Examples draft

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@ -10,6 +10,22 @@
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/HES6WJTP/(Wiley science paperback series) Craig F. Bohren, Donald R. Huffman-Absorption and scattering of light by small particles-Wiley-VCH (1998).djvu} file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/HES6WJTP/(Wiley science paperback series) Craig F. Bohren, Donald R. Huffman-Absorption and scattering of light by small particles-Wiley-VCH (1998).djvu}
} }
@article{johnson_optical_1972,
title = {Optical {{Constants}} of the {{Noble Metals}}},
volume = {6},
abstract = {The optical constants n and k were obtained for the noble metals (copper, silver, and gold) from reflection and transmission measurements on vacuum-evaporated thin films at room temperature, in the spectral range 0.5-6.5 eV. The film-thickness range was 185-500 {\AA}. Three optical measurements were inverted to obtain the film thickness d as well as n and k. The estimated error in d was {$\pm$} 2 {\AA}, and that in n, k was less than 0.02 over most of the spectral range. The results in the film-thickness range 250-500 {\AA} were independent of thickness, and were unchanged after vacuum annealing or aging in air. The free-electron optical effective masses and relaxation times derived from the results in the near infrared agree satisfactorily with previous values. The interband contribution to the imaginary part of the dielectric constant was obtained by subtracting the free-electron contribution. Some recent theoretical calculations are compared with the results for copper and gold. In addition, some other recent experiments are critically compared with our results.},
number = {12},
urldate = {2015-10-06},
journal = {Phys. Rev. B},
doi = {10.1103/PhysRevB.6.4370},
url = {http://link.aps.org/doi/10.1103/PhysRevB.6.4370},
author = {Johnson, P. B. and Christy, R. W.},
month = dec,
year = {1972},
pages = {4370-4379},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/ANQIIJA5/PhysRevB.6.html}
}
@misc{SCUFF2, @misc{SCUFF2,
title = {{{SCUFF}}-{{EM}}}, title = {{{SCUFF}}-{{EM}}},
url = {http://homerreid.dyndns.org/scuff-EM/}, url = {http://homerreid.dyndns.org/scuff-EM/},

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@ -99,6 +99,12 @@
\begin_body \begin_body
\begin_layout Standard \begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\SI}[2]{}
{#1\,\mathrm{#2}}
\end_inset
\begin_inset FormulaMacro \begin_inset FormulaMacro
\newcommand{\uoft}[1]{\mathfrak{F}#1} \newcommand{\uoft}[1]{\mathfrak{F}#1}
\end_inset \end_inset
@ -747,8 +753,8 @@ Maybe put the numerical results separately in the end.
\end_layout \end_layout
\begin_layout Section \begin_layout Section*
TODOs TODO
\end_layout \end_layout
\begin_layout Itemize \begin_layout Itemize

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@ -104,5 +104,214 @@ name "sec:Applications"
\end_layout \end_layout
\begin_layout Standard
Finally, we present some results obtained with the QPMS suite as well as
benchmarks with BEM.
Scripts to reproduce these results are available under the
\family typewriter
examples
\family default
directory of the QPMS source repository.
The benchmarks require SCUFF-EM of version xxx
\begin_inset Marginal
status open
\begin_layout Plain Layout
Add the version when possible.
\end_layout
\end_inset
or newer.
\end_layout
\begin_layout Subsection
Response of a rectangular nanoplasmonic array
\end_layout
\begin_layout Standard
Our first example deals with a plasmonic array made of golden nanoparticles
placed in a rectangular planar configuration.
The nanoparticles have shape of right circular cylinder with radius 50
nm and height 50 nm.
The particles are placed with periodicities
\begin_inset Formula $p_{x}=\SI{621}{nm}$
\end_inset
,
\begin_inset Formula $p_{y}=\SI{571}{nm}$
\end_inset
into an isotropic medium with a constant refraction index
\begin_inset Formula $n=1.52$
\end_inset
.
For gold, we use the optical properties listed in
\begin_inset CommandInset citation
LatexCommand cite
key "johnson_optical_1972"
literal "false"
\end_inset
interpolated with cubical splines.
The particles' cylindrical shape is approximated with a triangular mesh
with XXX boundary elements.
\begin_inset Marginal
status open
\begin_layout Plain Layout
Show the mesh as well?
