730 lines
12 KiB
Plaintext
730 lines
12 KiB
Plaintext
#LyX 2.0 created this file. For more info see http://www.lyx.org/
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\end_header
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\begin_body
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\begin_layout Standard
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\lang finnish
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\begin_inset FormulaMacro
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\newcommand{\ket}[1]{\left|#1\right\rangle }
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\bra}[1]{\left\langle #1\right|}
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\lang english
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\begin_inset FormulaMacro
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\newcommand{\vect}[1]{\mathbf{\boldsymbol{#1}}}
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{\boldsymbol{\mathbf{#1}}}
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\end_inset
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\end_layout
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\begin_layout Title
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Technical notes on quantum electromagnetic multiple scattering
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\end_layout
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\begin_layout Author
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Marek Nečada
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\end_layout
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\begin_layout Affiliation
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COMP Centre of Excellence, Department of Applied Physics, Aalto University,
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P.O.
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Box 15100, Fi-00076 Aalto, Finland
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\end_layout
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\begin_layout Date
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\begin_inset ERT
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status open
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\begin_layout Plain Layout
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\backslash
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today
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Abstract
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...
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\end_layout
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\begin_layout Section
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Theory of quantum electromagnetic multiple scattering
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\end_layout
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\begin_layout Subsection
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Incoherent pumping
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\end_layout
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\begin_layout Standard
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Cf.
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Wubs
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\begin_inset CommandInset citation
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LatexCommand cite
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key "wubs_multiple-scattering_2004"
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\end_inset
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, Delga
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\begin_inset CommandInset citation
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LatexCommand cite
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key "delga_quantum_2014,delga_theory_2014"
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\end_inset
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.
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\end_layout
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\begin_layout Subsection
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General initial states
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\end_layout
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\begin_layout Standard
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Look at
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\begin_inset CommandInset citation
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LatexCommand cite
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key "landau_computational_2015"
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\end_inset
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for an inspiration for solving the LS equation with an arbitrary initial
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state.
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\end_layout
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\begin_layout Section
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Computing classical Green's functions
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\end_layout
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\begin_layout Subsection
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Boundary element method
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\end_layout
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\begin_layout Subsection
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T-Matrix method
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\end_layout
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\begin_layout Subsection
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T-Matrix resummation (multiple scatterers)
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\end_layout
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\begin_layout Subsection
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BEM→TM
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\end_layout
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\begin_layout Standard
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Cf.
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SCUFF-TMATRIX (
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "sub:SCUFF-TMATRIX"
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\end_inset
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)
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\end_layout
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\begin_layout Section
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Available software
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\end_layout
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\begin_layout Subsection
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SCUFF-EM
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\begin_inset CommandInset citation
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LatexCommand cite
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key "reid_scuff-em_2015"
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\end_inset
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\end_layout
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\begin_layout Subsubsection
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\family typewriter
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SCUFF-TMATRIX
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\family default
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\begin_inset CommandInset label
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LatexCommand label
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name "sub:SCUFF-TMATRIX"
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\end_inset
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\end_layout
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\begin_layout Subsubsection
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\family typewriter
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SCUFF-SCATTER
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\family default
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\begin_inset CommandInset label
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LatexCommand label
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name "sub:SCUFF-SCATTER"
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\end_inset
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\end_layout
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\begin_layout Subsubsection
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Caveats
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\end_layout
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\begin_layout Description
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Units.
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\family typewriter
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SCUFF-SCATTER
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\family default
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's Angular frequencies specified using the
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\family typewriter
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--Omega
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\family default
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or
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\family typewriter
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--OmegaFile
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\family default
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arguments are interpreted in units of
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\begin_inset Formula $c/1\,\mathrm{μm}=3\cdot10^{14}\,\mathrm{rad/s}$
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\end_inset
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\begin_inset Foot
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status open
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\begin_layout Plain Layout
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\family typewriter
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\begin_inset CommandInset href
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LatexCommand href
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name "http://homerreid.dyndns.org/scuff-EM/scuff-scatter/scuffScatterExamples.shtml"
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target "http://homerreid.dyndns.org/scuff-EM/scuff-scatter/scuffScatterExamples.shtml"
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\end_inset
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\end_layout
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\end_inset
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.
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\emph on
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TODO what are the output units?
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\end_layout
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\begin_layout Subsection
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MSTM
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\begin_inset CommandInset citation
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LatexCommand cite
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key "mackowski_mstm_2013"
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\end_inset
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\end_layout
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\begin_layout Itemize
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The incident field is a gaussian beam or a plane wave in the vanilla code
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(no multipole radiation as input!).
