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Implement Päivi's suggestions except the Applications part. 

Former-commit-id: 1a2846bf8762bfa4c22ce7ff2eb83c37cc17da37
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Marek Nečada 2020-06-16 23:28:40 +03:00
parent 7573c2987b
commit 5aa40c12f7
4 changed files with 117 additions and 31 deletions
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3
lepaper/Tmatrix.bib
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@ -1040,8 +1040,7 @@ matrix method for multilayer calculations.},
number = {1}
}
@article{vakevainen_plasmonic_2014-1,
ids = {vakevainen\_plasmonic\_2014},
@article{vakevainen_plasmonic_2014,
title = {Plasmonic {{Surface Lattice Resonances}} at the {{Strong Coupling Regime}}},
author = {V{\"a}kev{\"a}inen, A. I. and Moerland, R. J. and Rekola, H. T. and Eskelinen, A.-P. and Martikainen, J.-P. and Kim, D.-H. and T{\"o}rm{\"a}, P.},
year = {2014},

87
lepaper/arrayscat.lyx
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@ -491,6 +491,67 @@ These are compatibility macros for the (...)-old files:
\end_layout
\begin_layout Title
Multiple-scattering
\begin_inset Formula $T$
\end_inset
-matrix simulations for nanophotonics: symmetries and periodic lattices
\end_layout
\begin_layout Author
Marek Nečada
\begin_inset Foot
status open
\begin_layout Plain Layout
\begin_inset CommandInset href
LatexCommand href
target "marek@necada.org"
type "mailto:"
literal "false"
\end_inset
\end_layout
\end_inset
, Päivi Törmä
\begin_inset Foot
status open
\begin_layout Plain Layout
\begin_inset CommandInset href
LatexCommand href
target "paivi.torma@aalto.fi"
type "mailto:"
literal "false"
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Address
Department of Applied Physics, Aalto University School of Science, P.O.
Box 15100, FI-00076 Aalto, Finland
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
Alternative titles:
\end_layout
\begin_layout Itemize
Many-particle
\begin_inset Formula $T$
\end_inset
@ -499,18 +560,6 @@ Many-particle
modes
\end_layout
\begin_layout Standard
Alternative titles:
\end_layout
\begin_layout Itemize
Multiple-scattering
\begin_inset Formula $T$
\end_inset
-matrix simulations for nanophotonics: symmetries and periodic lattices.
\end_layout
\begin_layout Itemize
Many-particle
\begin_inset Formula $T$
@ -527,6 +576,11 @@ Many-particle
-matrix simulations in finite and infinite systems of electromagnetic scatterers
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
@ -610,10 +664,7 @@ The T-matrix multiple scattering method (TMMSM) can be used to solve the
retaining a good level of accuracy while using relatively few degrees of
freedom, largely surpassing other methods in the number of scatterers it
can deal with.
\end_layout
\begin_layout Abstract
Here we extend the method to infinite periodic structures using Ewald-type
Here we extend the method to infinite periodic structures using Ewald-type
lattice summation, and we exploit the possible symmetries of the structure
to further improve its efficiency, so that systems containing tens of thousands
of particles can be studied with relative ease.
@ -636,10 +687,6 @@ Should I mention also the cross sections formulae in abstract / intro?
\end_inset
\end_layout
\begin_layout Abstract
We release a modern implementation of the method, including the theoretical
improvements presented here, under GNU General Public Licence.
\end_layout

40
lepaper/examples.lyx
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@ -289,6 +289,11 @@ wide false
sideways false
status open
\begin_layout Plain Layout
\align center
\begin_inset Note Note
status open
\begin_layout Plain Layout
\align center
\begin_inset Graphics
@ -305,6 +310,11 @@ status open
\end_inset
\end_layout
\end_inset
\begin_inset Caption Standard
\begin_layout Plain Layout
@ -361,6 +371,11 @@ status open
\end_layout
\begin_layout Plain Layout
\align center
\begin_inset Note Note
status open
\begin_layout Plain Layout
\align center
\begin_inset Graphics
@ -370,6 +385,11 @@ status open
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Plain Layout
@ -570,6 +590,11 @@ wide false
sideways false
status open
\begin_layout Plain Layout
\align center
\begin_inset Note Note
status open
\begin_layout Plain Layout
\align center
\begin_inset Graphics
@ -579,6 +604,11 @@ status open
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Plain Layout
@ -690,6 +720,11 @@ wide false
sideways false
status open
\begin_layout Plain Layout
\align center
\begin_inset Note Note
status open
\begin_layout Plain Layout
\align center
\begin_inset Graphics
@ -699,6 +734,11 @@ status open
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Plain Layout

18
lepaper/infinite.lyx
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@ -2139,7 +2139,7 @@ If we assume that
is chosen to represent the (rough) maximum tolerated magnitude of the summand
with regard to target accuracy.
