[Tex/LaTex] How to draw an optical lattice

metaposttechnical-drawingtikz-pgf

I want to make in TikZ or MetaPost an image of a two dimensional lattice with oscillations like these:

optical lattice
another optical lattice

_{(Source: http://www.uibk.ac.at/th-physik/qo/research/opticallattices.html)}

or this one:

yet another optical lattice

_{(Source: http://news.sciencemag.org/sciencenow/2008/09/12-01.html)}

I don't know even know how to begin.

Best Answer

Here's something to get you (or perhaps someone else) started

enter image description here

I realize that the balls aren't exactly where you want them, but you can tweak the positions yourself.

The idea was to use a surface plot of the function f(x,y)=cos(x)*cos(y) using the pgfplots package.

The only subtlety is to loop through the balls, which requires the loop to be wrapped in \pgfplotsextra{ ... }.

I borrowed Altermundus' ball shading from How can we draw a Christmas tree with decorations, using TikZ?

\documentclass{article}
\usepackage{pgfplots}

% borrowed from Altermundus' Christmas tree
% https://tex.stackexchange.com/questions/39149/how-can-we-draw-a-christmas-tree-with-decorations-using-tikz/39250#39250
\newsavebox{\ball}
\savebox{\ball}{ 
\begin{tikzpicture}[scale=.1]
 \shadedraw[ball color=red] (0,0) circle (60pt);
\end{tikzpicture}
} 

\begin{document}

\begin{tikzpicture}
 \begin{axis}[xmin=-5,xmax=5,ymin=-5,ymax=5,zmin=-5,zmax=5,colormap/cool]
  \addplot3[
    surf,
    shader=flat,
    samples=50,
    domain=-2*pi:2*pi,
    y domain=-2*pi:2*pi
  ]{cos(deg(x))*cos(deg(y))};
  \pgfplotsextra{
    \foreach \deco in {
        (axis cs:-1,-1,1),
        (axis cs:-2,-2,1),
        (axis cs:3,3,1),
        (axis cs:-3,-3,1),
        (axis cs:4,4,1)
    }{%
        \node at \deco {\usebox{\ball}};
    }
  }
 \end{axis}
\end{tikzpicture}
\end{document}

Related Solutions

TikZ – How to Draw a Joining Line Between Two Pictures

You can name the nodes and, since the two nodes belong to different tikzpictures, you need to use the remember picture, overlay options to draw a line connecting them:

\documentclass{beamer}
\usepackage{tikz}

\begin{document}

 \begin{frame}

 \begin{columns}[c]
 \begin{column}{2cm}
    \begin{tikzpicture}[remember picture,overlay,scale=0.5] 
    \tikzstyle{level 1}=[sibling distance=10mm] 
    \node{f} 
    child{node{a}}
    child{node{f} child{node{b}} child{[red] node (f1) {f }   child{node{a}} child{node{f} child{node{b}}child{node{b}}}      }}
    ;
    \end{tikzpicture}
\end{column}    
\begin{column}{2cm}
   \begin{tikzpicture}[remember picture,overlay,scale=0.5] 
   \tikzstyle{level 1}=[sibling distance=10mm] 
   \node (f2) {f} 
    child{node{a}}
    child{node{f} child{node{b}} child{ node{f }   child{node{a}} child{node{g} child[missing] child{node{a}}}      }}
    ;
\draw (f1) .. controls (-3,3) .. (f2);
   \end{tikzpicture}
 \end{column}
 \end{columns}
\end{frame}

\end{document}

enter image description here

If both trees are part of the same tikzpicture, there's no need to use remember picture,overlay (but I don't know if using two environments is esential in your actual document).

TikZ 3D Diagrams – Creating Solid Cylinders Along a Path for Crystal Lattice Diagram

enter image description here

This model uses cylinders for connection, rendered in Asymptote, cr.asy:

size(300);
import solids;

currentprojection=orthographic (
camera=(8,5,4),
up=(0,0,1),
target=(2,2,2),
zoom=0.5
);

// save predefined 2D orientation vectors
pair NN=N;
pair SS=S;
pair EE=E;
pair WW=W;

//%points on cube

triple A = (0,0,0);
triple B = (0,0,4);
triple D = (0,4,0);
triple C = (0,4,4);
triple E = (4,0,0);
triple F = (4,0,4);
triple H = (4,4,0);
triple G = (4,4,4);

triple[] cubicCornerA={  
  A,C,F,H,
};

triple[] cubicCornerB={  
  B,D,E,G,
};


//%center of faces

triple I = (A+B+C+D)/4; //%center of face ABCD
triple J = (E+F+G+H)/4; //%center of face EFGH
triple K = (D+C+G+H)/4; //%center of face DCGH
triple L = (A+B+F+E)/4; //%center of face ABFE
triple M = (C+B+G+F)/4; //%center of face CBGF
triple N = (D+A+E+H)/4; //%center of face DAEH

triple[] faceCenter={  
  I,J,K,L,M,N,
};


//%connectors
triple O = (1,1,3);
triple P = (1,3,1);
triple Q = (3,1,1);
triple R = (3,3,3);

triple[] connectors={  
  O,P,Q,R,
};

//%place non-atom cube corners

real cornerAR=0.05;
real cornerBR=0.2;
real faceCR=0.2;
real connR=faceCR;

draw(A--B--C--D--cycle,dashed);
draw(E--F--G--H--cycle,dashed);
draw(A--E,dashed);
draw(B--F,dashed);
draw(C--G,dashed);
draw(D--H,dashed);

real cylR=0.062;

void Draw(guide3 g,pen p=currentpen){
  draw(
    cylinder(
      point(g,0),cylR,arclength(g),point(g,1)-point(g,0)
    ).surface(
               new pen(int i, real j){
                 return p;
               }
             )
  );
}

//%connections from faces to O
pen connectPen=lightgray;
Draw(B--O,connectPen);
Draw(I--O,connectPen);
Draw(M--O,connectPen);
Draw(L--O,connectPen);

//%connections from faces to P
Draw(N--P,connectPen);
Draw(I--P,connectPen);
Draw(D--P,connectPen);
Draw(K--P,connectPen);

//%connections from faces to Q
Draw(E--Q,connectPen);
Draw(J--Q,connectPen);
Draw(N--Q,connectPen);
Draw(L--Q,connectPen);

//%connections from faces to R
Draw(G--R,connectPen);
Draw(M--R,connectPen);
Draw(J--R,connectPen);
Draw(K--R,connectPen);

void drawSpheres(triple[] C, real R, pen p=currentpen){
  for(int i=0;i<C.length;++i){
    draw(sphere(C[i],R).surface(
                        new pen(int i, real j){return p;}
                        )
    );
  }
}

drawSpheres(cubicCornerA,cornerAR,lightgray);
drawSpheres(cubicCornerB,cornerBR,darkgray);
drawSpheres(faceCenter,faceCR,red);
drawSpheres(connectors,connR,lightblue);

Process with asy -f pdf cr.asy to get an interactive (Adobe Reader only) standalone cr.pdf, or with asy -f pdf -noprc -render=0 cr.asy to get an ordinary cr.pdf, or asy -f png -render=5 cr.asy to get a smaller raster image cr.png.

Best Answer

Related Solutions

TikZ – How to Draw a Joining Line Between Two Pictures

TikZ 3D Diagrams – Creating Solid Cylinders Along a Path for Crystal Lattice Diagram

Related Question