qpms/lepaper/finite.lyx

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#LyX 2.1 created this file. For more info see http://www.lyx.org/
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\pdf_author "Marek Nečada"
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\begin_layout Section
Finite systems
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LatexCommand label
name "sec:Finite"
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\begin_layout Itemize
\lang english
motivation (classes of problems that this can solve: response to external
radiation, resonances, ...)
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\begin_deeper
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\lang english
theory
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\begin_deeper
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\lang english
T-matrix definition, basics
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\begin_deeper
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\lang english
How to get it?
\end_layout
\end_deeper
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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
\lang english
employing point group symmetries and decomposing the problem to decrease
the computational complexity (maybe separately)
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Motivation
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Single-particle scattering
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In order to define the basic concepts, let us first consider the case of
EM radiation scattered by a single particle.
We assume that the scatterer lies inside a closed sphere
\begin_inset Formula $\particle$
\end_inset
, the space outside this volume
\begin_inset Formula $\medium$
\end_inset
is filled with an homogeneous isotropic medium with relative electric permittiv
ity
\begin_inset Formula $\epsilon(\vect r,\omega)=\epsbg(\omega)$
\end_inset
and magnetic permeability
\begin_inset Formula $\mu(\vect r,\omega)=\mubg(\omega)$
\end_inset
, and that the whole system is linear, i.e.
the material properties of neither the medium nor the scatterer depend
on field intensities.
Under these assumptions, the EM fields in
\begin_inset Formula $\medium$
\end_inset
must satisfy the homogeneous vector Helmholtz equation
\begin_inset Formula $\left(\nabla^{2}+k^{2}\right)\Psi\left(\vect r,\vect{\omega}\right)=0$
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\begin_inset Note Note
status open
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todo define
\begin_inset Formula $\Psi$
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, mention transversality
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\end_inset
with
\begin_inset Formula $k=TODO$
\end_inset
[TODO REF Jackson?].
Its solutions (TODO under which conditions? What vector space do the SVWFs
actually span? Check Comment 9.2 and Appendix f.9.1 in Kristensson)
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Throughout this text, we will use the same normalisation conventions as
in
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key "kristensson_scattering_2016"
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.
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\begin_layout Subsubsection
\lang english
Spherical waves
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\begin_layout Standard
\lang english
\begin_inset Note Note
status open
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\lang english
TODO small note about cartesian multipoles, anapoles etc.
(There should be some comparing paper that the Russians at META 2018 mentioned.)
\end_layout
\end_inset
\end_layout
\begin_layout Subsubsection
\lang english
T-matrix definition
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\begin_layout Subsubsection
Absorbed power
\end_layout
\begin_layout Subsubsection
\lang english
T-matrix compactness, cutoff validity
\end_layout
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\lang english
Multiple scattering
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\lang english
Translation operator
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Numerical complexity, comparison to other methods
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