\end_layout
\end_inset
\end_layout
\begin_layout Standard
We consider finite arrays with
\begin_inset Formula $N_{x}\times N_{y}=\ldots\times\ldots,\ldots\times\ldots,\ldots\times\ldots$
\end_inset
particles and also the corresponding infinite array, and simulate their
absorption when irradiated by circularly polarised plane waves with energies
from xx to yy and incidence direction lying in the
\begin_inset Formula $xz$
\end_inset
plane.
The results are shown in Figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Example rectangular absorption"
plural "false"
caps "false"
noprefix "false"
\end_inset
.
\begin_inset Marginal
status open
\begin_layout Plain Layout
Mention lMax.
\end_layout
\end_inset
\begin_inset Float figure
placement document
alignment document
wide false
sideways false
status open
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
\begin_inset Caption Standard
\begin_layout Plain Layout
Absorption of rectangular arrays of golden nanoparticles with periodicities
\begin_inset Formula $p_{x}=\SI{621}{nm}$
\end_inset
,
\begin_inset Formula $p_{y}=\SI{571}{nm}$
\end_inset
with a)
\begin_inset Formula $\ldots\times\ldots$
\end_inset
, b)
\begin_inset Formula $\ldots\times\ldots$
\end_inset
, c)
\begin_inset Formula $\ldots\times\ldots$
\end_inset
and d) infinitely many particles, irradiated by circularly polarised plane
waves.
e) Absoption profile of a single nanoparticle.
\begin_inset CommandInset label
LatexCommand label
name "fig:Example rectangular absorption"
\end_inset
\end_layout
\end_inset
\end_layout
\end_inset
We compared the
\begin_inset Formula $\ldots\times\ldots$
\end_inset
case with a purely BEM-based solution obtained using the
\family typewriter
scuff-scatter
\family default
utility.
TODO WHAT DO WE GET?
\end_layout
\begin_layout Standard
In the infinite case, we benchmarked against a pseudorandom selection of
\begin_inset Formula $\left(\vect k,\omega\right)$
\end_inset
pairs and the difference was TODO WHAT? We note that evaluating one
\begin_inset Formula $\left(\vect k,\omega\right)$
\end_inset
pair took xxx miliseconds with MSTMM and truncation degree
\begin_inset Formula $L=?$
\end_inset
, the same took xxx hours with BEM.
\begin_inset Marginal
status open
\begin_layout Plain Layout
TODO also details about the machines used.
More info about time also at least for the largest case.
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Modes of a rectangular nanoplasmonic array
\end_layout
\begin_layout Standard
Next, we study the eigenmode problem of the same rectangular arrays.
The system is lossy, therefore the eigenfrequencies are complex and we
need to have a model of the material optical properties also for complex
frequencies.
So in this case we use the Drude-Lorentz model for gold with parameters
as in [TODO REF].
\end_layout
\end_body \end_body
\end_document \end_document

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@ -318,14 +318,14 @@ noprefix "false"
and the properties of the gradient operator under coordinate transforms, and the properties of the gradient operator under coordinate transforms,
vector spherical harmonics vector spherical harmonics
\begin_inset Formula $\vsh2lm,\vsh3lm$ \begin_inset Formula $\vsh 2lm,\vsh 3lm$
\end_inset \end_inset
transform in the same way, transform in the same way,
\begin_inset Formula \begin_inset Formula
\begin{align*} \begin{align*}
\left(\groupop g\vsh2lm\right)\left(\uvec r\right) & =\sum_{m'=-l}^{l}D_{m,m'}^{l}\left(g\right)\vsh2l{m'}\left(\uvec r\right),\\ \left(\groupop g\vsh 2lm\right)\left(\uvec r\right) & =\sum_{m'=-l}^{l}D_{m,m'}^{l}\left(g\right)\vsh 2l{m'}\left(\uvec r\right),\\
