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\pdf_author "Marek Nečada"
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\begin_body

\begin_layout Section
Finite systems
\end_layout

\begin_layout Itemize
motivation (classes of problems that this can solve: response to external
 radiation, resonances, ...)
\begin_inset Separator latexpar
\end_inset


\end_layout

\begin_deeper
\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
\end_deeper
\begin_layout Subsection
Motivation
\end_layout

\begin_layout Standard
The basic idea of MSTMM is quite simple: the driving electromagnetic field
 incident onto a scatterer is expanded into a vector spherical wavefunction
 (VSWF) basis in which the single scattering problem is solved, and the
 scattered field is then re-expanded into VSWFs centered at the other scatterers.
 Repeating the same procedure with all (pairs of) scatterers yields a set
 of linear equations, solution of which gives the coefficients of the scattered
 field in the VSWF bases.
 However, 
\end_layout

\begin_layout Subsection
Single-particle scattering
\end_layout

\begin_layout Standard
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 $\left(\nabla^{2}+k^{2}\right)\Psi\left(\vect r,\vect{\omega}\right)=0$
\end_inset

 
\begin_inset Note Note
status open

\begin_layout Plain Layout
todo define 
\begin_inset Formula $\Psi$
\end_inset

, mention transversality
\end_layout

\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)
\end_layout

\begin_layout Standard
Throughout this text, we will use the same normalisation conventions as
 in 
\begin_inset CommandInset citation
LatexCommand cite
key "kristensson_scattering_2016"
literal "true"

\end_inset

.
\end_layout

\begin_layout Subsubsection
Spherical waves
\end_layout

\begin_layout Standard
\begin_inset Note Note
status open

\begin_layout Plain Layout
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
T-matrix definition
\end_layout

\begin_layout Subsubsection
Absorbed power
\end_layout

\begin_layout Subsubsection
T-matrix compactness, cutoff validity
\end_layout

\begin_layout Subsection
Multiple scattering
\end_layout

\begin_layout Subsubsection
Translation operator
\end_layout

\begin_layout Subsubsection
Numerical complexity, comparison to other methods
\end_layout

\end_body
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