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% Illustrates the use fo 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 0];
overlaponly=0; showfigure=0;
clear domain;
screensize=0.0125;
nptsr=500;
nptstheta=100;
accuracy=0.001;
n=30;
[rmesh,thetamesh,xmesh,ymesh]=polarmesh([0,screensize,nptsr],[0 2*pi nptstheta],'lin');
domain(:,:,1)=rmesh; domain(:,:,2)=thetamesh;
w=0.002;
R=-1e3;
lambda=0.795e-6;
q=q_(w,R,lambda);
%deltax=1.5*w;
%deltay=1.5*w;
deltax=0;
deltay=0;
wfactor=1;
mask_R = (w/2);
mask = 1.0*((xmesh.^2+ymesh.^2) > mask_R^2);
%mask = 1.0;
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)
if showfigure
figure(4);
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
z_before_mask=LaguerreGaussianE([0,0,q_(w*wfactor,R,lambda),lambda],xmesh+deltax,ymesh+deltay,'cart');
zin=mask.*z_before_mask;
clear tmat tmat_in
tmat_in(1:n,1,1)=1;
tmat_in(1:n,1,2)=0;
%[coeffs,tmat]=decompose(zin,domain,'lg',n,[q,lambda,accuracy]);
[coeffs,tmat]=decompose(zin,domain,'lg',tmat_in,[q,lambda,accuracy]);
disp(' '); disp('horizontal');
dispmat(abs(coeffs(:,:,1)));
disp(' '); disp('vertical')
dispmat(abs(coeffs(:,:,2)));
%[rmesh,thetamesh,xmesh,ymesh]=polarmesh([0,screensize/10,nptsr],[0 2*pi nptstheta],'lin');
%domain(:,:,1)=rmesh; domain(:,:,2)=thetamesh;
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
figure(3)
z_test=LaguerreGaussianE([30,0,q_(w*wfactor,R,lambda),lambda],xmesh+deltax,ymesh+deltay,'cart');
h=pcolor(xmesh,ymesh,abs(z_test).^2); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
title('high order LG');
figure(4)
[rmesh,thetamesh,xmesh,ymesh]=polarmesh([0,screensize/10,nptsr],[0 2*pi nptstheta],'lin');
domain(:,:,1)=rmesh; domain(:,:,2)=thetamesh;
mask = 1.0*((xmesh.^2+ymesh.^2) > mask_R^2);
z_before_mask_magn=LaguerreGaussianE([0,0,q_(w*wfactor,R,lambda),lambda],xmesh+deltax,ymesh+deltay,'cart');
zin_magn=mask.*z_before_mask_magn;
zout_magn=recompose(domain,'lg',coeffs,[q,lambda,accuracy]);
subplot(221);
h=pcolor(xmesh,ymesh,abs(z_before_mask_magn).^2); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
title('before mask enlaged');
subplot(222);
h=pcolor(xmesh,ymesh,abs(zin_magn).^2); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
title('masked enlaged');
subplot(223);
h=pcolor(xmesh,ymesh,abs(zin_magn).^2 - abs(zout_magn).^2); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
title('intensity diff enlaged');
subplot(224);
h=pcolor(xmesh,ymesh,abs(zout_magn).^2); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;
title('recomposed enlaged');
% beam crossections
figure(5)
clear mask domain;
[rmesh,thetamesh,xmesh,ymesh]=polarmesh([0,screensize/5,nptsr],[0 2*pi 2],'lin');
domain(:,:,1)=rmesh; domain(:,:,2)=thetamesh;
mask = 1.0*((xmesh.^2+ymesh.^2) > mask_R.^2);
z_before_mask_magn=LaguerreGaussianE([0,0,q_(w*wfactor,R,lambda),lambda],xmesh,ymesh,'cart');
zin_magn=mask.*z_before_mask_magn;
zout_magn=recompose(domain,'lg',coeffs,[q,lambda,accuracy]);
hold off
plot(xmesh(1,:), abs( z_before_mask_magn(1,:)).^2 )
hold all
plot(xmesh(1,:), abs( zin_magn(1,:)).^2 )
plot(xmesh(1,:), abs( zout_magn(1,:)).^2 )
title('beam crossection');
hold off
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