diff --git a/src/qcl-model/README.md b/src/qcl-model/README.md new file mode 100644 index 0000000..2159628 --- /dev/null +++ b/src/qcl-model/README.md @@ -0,0 +1,4 @@ +# qcl-model + +This project contains figures related to mathematical modelling of quantum +cascade lasers. diff --git a/src/qcl-model/math_model.tex b/src/qcl-model/math_model.tex new file mode 100644 index 0000000..1295057 --- /dev/null +++ b/src/qcl-model/math_model.tex @@ -0,0 +1,97 @@ +% +% qclsip: The Quantum Cascade Laser Stock Image Project. +% +% Copyright (c) 2019, Computational Photonics Group, Technical University of +% Munich. +% +% Mathematical model of a QCL (Schrödinger-Poisson, Ensemble Monte Carlo, +% Maxwell's equation, Lindblad equation). +% Created by Michael Riesch (2019) +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 3 of the License, or +% (at your option) any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with this program; if not, write to the Free Software Foundation, +% Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA +\documentclass[tikz]{standalone} + +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{tikz} +\usetikzlibrary{calc} + +% set colors +\usepackage{xcolor} +\definecolor{sipblue}{RGB}{0,101,189} % Pantone 300 +\definecolor{sipdarkblue}{RGB}{0,82,147} % Pantone 301 +\definecolor{siplightblue}{RGB}{152,198,234} % Pantone 283 +\definecolor{sipmedblue}{RGB}{100,160,200} % Pantone 542 +\definecolor{sipivory}{RGB}{218,215,203} % Pantone 7527 +\definecolor{sipgreen}{RGB}{162,173,0} % Pantone 383 +\definecolor{siporange}{RGB}{227,114,34} % Pantone 158 +\definecolor{sipgray}{gray}{0.6} % Gray 60% + +% set font +\usepackage{helvet} +\renewcommand{\familydefault}{\sfdefault} + +\begin{document} +\begin{tikzpicture} + \tikzstyle{myline}=[very thick, line cap=round,line join=round]; + \tikzstyle{mytext}=[draw, text=black, align=left]; + \tikzstyle{myconn}=[myline, ->, >=stealth]; + + % static part + \node[mytext, myline, draw=siporange, anchor=north west] (sp) at (0, 7) { + \textcolor{siporange}{Energy levels}\\Schrödinger-Poisson equation}; + + \node[mytext, myline, draw=siporange, anchor=east] (mc) at (8, 5) { + \textcolor{siporange}{Carrier transport}\\Ensemble Monte Carlo (EMC)/\\ + Density Matrix EMC}; + + % dynamic part + \node[mytext, myline, draw=sipblue, anchor=west] (lb) at (0, 3) { + \textcolor{sipblue}{Electron dynamics}\\Lindblad equation\\ + $\partial_t \hat{\rho} = -\mathrm{i}\hbar^{-1} \left[ \hat{H}_0 - + \hat \mu E_z, \hat{\rho} \right] + \hat{\rho}_{\mathrm{diss}}$}; + + \node[mytext, myline, draw=sipblue, anchor=south east] (mw) at (8, 0) { + \textcolor{sipblue}{Optical field}\\Maxwell's equations in 1D\\ + $\partial_t H_y = \mu^{-1} \partial_x E_z$\\ + $\partial_t E_z = \epsilon^{-1} \left( -\sigma E_z - \partial_t P_z + + \partial_x H_y \right)$}; + + % connections + \draw[myconn, draw=siporange] (sp.east) to[bend left] node[midway, right] { + $E_i, \Psi_i$} (mc.north); + + \draw[myconn, draw=siporange] (mc.west) to[bend left] node[midway, left] { + $f_i$} (sp.south); + + \draw[myconn, draw=siporange] ($(sp.south west) + (1.1, 0)$) + -- node[midway, left] {$\hat H_0, \hat \mu$} + ($(lb.north west) + (1.1, 0)$); + + \draw[myconn, draw=siporange] ($(mc.west) - (0, 0.3)$) + -| node[midway, left] {$\hat{\rho}_{\mathrm{diss}}$} + ($(lb.north) - (0.5, 0)$); + + \draw[myconn, draw=sipblue] (mw.west) + to[bend left] node[midway, below, outer sep=3pt] {$E_z$} + ($(lb.south west) + (1.1, 0)$) ; + + \draw[myconn, draw=sipblue] (lb.east) + to[bend left] node[midway, above, outer sep=3pt] {$\partial_t P_z$ + % $= N \mathrm{Tr}\left\{\hat \mu \partial_t \hat \rho\right\}$ + } + ($(mw.north east) - (1.1, 0)$); +\end{tikzpicture} +\end{document}