diff --git a/Doc/UserManual/Multilayers.tex b/Doc/UserManual/Multilayers.tex index 7c25866042d5e21806ea0e8fe8313392dc0db375..607b501916e4f4975ab0d0bc5008a95289730af7 100644 --- a/Doc/UserManual/Multilayers.tex +++ b/Doc/UserManual/Multilayers.tex @@ -154,8 +154,8 @@ We write k_\perp \eqqcolon k_\perp' + i k_\perp'' \end{equation} for its decomposition into a real and an imaginary part. -With (\ref{Endb1}) and $\beta\ge0$, -we have always $k_\perp'\ge0$ and $k_\perp''\ge0$. +With (\ref{Endb1}), $\beta\ge0$ and $\delta<1$, +we always have $k_\perp'\cdot k_\perp''\ge0$. In analogy with (\ref{decompkperp}), full wavevectors have the decomposition \begin{equation} @@ -179,20 +179,22 @@ associated with the plane-wave solution (\ref{Eplawafa},\ref{Ephizwj}): \end{array} \end{equation} The first two terms describe the exponential intensity decrease -due to absorption. -The oscillatory term in square brackets -is a wave-mechanical subtlety -of no interest for us. -In the special case of a pure imaginary~$k_{\perp \il}$, -the flux direction is $\k'=\k_\plll$. -Then $\psi_\il(\r)$ is an \E{evanescent wave}, +due to absorption, while +the oscillatory term in square brackets +is responsible for waveguide effects in layers with finite thickness. +In the special case of a purely imaginary~$k_{\perp \il}$, +the flux becomes: +\begin{equation} + \v{J}(\r) = \left| \psi \right|^2 \k_\plll + 2 \Im (A^-{A^+}^*) k_\perp''\v{\hat z}. +\end{equation} +This flux consists of two clearly distinct parts: an \E{evanescent wave}, \index{Evanescent wave}% -travelling horizontally. -Since a stationary evanescent wave implies that there is -no vertical energy transport, -all incoming radiation undergoes \E{total reflection}. +travelling horizontally + and a vertical component that is independent of the $z$ position. The vertical component is a necessary + degree of freedom to fulfill the boundary conditions at the layer's top and bottom interfaces. +In the case of a semi-infinite layer, the vertical component becomes zero and + all incoming radiation at the top of the layer undergoes \E{total reflection}. \index{Total reflection}% - %=============================================================================== \section{DWBA matrix element} %===============================================================================