diff --git a/notes/radpower.lyx b/notes/radpower.lyx index d7b0a39..8ecf05c 100644 --- a/notes/radpower.lyx +++ b/notes/radpower.lyx @@ -567,6 +567,82 @@ generated \end_inset . + Quantities without such indices apply +\begin_inset Note Note +status open + +\begin_layout Plain Layout +se vztahují +\end_layout + +\end_inset + + to the whole system, so +\begin_inset Formula $P$ +\end_inset + + will now denote the total power generated by the system. + Now +\begin_inset Formula $\ket{a_{0}^{\sci k}}$ +\end_inset + + is the expansion of the external driving field in the location of nanoparticle + +\begin_inset Formula $\sci k$ +\end_inset + + and +\begin_inset Formula $\ket{a^{\sci k}}$ +\end_inset + + is the expansion of the external field together with the fields scattered + from other nanoparticles, +\begin_inset Formula +\[ +\ket{a^{\sci k}}=\ket{a_{0}^{\sci k}}+\sum_{\sci l\ne\sci k}S_{\sci k\leftarrow\sci l}\ket{f^{\sci l}}. +\] + +\end_inset + +Rewriting +\begin_inset Formula $\ket{f^{\sci l}}=T^{\sci l}\ket{a^{\sci l}}$ +\end_inset + +, this gives the scattering problem in terms of +\begin_inset Formula $\ket{a^{\sci k}}$ +\end_inset + +, +\begin_inset Formula +\[ +\ket{a^{\sci k}}=\ket{a_{0}^{\sci k}}+\sum_{\sci l\ne\sci k}S_{\sci k\leftarrow\sci l}T^{\sci l}\ket{a^{\sci l}} +\] + +\end_inset + +or, in the indexless notation for the whole system +\begin_inset Formula +\begin{eqnarray*} +\ket a & = & \ket{a_{0}}+ST\ket a,\\ +\left(1-ST\right)\ket a & = & \ket{a_{0}} +\end{eqnarray*} + +\end_inset + + Alternatively, multiplication by +\begin_inset Formula $T$ +\end_inset + + from the left gives the problem in terms of the outgoing wave coefficients, +\begin_inset Formula +\begin{eqnarray*} +\ket f & = & T\ket{a_{0}}+TS\ket f,\\ +\left(1-TS\right)\ket f & = & T\ket{a_{0}}. +\end{eqnarray*} + +\end_inset + + \end_layout \end_body