WIP

Former-commit-id: 3ab2f0803f9399fe32c41325b9404f8e0b1ba18c

lepaper/arrayscat.lyx

@@ -491,21 +491,12 @@ These are compatibility macros for the (...)-old files:
 \end_layout
 
 \begin_layout Title
+Many-particle 
 \begin_inset Formula $T$
 \end_inset
 
--matrix simulations in finite and infinite systems of electromagnetic scatterers
+-matrix simulations for nanophotonics: symmetries, scattering and lattice
- 
+ modes
-\begin_inset Marginal
-status open
-
-\begin_layout Plain Layout
-(TODO better title)
-\end_layout
-
-\end_inset
-
-
 \end_layout
 
 \begin_layout Standard
@@ -521,7 +512,7 @@ Multiple-scattering
 \end_layout
 
 \begin_layout Itemize
-Multiple-scattering 
+Many-particle 
 \begin_inset Formula $T$
 \end_inset
 
@@ -529,6 +520,13 @@ Multiple-scattering
  modes.
 \end_layout
 
+\begin_layout Itemize
+\begin_inset Formula $T$
+\end_inset
+
+-matrix simulations in finite and infinite systems of electromagnetic scatterers
+\end_layout
+
 \begin_layout Standard
 \begin_inset Note Note
 status open
@@ -617,8 +615,13 @@ The T-matrix multiple scattering method (TMMSM) can be used to solve the
 \begin_layout Abstract
 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.
+ to further improve its efficiency, so that systems containing tens of thousands
+ of particles can be studied with relative ease.
  
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
 \begin_inset Marginal
 status open
 
@@ -629,6 +632,11 @@ Should I mention also the cross sections formulae in abstract / intro?
 \end_inset
 
 
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Abstract
@@ -862,7 +870,7 @@ Given up
 
 \end_layout
 
-\begin_layout Itemize
+\begin_layout Standard
 \begin_inset Note Note
 status open
 

lepaper/infinite.lyx

@@ -370,7 +370,13 @@ noprefix "false"
 
 describes the 
 \emph on
-lattice modes.
+lattice modes
+\emph default
+, i.e.
+ electromagnetic excitations that can sustain themselves for prolonged time
+ even without external driving
+\emph on
+.
 
 \emph default
  Non-trivial solutions to 
@@ -1700,7 +1706,32 @@ One pecularity of the two-dimensional case is the two-branchedness of the
 \begin_inset Formula $\Gamma\left(\frac{1}{2}-j,z\right)$
 \end_inset
 
- appearing in the long-range part.
+ appearing in the long-range part (in the cases 
+\begin_inset Formula $d=1,3$
+\end_inset
+
+ the function 
+\begin_inset Formula $\gamma\left(z\right)$
+\end_inset
+
+ appears with even powers, and 
+\begin_inset Formula $\Gamma\left(-j,z\right)$
+\end_inset
+
+ is meromorphic for integer 
+\begin_inset Formula $j$
+\end_inset
+
+  
+\begin_inset CommandInset citation
+LatexCommand cite
+after "8.2.9"
+key "NIST:DLMF"
+literal "false"
+
+\end_inset
+
+).
  As a consequence, if we now explicitly label the dependence on the wavenumber,
  
 \begin_inset Formula $\sigma_{l,m}^{\left(\mathrm{L},\eta\right)}\left(\kappa,\vect k,\vect s\right)$
@@ -2213,8 +2244,8 @@ 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)\vswfrtlm 21{m'}\left(0\right),\nonumber \\
+\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)\vswfrtlm 21{m'}\left(0\right),\label{eq:VSWFs expressed as translated dipole waves}
+\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}
 \end{align}
 
 \end_inset
@@ -2241,7 +2272,7 @@ noprefix "false"
 \end_inset
 
  and the fact that all the other regular VSWFs except for 
-\begin_inset Formula $\vswfrtlm 21{m'}$
+\begin_inset Formula $\vswfrtlm21{m'}$
 \end_inset
 
  vanish at origin.
@@ -2314,10 +2345,10 @@ 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{\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{\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{\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{\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{\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_{\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{\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)
+ & =\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)
 \end{align*}
 
 \end_inset
@@ -2335,7 +2366,7 @@ 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{\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).
+ & =\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).
 \end{align*}
 
 \end_inset