1 files changed, 97 insertions, 0 deletions
diff --git a/examples/Laguerre_demo.m b/examples/Laguerre_demo.m
new file mode 100644
index 0000000..f9d541a
--- /dev/null
+++ b/examples/Laguerre_demo.m
@@ -0,0 +1,97 @@
+% Illustrates the use of LaguerreGaussianE.m, decompose.m and recompose.m by
+% defining an off-center Guassian beam (Fig. 1, Col. 1) and recomposing it 
+% in a basis of Laguerre Gaussians defined about the center on the figure.
+% The recomposed beam is shown in Fig. 1, Col. 2, where we have used the
+% first 40 Laguerre Gaussian modes.  Figure 1, Col. 3 shows the
+% difference between the recomposed beam and the original.  Figure 2 shows
+% the magnitude of the coefficients of the various modes in the
+% decomposition.
+
+
+ploton=[1 1];
+overlaponly=0; showfigure=0;
+
+clear domain;
+
+screensize=0.1;
+nptsr=50;
+nptstheta=100;
+accuracy=0.001;
+n=400;
+
+[rmesh,thetamesh,xmesh,ymesh]=polarmesh([0,screensize,nptsr],[0 2*pi nptstheta],'lin');
+domain(:,:,1)=rmesh; domain(:,:,2)=thetamesh;
+
+w=0.02;
+R=-1e3;
+lambda=1.064e-6;
+q=q_(w,R,lambda);
+
+deltax=1.5*w;
+deltay=1.5*w;
+wfactor=1;
+
+if overlaponly
+    z1=LaguerreGaussianE([0,2,q_(w,R,lambda),lambda],xmesh,ymesh,'cart');
+    z2=LaguerreGaussianE([0,2,q_(w,R,lambda),lambda],xmesh,ymesh,'cart');
+    a=overlap(z1,conj(z2),domain,rmesh) %#ok<NOPTS>
+    if showfigure
+        figure(1);
+        subplot(221); h=pcolor(xmesh,ymesh,abs(z1).^2); shg; colorbar; axis square; set(h,'edgecolor','none');
+        subplot(222); h=pcolor(xmesh,ymesh,abs(z2).^2); shg; colorbar; axis square; set(h,'edgecolor','none');
+        subplot(223); h=pcolor(xmesh,ymesh,angle(z1)); shg; colorbar; axis square; set(h,'edgecolor','none');
+        subplot(224); h=pcolor(xmesh,ymesh,angle(z2)); shg; colorbar; axis square; set(h,'edgecolor','none');
+    end
+    return
+end
+
+zin=LaguerreGaussianE([0,0,q_(w*wfactor,R,lambda),lambda],xmesh+deltax,ymesh+deltay,'cart');
+[coeffs,tmat]=decompose(zin,domain,'lg',n,[q,lambda,accuracy]);
+disp(' '); disp('horizontal');
+dispmat(abs(coeffs(:,:,1)));
+disp(' '); disp('vertical')
+dispmat(abs(coeffs(:,:,2)));
+zout=recompose(domain,'lg',coeffs,[q,lambda,accuracy]);
+
+
+if ploton(1)==1
+    figure(1);
+    subplot(331);
+    h=pcolor(xmesh,ymesh,abs(zin).^2); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
+    title('original intensity');    
+    subplot(332);
+    h=pcolor(xmesh,ymesh,abs(zout).^2); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
+    title('recomposed');
+    subplot(333);
+    h=pcolor(xmesh,ymesh,abs(zout).^2-abs(zin).^2); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
+    title('difference');
+    subplot(334);
+    h=pcolor(xmesh,ymesh,real(zin)); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
+    title('original real part');
+    subplot(335);
+    h=pcolor(xmesh,ymesh,real(zout)); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
+    title('recomposed');
+    subplot(336);
+    h=pcolor(xmesh,ymesh,real(zout)-real(zin)); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
+    title('difference');
+    subplot(337);
+    h=pcolor(xmesh,ymesh,imag(zin)); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
+    title('original imaginary part')
+    subplot(338);
+    h=pcolor(xmesh,ymesh,imag(zout)); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
+    title('recomposed');
+    subplot(339);
+    h=pcolor(xmesh,ymesh,imag(zout)-imag(zin)); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
+    title('difference');
+end
+
+if length(ploton)>=2 && ploton(2)==1
+    figure(2);
+    coeffplotmat=[coeffs(:,end:-1:2,2),coeffs(:,:,1)];
+    ps=(-size(coeffs(:,:,2),1)+1:size(coeffs(:,:,1),1)-1);
+    ms=(0:size(coeffs(:,:,2))-1);
+    [psmesh,msmesh]=meshgrid(ps,ms);
+    h=pcolor(psmesh,msmesh,log10(abs(coeffplotmat))); axis square; colorbar; drawnow; shg;
+    title('Log_{10} of coefficients of the modes in the decomposition');
+    xlabel('m'); ylabel('p');
+ end
+\ No newline at end of file