From 5aa40c12f76aa1b384fe4d01cdf62198f2410906 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= Date: Tue, 16 Jun 2020 23:28:40 +0300 Subject: [PATCH] =?UTF-8?q?Implement=20P=C3=A4ivi's=20suggestions=20except?= =?UTF-8?q?=20the=20Applications=20part.?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Former-commit-id: 1a2846bf8762bfa4c22ce7ff2eb83c37cc17da37 --- lepaper/Tmatrix.bib | 3 +- lepaper/arrayscat.lyx | 87 +++++++++++++++++++++++++++++++++---------- lepaper/examples.lyx | 40 ++++++++++++++++++++ lepaper/infinite.lyx | 18 ++++----- 4 files changed, 117 insertions(+), 31 deletions(-) diff --git a/lepaper/Tmatrix.bib b/lepaper/Tmatrix.bib index 4a671b6..fab6b39 100644 --- a/lepaper/Tmatrix.bib +++ b/lepaper/Tmatrix.bib @@ -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}, diff --git a/lepaper/arrayscat.lyx b/lepaper/arrayscat.lyx index 40f5314..47ae6d8 100644 --- a/lepaper/arrayscat.lyx +++ b/lepaper/arrayscat.lyx @@ -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 diff --git a/lepaper/examples.lyx b/lepaper/examples.lyx index 33b18ec..9987060 100644 --- a/lepaper/examples.lyx +++ b/lepaper/examples.lyx @@ -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 diff --git a/lepaper/infinite.lyx b/lepaper/infinite.lyx index 2b4ecb7..5821ea1 100644 --- a/lepaper/infinite.lyx +++ b/lepaper/infinite.lyx @@ -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