This adjustment means that, in worst-case scenario, with growing wavenumber
This adjustment means that, in the worst-case scenario, with growing wavenumber
one has to include an increasing number of terms in the long-range sum
in order to achieve a given accuracy, the number of terms being proportional
to
@ -2271,8 +2271,8 @@ noprefix "false"
translation operator:
\begin_inset Formula
\begin{align}
\vswfrtlm{\tau}lm\left(\kappa\vect r\right) & =\sum_{m'=-1}^{1}\tropr_{\tau lm;21m'}\left(\kappa\vect r\right)\vswfrtlm21{m'}\left(0\right),\nonumber \\
\vswfouttlm{\tau}lm\left(\kappa\vect r\right) & =\sum_{m'=-1}^{1}\trops_{\tau lm;21m'}\left(\kappa\vect r\right)\vswfrtlm21{m'}\left(0\right),\label{eq:VSWFs expressed as translated dipole waves}
\vswfrtlm{\tau}lm\left(\kappa\vect r\right) & =\sum_{m'=-1}^{1}\tropr_{\tau lm;21m'}\left(\kappa\vect r\right)\vswfrtlm 21{m'}\left(0\right),\nonumber \\
\vswfouttlm{\tau}lm\left(\kappa\vect r\right) & =\sum_{m'=-1}^{1}\trops_{\tau lm;21m'}\left(\kappa\vect r\right)\vswfrtlm 21{m'}\left(0\right),\label{eq:VSWFs expressed as translated dipole waves}
\end{align}
\end_inset
@ -2299,7 +2299,7 @@ noprefix "false"
\end_inset
and the fact that all the other regular VSWFs except for
\begin_inset Formula $\vswfrtlm21{m'}$
\begin_inset Formula $\vswfrtlm 21{m'}$
\end_inset
vanish at origin.
@ -2372,10 +2372,10 @@ status open
\begin_inset Formula
\begin{align*}
\vect E_{\mathrm{scat}}\left(\vect r\right) & =\sum_{\left(\vect n,\alpha\right)\in\mathcal{P}}\sum_{\tau lm}\outcoeffptlm{\vect n,\alpha}{\tau}lm\vect u_{\tau lm}\left(\kappa\left(\vect r-\text{\vect R_{\vect n}-\vect r_{\alpha}}\right)\right)\\
& =\sum_{\left(\vect n,\alpha\right)\in\mathcal{P}}\sum_{\tau lm}\outcoeffptlm{\vect0,\alpha}{\tau}lme^{i\vect k\cdot\vect R_{\vect n}}\sum_{m'=-1}^{1}\trops_{\tau lm;21m'}\left(\kappa\left(\vect r-\text{\vect R_{\vect n}-\vect r_{\alpha}}\right)\right)\vswfrtlm21{m'}\left(0\right)\\
& =\sum_{\left(\vect n,\alpha\right)\in\mathcal{P}}\sum_{\tau lm}\outcoeffptlm{\vect0,\alpha}{\tau}lme^{-i\vect k\cdot\vect R_{\vect n}}\sum_{m'=-1}^{1}\trops_{\tau lm;21m'}\left(\kappa\left(\vect r+\text{\vect R_{\vect n}-\vect r_{\alpha}}\right)\right)\vswfrtlm21{m'}\left(0\right),\text{FIXME signs}\\
& =\sum_{\left(\vect n,\alpha\right)\in\mathcal{P}}\sum_{\tau lm}\outcoeffptlm{\vect0,\alpha}{\tau}lme^{-i\vect k\cdot\vect R_{\vect n}}\sum_{m'=-1}^{1}\sum_{\lambda=\left|l-1\right|+\left|\tau-2\right|}^{l+1}\tropcoeff_{\tau lm;21m'}^{\lambda}\psi_{\lambda,m-m'}\left(\kappa\left(\vect r+\text{\vect R_{\vect n}-\vect r_{\alpha}}\right)\right)\vswfrtlm21{m'}\left(0\right)\\