\left(\groupop g\vsh3lm\right)\left(\uvec r\right) & =\sum_{m'=-l}^{l}D_{m,m'}^{l}\left(g\right)\vsh3l{m'}\left(\uvec r\right), \left(\groupop g\vsh 3lm\right)\left(\uvec r\right) & =\sum_{m'=-l}^{l}D_{m,m'}^{l}\left(g\right)\vsh 3l{m'}\left(\uvec r\right),
\end{align*} \end{align*}
\end_inset \end_inset
@ -337,8 +337,8 @@ status open
\begin_layout Plain Layout \begin_layout Plain Layout
\begin_inset Formula \begin_inset Formula
\begin{align*} \begin{align*}
\left(\groupop g\vsh2lm\right)\left(\uvec r\right) & =R_{g}\vsh2lm\left(R_{g}^{-1}\uvec r\right)=\sum_{m'=-l}^{l}D_{m,m'}^{l}\left(g\right)\vsh2l{m'}\left(\uvec r\right),\\ \left(\groupop g\vsh 2lm\right)\left(\uvec r\right) & =R_{g}\vsh 2lm\left(R_{g}^{-1}\uvec r\right)=\sum_{m'=-l}^{l}D_{m,m'}^{l}\left(g\right)\vsh 2l{m'}\left(\uvec r\right),\\
\left(\groupop g\vsh3lm\right)\left(\uvec r\right) & =R_{g}\vsh2lm\left(R_{g}^{-1}\uvec r\right)=\sum_{m'=-l}^{l}D_{m,m'}^{l}\left(g\right)\vsh3l{m'}\left(\uvec r\right), \left(\groupop g\vsh 3lm\right)\left(\uvec r\right) & =R_{g}\vsh 2lm\left(R_{g}^{-1}\uvec r\right)=\sum_{m'=-l}^{l}D_{m,m'}^{l}\left(g\right)\vsh 3l{m'}\left(\uvec r\right),
\end{align*} \end{align*}
\end_inset \end_inset
@ -349,14 +349,14 @@ status open
\end_inset \end_inset
but the remaining set but the remaining set
\begin_inset Formula $\vsh1lm$ \begin_inset Formula $\vsh 1lm$
\end_inset \end_inset
transforms differently due to their pseudovector nature stemming from the transforms differently due to their pseudovector nature stemming from the
cross product in their definition: cross product in their definition:
\begin_inset Formula \begin_inset Formula
\[ \[
\left(\groupop g\vsh1lm\right)\left(\uvec r\right)=\sum_{m'=-l}^{l}\widetilde{D_{m,m'}^{l}}\left(g\right)\vsh1l{m'}\left(\uvec r\right), \left(\groupop g\vsh 1lm\right)\left(\uvec r\right)=\sum_{m'=-l}^{l}\widetilde{D_{m,m'}^{l}}\left(g\right)\vsh 1l{m'}\left(\uvec r\right),
\] \]
\end_inset \end_inset
@ -411,8 +411,8 @@ noprefix "false"
: :
\begin_inset Formula \begin_inset Formula
\begin{align*} \begin{align*}
\left(\groupop g\vswfouttlm1lm\right)\left(\vect r\right) & =\sum_{m'=-l}^{l}\widetilde{D_{m,m'}^{l}}\left(g\right)\vswfouttlm1l{m'}\left(\vect r\right),\\ \left(\groupop g\vswfouttlm 1lm\right)\left(\vect r\right) & =\sum_{m'=-l}^{l}\widetilde{D_{m,m'}^{l}}\left(g\right)\vswfouttlm 1l{m'}\left(\vect r\right),\\
\left(\groupop g\vswfouttlm2lm\right)\left(\vect r\right) & =\sum_{m'=-l}^{l}D_{m,m'}^{l}\left(g\right)\vswfouttlm2l{m'}\left(\vect r\right), \left(\groupop g\vswfouttlm 2lm\right)\left(\vect r\right) & =\sum_{m'=-l}^{l}D_{m,m'}^{l}\left(g\right)\vswfouttlm 2l{m'}\left(\vect r\right),
\end{align*} \end{align*}
\end_inset \end_inset
@ -581,7 +581,18 @@ noprefix "false"
\end_inset \end_inset
, we have (CHECK THIS CAREFULLY AND EXPLAIN) , we have
\begin_inset Marginal
status open
\begin_layout Plain Layout
Check this carefully.
Maybe explain in more detail?
\end_layout
\end_inset
\begin_inset Formula \begin_inset Formula
\begin{multline} \begin{multline}
\left(\groupop g\vect E\right)\left(\omega,\vect r\right)=\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm p{\tau}lmD_{m',\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(k\left(\vect r-R_{g}\vect r_{p}\right)\right)\right.+\\ \left(\groupop g\vect E\right)\left(\omega,\vect r\right)=\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm p{\tau}lmD_{m',\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(k\left(\vect r-R_{g}\vect r_{p}\right)\right)\right.+\\