emph default \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 a limited subset of problems (TODO refs and list the limitations of the
available). available).