& =\sum_{\alpha\in\mathcal{P}_{1}}e^{-i\vect k\cdot\left(\vect r-\vect r_{\alpha}\right)}\sum_{\tau lm}\outcoeffptlm{\vect0,\alpha}{\tau}lm\sum_{m'=-1}^{1}\sum_{\lambda=\left|l-1\right|+\left|\tau-2\right|}^{l+1}\tropcoeff_{\tau lm;21m'}^{\lambda}\sigma_{\lambda,m-m'}\left(\vect k,\vect r-\vect r_{\alpha}\right)
& =\sum_{\left(\vect n,\alpha\right)\in\mathcal{P}}\sum_{\tau lm}\outcoeffptlm{\vect 0,\alpha}{\tau}lme^{i\vect k\cdot\vect R_{\vect n}}\sum_{m'=-1}^{1}\trops_{\tau lm;21m'}\left(\kappa\left(\vect r-\text{\vect R_{\vect n}-\vect r_{\alpha}}\right)\right)\vswfrtlm 21{m'}\left(0\right)\\
& =\sum_{\left(\vect n,\alpha\right)\in\mathcal{P}}\sum_{\tau lm}\outcoeffptlm{\vect 0,\alpha}{\tau}lme^{-i\vect k\cdot\vect R_{\vect n}}\sum_{m'=-1}^{1}\trops_{\tau lm;21m'}\left(\kappa\left(\vect r+\text{\vect R_{\vect n}-\vect r_{\alpha}}\right)\right)\vswfrtlm 21{m'}\left(0\right),\text{FIXME signs}\\
& =\sum_{\left(\vect n,\alpha\right)\in\mathcal{P}}\sum_{\tau lm}\outcoeffptlm{\vect 0,\alpha}{\tau}lme^{-i\vect k\cdot\vect R_{\vect n}}\sum_{m'=-1}^{1}\sum_{\lambda=\left|l-1\right|+\left|\tau-2\right|}^{l+1}\tropcoeff_{\tau lm;21m'}^{\lambda}\psi_{\lambda,m-m'}\left(\kappa\left(\vect r+\text{\vect R_{\vect n}-\vect r_{\alpha}}\right)\right)\vswfrtlm 21{m'}\left(0\right)\\
& =\sum_{\alpha\in\mathcal{P}_{1}}e^{-i\vect k\cdot\left(\vect r-\vect r_{\alpha}\right)}\sum_{\tau lm}\outcoeffptlm{\vect 0,\alpha}{\tau}lm\sum_{m'=-1}^{1}\sum_{\lambda=\left|l-1\right|+\left|\tau-2\right|}^{l+1}\tropcoeff_{\tau lm;21m'}^{\lambda}\sigma_{\lambda,m-m'}\left(\vect k,\vect r-\vect r_{\alpha}\right)
\end{align*}
\end_inset
@ -2393,7 +2393,7 @@ TODO fix signs and exponential phase factors
\begin_inset Formula
\begin{align*}
\vect E_{\mathrm{scat}}\left(\vect r\right) & =\sum_{\left(\vect n,\alpha\right)\in\mathcal{P}}\sum_{\tau lm}\outcoeffptlm{\vect n,\alpha}{\tau}lm\vect u_{\tau lm}\left(\kappa\left(\vect r-\text{\vect R_{\vect n}-\vect r_{\alpha}}\right)\right)\\
& =\sum_{\alpha\in\mathcal{P}_{1}}e^{-i\vect k\cdot\left(\vect r-\vect r_{\alpha}\right)}\sum_{\tau lm}\outcoeffptlm{\vect0,\alpha}{\tau}lm\sum_{m'=-1}^{1}\sum_{\lambda=\left|l-1\right|+\left|\tau-2\right|}^{l+1}\tropcoeff_{\tau lm;21m'}^{\lambda}\sigma_{\lambda,m-m'}\left(\vect k,\vect r-\vect r_{\alpha}\right).
& =\sum_{\alpha\in\mathcal{P}_{1}}e^{-i\vect k\cdot\left(\vect r-\vect r_{\alpha}\right)}\sum_{\tau lm}\outcoeffptlm{\vect 0,\alpha}{\tau}lm\sum_{m'=-1}^{1}\sum_{\lambda=\left|l-1\right|+\left|\tau-2\right|}^{l+1}\tropcoeff_{\tau lm;21m'}^{\lambda}\sigma_{\lambda,m-m'}\left(\vect k,\vect r-\vect r_{\alpha}\right).
\end{align*}
\end_inset