Implement Päivi's suggestions except the Applications part.
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@ -1040,8 +1040,7 @@ matrix method for multilayer calculations.},
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number = {1}
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}
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@article{vakevainen_plasmonic_2014-1,
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ids = {vakevainen\_plasmonic\_2014},
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@article{vakevainen_plasmonic_2014,
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title = {Plasmonic {{Surface Lattice Resonances}} at the {{Strong Coupling Regime}}},
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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.},
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year = {2014},
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@ -491,6 +491,67 @@ These are compatibility macros for the (...)-old files:
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\end_layout
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\begin_layout Title
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Multiple-scattering
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\begin_inset Formula $T$
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\end_inset
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-matrix simulations for nanophotonics: symmetries and periodic lattices
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\end_layout
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\begin_layout Author
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Marek Nečada
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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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\begin_inset CommandInset href
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LatexCommand href
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target "marek@necada.org"
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type "mailto:"
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literal "false"
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\end_inset
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\end_layout
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\end_inset
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, Päivi Törmä
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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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\begin_inset CommandInset href
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LatexCommand href
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target "paivi.torma@aalto.fi"
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type "mailto:"
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literal "false"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Address
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Department of Applied Physics, Aalto University School of Science, P.O.
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Box 15100, FI-00076 Aalto, Finland
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\end_layout
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\begin_layout Standard
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\begin_inset Note Note
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status open
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\begin_layout Plain Layout
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Alternative titles:
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\end_layout
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\begin_layout Itemize
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Many-particle
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\begin_inset Formula $T$
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\end_inset
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@ -499,18 +560,6 @@ Many-particle
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modes
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\end_layout
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\begin_layout Standard
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Alternative titles:
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\end_layout
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\begin_layout Itemize
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Multiple-scattering
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\begin_inset Formula $T$
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\end_inset
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-matrix simulations for nanophotonics: symmetries and periodic lattices.
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\end_layout
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\begin_layout Itemize
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Many-particle
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\begin_inset Formula $T$
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@ -527,6 +576,11 @@ Many-particle
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-matrix simulations in finite and infinite systems of electromagnetic scatterers
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Note Note
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status open
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@ -610,10 +664,7 @@ The T-matrix multiple scattering method (TMMSM) can be used to solve the
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retaining a good level of accuracy while using relatively few degrees of
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freedom, largely surpassing other methods in the number of scatterers it
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can deal with.
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\end_layout
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\begin_layout Abstract
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Here we extend the method to infinite periodic structures using Ewald-type
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Here we extend the method to infinite periodic structures using Ewald-type
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lattice summation, and we exploit the possible symmetries of the structure
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to further improve its efficiency, so that systems containing tens of thousands
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of particles can be studied with relative ease.
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@ -636,10 +687,6 @@ Should I mention also the cross sections formulae in abstract / intro?
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\end_inset
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\end_layout
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\begin_layout Abstract
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We release a modern implementation of the method, including the theoretical
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improvements presented here, under GNU General Public Licence.
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\end_layout
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@ -289,6 +289,11 @@ wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Note Note
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Graphics
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@ -305,6 +310,11 @@ status open
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\end_inset
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\end_layout
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\end_inset
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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@ -361,6 +371,11 @@ status open
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\end_layout
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\begin_layout Plain Layout
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\align center
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\begin_inset Note Note
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Graphics
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@ -370,6 +385,11 @@ status open
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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@ -570,6 +590,11 @@ wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Note Note
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Graphics
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@ -579,6 +604,11 @@ status open
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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@ -690,6 +720,11 @@ wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Note Note
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Graphics
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@ -699,6 +734,11 @@ status open
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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@ -2139,7 +2139,7 @@ If we assume that
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is chosen to represent the (rough) maximum tolerated magnitude of the summand
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with regard to target accuracy.
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This adjustment means that, in worst-case scenario, with growing wavenumber
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This adjustment means that, in the worst-case scenario, with growing wavenumber
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one has to include an increasing number of terms in the long-range sum
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in order to achieve a given accuracy, the number of terms being proportional
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to
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@ -2271,8 +2271,8 @@ noprefix "false"
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translation operator:
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\begin_inset Formula
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\begin{align}
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\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 \\
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\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}
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\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 \\
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\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}
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\end{align}
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\end_inset
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@ -2299,7 +2299,7 @@ noprefix "false"
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\end_inset
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and the fact that all the other regular VSWFs except for
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\begin_inset Formula $\vswfrtlm21{m'}$
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\begin_inset Formula $\vswfrtlm 21{m'}$
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\end_inset
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vanish at origin.
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@ -2372,10 +2372,10 @@ status open
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\begin_inset Formula
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\begin{align*}
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\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)\\
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& =\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)\\
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& =\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}\\
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& =\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)\\
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& =\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)
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& =\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)\\
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& =\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}\\
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& =\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)\\
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& =\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)
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\end{align*}
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\end_inset
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@ -2393,7 +2393,7 @@ TODO fix signs and exponential phase factors
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\begin_inset Formula
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\begin{align*}
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\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)\\
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& =\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).
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& =\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).
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\end{align*}
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\end_inset
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