diff --git a/lepaper/arrayscat.lyx b/lepaper/arrayscat.lyx index 437e971..021b04c 100644 --- a/lepaper/arrayscat.lyx +++ b/lepaper/arrayscat.lyx @@ -7,6 +7,7 @@ \textclass article \begin_preamble \DeclareUnicodeCharacter{0428}{Ш } +\usepackage{tikz} \end_preamble \use_default_options true \maintain_unincluded_children false diff --git a/lepaper/orbits.tex b/lepaper/orbits.tex new file mode 100644 index 0000000..b554252 --- /dev/null +++ b/lepaper/orbits.tex @@ -0,0 +1,25 @@ +\tikzstyle{orbit1}=[rectangle,draw=blue!50,fill=blue!20] +\tikzstyle{orbit2}=[rectangle,draw=green!50,fill=green!20] +\begin{tikzpicture} + \draw (-4,0) -- (4,0); + \draw (0,-2) -- (0,2); + + \node (O) at (0,0) [circle, draw=red!50,fill=red!20] {O}; + + + \node (A) at (-3.0,0.5) [orbit1] {A}; + \node (B) at (3.0,0.5) [orbit1] {B}; + \node (C) at (3.0,-0.5) [orbit1] {C}; + \node (D) at (-3.0,-0.5) [orbit1] {D}; + + \node (E) at (0,-1) [orbit2] {E}; + \node (F) at (0,1) [orbit2] {F}; + + \draw [->] (A) to (B); + \draw [->] (A) to [bend right=18] (C); + \draw [->] (A) to (D); + + \draw [<->] (E.east) to [bend right=30] (F.east); + + +\end{tikzpicture} diff --git a/lepaper/symmetries.lyx b/lepaper/symmetries.lyx index 19175fc..68e197b 100644 --- a/lepaper/symmetries.lyx +++ b/lepaper/symmetries.lyx @@ -506,8 +506,6 @@ noprefix "false" \end_inset , we have -\lang english - \begin_inset Formula \begin{multline} \vect E\left(\omega,R_{g}\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.+\\ @@ -527,6 +525,18 @@ wide false sideways false status open +\begin_layout Plain Layout +\align center +\begin_inset CommandInset include +LatexCommand input +filename "orbits.tex" +literal "true" + +\end_inset + + +\end_layout + \begin_layout Plain Layout \begin_inset Caption Standard @@ -551,12 +561,12 @@ Scatterer orbits under \end_inset lie on the -\begin_inset Formula $xz$ +\begin_inset Formula $yz$ \end_inset plane, hence the corresponding reflection maps each of them to itself, but the -\begin_inset Formula $yz$ +\begin_inset Formula $xz$ \end_inset reflection (or the @@ -685,8 +695,6 @@ status open \end_inset one has -\lang english - \begin_inset Formula \begin{align} \vect E\left(\omega,R_{g}\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-\vect r_{\pi_{g}(p)}\right)\right)\right.+\label{eq:rotated E field expansion around outside origin-1}\\ @@ -726,8 +734,6 @@ noprefix "false" \end_layout \begin_layout Standard - -\lang english \begin_inset Formula \begin{align} \rcoeff & \mapsto J\left(g\right)a,\nonumber \\ @@ -741,8 +747,6 @@ noprefix "false" status open \begin_layout Plain Layout - -\lang english The matrices \begin_inset Formula $D\left(g\right)$ \end_inset @@ -1184,8 +1188,6 @@ name "Phase factor illustration" \begin_layout Standard More rigorous analysis can be found e.g. in -\lang english - \begin_inset CommandInset citation LatexCommand cite after "chapters 10–11" @@ -1211,14 +1213,10 @@ In the group-theoretical terminology, blablabla little groups blabla bla... \end_layout \begin_layout Standard - -\lang english \begin_inset Note Note status open \begin_layout Plain Layout - -\lang english A general overview of utilizing group theory to find lattice modes at high-symme try points of the Brillouin zone can be found e.g. in @@ -1234,8 +1232,6 @@ literal "true" \end_layout \begin_layout Plain Layout - -\lang english We analyse the symmetries of the system in the same VSWF representation as used in the \begin_inset Formula $T$ @@ -1389,8 +1385,6 @@ where \end_layout \begin_layout Plain Layout - -\lang english Each mode at the \begin_inset Formula $\Kp$ \end_inset