Multiple reflections from thin film

thin-fim-multiple-reflections.tex

% Multiple reflections in thin film
% Author: Jimmy Touma

%	adapted from: Jimi Oke (http://www.texample.net/tikz/examples/refraction/)



\documentclass[11pt]{article}
 \usepackage{tikz}
 \usetikzlibrary{%
 	decorations.pathreplacing,%
 	decorations.pathmorphing%
 }
 \usepackage{verbatim}

\begin{comment}
:Title: Multiple Reflections in Thin Film
:Tags: Arrows;Decorations;Postactions;Markings;Angles;Optics;Physics;Geometry;Mathematics;Reflection;Thin Film
:Author: Jimmy Touma
:Slug: Thin film multiple reflections
: See M. S. Wartak's Computational Photonics An Introduction with MATLAB for the derivation of the 
results.
\end{comment}
\usetikzlibrary{arrows,shapes,positioning}
\usetikzlibrary{decorations.markings}
\tikzstyle arrowstyle=[scale=1]
\tikzstyle directed=[postaction={decorate,decoration={markings,
    mark=at position .65 with {\arrow[arrowstyle]{stealth}}}}]
\tikzstyle reverse directed=[postaction={decorate,decoration={markings,
    mark=at position .65 with {\arrowreversed[arrowstyle]{stealth};}}}]
\begin{document}
	\pagestyle{empty}
\begin{tikzpicture}[
media/.style={font={\footnotesize\sffamily}},
wave/.style={
	decorate,decoration={snake,post length=1.4mm,amplitude=2mm,
		segment length=2mm},thick},
interface/.style={
	% The border decoration is a path replacing decorator. 
	% For the interface style we want to draw the original path.
	% The postaction option is therefore used to ensure that the
	% border decoration is drawn *after* the original path.
	postaction={draw,decorate,decoration={border,angle=-45,
			amplitude=0.3cm,segment length=2mm}}},
]
% Round rectangle
\fill[gray!10,rounded corners] (-7,0) rectangle (7,-5);

% Interface
\draw[blue,line width=.5pt,interface](-7,0)--(7,0);

% horizontal dashed line
\draw[-,gray](-5,0)--(5,0);
    % define coordinates
    \coordinate (O) at (0,0) ;
    \coordinate (A) at (-3,5) ;
    \coordinate (B) at (-3,-5) ;
    
    % Media names
    \path[media] (-6,0.5)  node {$n_i$}
    (-6,-0.5) node {$n_t$};
    

    % axis
    \draw[dash pattern=on5pt off3pt] (A) -- (B) ;

    % rays
    \draw[ultra thick,reverse directed] (-3,0) -- (-5,5)node[above]{$\vec{E}_0$};
    \draw[ultra thick, directed] (-3,0) -- (-1,5)node[above]{$\vec{E}_1$};
    
    \draw[directed,ultra thick] (-3,0) -- (-2,-5);
    \draw[ultra thick,directed] (-2,-5) -- (-1,0);
    \draw[directed,ultra thick] (-1,0) -- (1,5)node[above]{$\vec{E}_2$};
    \path (-4,-3)++(0:1.3cm)node{$\phi_t$};
    \draw[->] (-2.5,-2.5) arc (-70:-110:0.8cm);
    
    \draw[ultra thick,directed] (-1,0) -- (0,-5);
    \draw[directed,ultra thick] (0,-5) -- (1,0);
    \draw[directed,ultra thick] (1,0) -- (3,5)node[above]{$\vec{E}_3$};
    
    \draw[directed,ultra thick] (1,0) -- (2,-5);
    \draw[directed,ultra thick] (2,-5) -- (3,0);
    \draw[directed,ultra thick] (3,0) -- (5,5)node[above]{$\vec{E}_4$};
    
    \draw[directed,ultra thick, dashed] (3,0) -- (4,-5);
    \draw[directed,ultra thick, dashed] (4,-5) -- (5,0);
    \draw[directed,ultra thick, dashed] (5,0) -- (7,5)node[above]{$\vec{E}_R$};

	% thickness
	\draw[<->, thick ] (6,0) -- (6,-5);
	\draw (6.3,-2.5) node {$d$};
\end{tikzpicture}
\[
E_R=r\,E_0\ e^{i\omega t}\ \frac{1-e^{-i\delta}}{1-r^2e^{-i\delta}}
\]
\[
\delta = 2\,k\,d\,n_t\,\cos\phi_t
\]
$r$ is the reflection coefficient in $n_i$. See M. S. Wartak for reference. 
\end{document}