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\end_layout
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\begin_layout Itemize
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The bulk of the useful code is in the
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\family typewriter
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mstm-modules-v3.0.f90
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\family default
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file.
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\end_layout
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\begin_layout Itemize
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For solving the interaction equations
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\begin_inset CommandInset citation
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LatexCommand cite
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after "(14)"
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key "mackowski_mstm_2013"
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\end_inset
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, the BCGM (biconjugate gradient method) is used.
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(According to Wikipedia, this method is numerically unstable but has a
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stabilized version (stabilized BCGM).)
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\end_layout
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\begin_layout Itemize
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According to the manual
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\begin_inset CommandInset citation
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LatexCommand cite
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after "2.3"
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key "mackowski_mstm_2013"
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\end_inset
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, they use some method (rotational-axial translation decomposition of the
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translation operation), which
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\begin_inset Quotes eld
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\end_inset
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reduces the operation from an
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\begin_inset Formula $L_{S}^{4}$
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\end_inset
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process to
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\begin_inset Formula $L_{S}^{3}$
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\end_inset
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process where
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\begin_inset Formula $L_{S}$
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\end_inset
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is the truncation order of the expansion
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\begin_inset Quotes erd
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\end_inset
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(more details can probably be found at
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\begin_inset CommandInset citation
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LatexCommand cite
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after "around (68)"
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key "mackowski_calculation_1996"
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\end_inset
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.
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\end_layout
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\begin_deeper
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\begin_layout Itemize
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\emph on
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Not sure if this holds also for nonspherical particles, I should either
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read carefully
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\emph default
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\begin_inset CommandInset citation
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LatexCommand cite
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key "mackowski_calculation_1996"
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\end_inset
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\emph on
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or look into
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\begin_inset CommandInset citation
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LatexCommand cite
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key "mishchenko_electromagnetic_2003"
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\end_inset
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which is also cited in the manual.
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\end_layout
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\end_deeper
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\begin_layout Itemize
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By default spheres, it is possible to add own T-Matrix coefficients instead.
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\end_layout
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\begin_deeper
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\begin_layout Itemize
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\emph on
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Is it then possible to insert a T-Matrix of an arbitrary shape, or is it
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somehow limited to
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\begin_inset Quotes eld
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\end_inset
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spherical-like
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\begin_inset Quotes erd
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\end_inset
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particles?
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\end_layout
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\end_deeper
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\begin_layout Itemize
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Why the heck are the T-matrix options listed in the
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\begin_inset Quotes eld
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\end_inset
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Options for random orientation calculations
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\begin_inset Quotes erd
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\end_inset
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?
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\end_layout
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\begin_layout Section
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Code integration
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\end_layout
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\begin_layout Section
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Testing and reproduction of foreign results
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\end_layout
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\begin_layout Subsection
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Delga PRL
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\begin_inset CommandInset citation
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LatexCommand cite
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key "delga_quantum_2014"
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\end_inset
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\end_layout
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\begin_layout Subsubsection
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Parameters
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\end_layout
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\begin_layout Itemize
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Surrounding lossless dielectric
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\series bold
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medium
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\series default
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with permittivity
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\begin_inset Formula $\epsilon_{d}=2.13$
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\end_inset
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.
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\end_layout
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\begin_layout Itemize
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\series bold
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QEs:
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\series default
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dipole moment
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\begin_inset Formula $\mu=0.19\, e\cdot\mathrm{nm}=9.12\,\mathrm{D}$
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\end_inset
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, count
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\begin_inset Formula $N\in\left\{ 1,50,100,200\right\} $
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\end_inset
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, radial orientation,
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\begin_inset Formula $h=1\,\mathrm{nm}$
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\end_inset
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above the sphere (except for Fig.
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5 where variable), natural frequency
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\begin_inset Formula $\Omega_{n}=\omega_{0}-i\gamma_{\mathrm{QE}}/2,$
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\end_inset
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\begin_inset Formula $\omega_{0}=$
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\end_inset
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varies,
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\begin_inset Formula $\gamma_{\mathrm{QE}}=15\,\mathrm{meV}$
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\end_inset
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.
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\end_layout
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\begin_layout Itemize
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\series bold
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Sphere:
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\end_layout
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\begin_deeper
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\begin_layout Itemize
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radius
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\begin_inset Formula $a=7\,\mathrm{nm}$
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\end_inset
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,
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\end_layout
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\begin_layout Itemize
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Drude model
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\begin_inset Formula $\epsilon_{m}(\omega)=\epsilon_{\infty}-\frac{\omega_{p}^{2}}{\omega\left(\omega+i\gamma_{p}\right)}$
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\end_inset
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\end_layout
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\begin_deeper
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\begin_layout Itemize
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Drude parameters
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\begin_inset Formula $\omega_{p}=9\,\mathrm{eV}$
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\end_inset
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,
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\begin_inset Formula $\epsilon_{\infty}=4.6$
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\end_inset
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,
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\begin_inset Formula $\gamma_{p}=0.1\,\mathrm{eV}$
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\end_inset
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\end_layout
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\end_deeper
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\begin_layout Itemize
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background permittivity
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\begin_inset Formula $\epsilon_{d}(\omega)=2.13$
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\end_inset
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\end_layout
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\begin_layout Itemize
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(approximate?; not really a parameter) LSP resonances
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\begin_inset Formula $\omega_{l}=\omega_{p}/\sqrt{\epsilon_{\infty}+\left(1+1/l\right)\epsilon_{d}}$
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\end_inset
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; particularly,
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\begin_inset Formula $\omega_{1}\approx3.0236\,\mathrm{eV}$
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\end_inset
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,
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\begin_inset Formula $\omega_{2}\approx3.2236\,\mathrm{eV}$
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\end_inset
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,
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\begin_inset Formula $\omega_{\infty}\approx3.4692\,\mathrm{eV}$
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\end_inset
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\end_layout
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\end_deeper
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\begin_layout Itemize
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\series bold
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Detector:
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\series default
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\end_layout
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\begin_deeper
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\begin_layout Itemize
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Far field:
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\begin_inset Formula $1\,\mathrm{\mu m}$
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\end_inset
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away from the center of the nanoparticle along the
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\begin_inset Formula $y$
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\end_inset
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axis (Fig.
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3).
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\end_layout
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\begin_layout Itemize
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Near field: position not specified in the paper; but in Fig.
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4(b) there are
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\begin_inset Quotes eld
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\end_inset
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polarization spectra
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\begin_inset Quotes erd
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\end_inset
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instead of
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\begin_inset Quotes eld
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\end_inset
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light spectra
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\begin_inset Quotes erd
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\end_inset
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(eq.
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4) in Fig.
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4(a).
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Does this mean that they are evaluated somewhere in/on the sphere? Or in
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the particle? The latter is likely, as it is given by
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\begin_inset Formula $P_{n}\left(\omega\right)=\left\langle \sigma_{n}^{+}\left(-\omega\right)\sigma_{n}^{-}(\omega)\right\rangle $
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\end_inset
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(cf.
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the column below Fig.
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3).
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\end_layout
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\end_deeper
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\begin_layout Subsubsection
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Testing
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\end_layout
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\begin_layout Standard
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In my
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\begin_inset Quotes eld
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\end_inset
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old
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\begin_inset Quotes erd
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\end_inset
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code, there no splitting observable around
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\begin_inset Formula $\omega\approx\omega_{0}\approx\omega_{\infty}\approx3.46\,\mathrm{eV}$
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\end_inset
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.
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This is perhaps because the couplings to the higher multipoles is miscalculated
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(too small).
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No splitting around the NP dipole (
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\begin_inset Formula $\approx3,02\,\mathrm{eV}$
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\end_inset
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) should be OK for single QE in far field (cf.
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Fig.
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3).
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And there are yet the
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\begin_inset Quotes eld
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\end_inset
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switched axes
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\begin_inset Quotes erd
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\end_inset
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...
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\end_layout
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\begin_layout Subsection
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Delga JoO
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\begin_inset CommandInset citation
|
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LatexCommand cite
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key "delga_theory_2014"
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\end_inset
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\end_layout
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\begin_layout Subsubsection
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Parameters
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\end_layout
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\begin_layout Itemize
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\series bold
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QEs:
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\series default
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dipole moment
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\begin_inset Formula $\mu=0.38\, e\cdot\mathrm{nm}=18.24\,\mathrm{D}$
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\end_inset
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(double), otherwise the same parameters as in
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\begin_inset CommandInset citation
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LatexCommand cite
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key "delga_quantum_2014"
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\end_inset
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.
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\end_layout
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\begin_layout Itemize
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\series bold
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|
Sphere:
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|
\series default
|
|
as in
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "delga_quantum_2014"
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|
\end_inset
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\end_layout
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\begin_layout Itemize
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\series bold
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Detector:
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|
\series default
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not stated in the paper
|
|
\end_layout
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|
\begin_layout Standard
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|
\begin_inset CommandInset bibtex
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|
LatexCommand bibtex
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bibfiles "dipdip"
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options "apsrev"
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\end_inset
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\end_layout
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\end_body
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\end_document
|