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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 1];

-overlaponly=0; showfigure=0;

-

-clear domain;

-

-screensize=0.0125;

-nptsr=500;

-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=0.001;

-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/10);

-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

-

-

-[rmesh,thetamesh,xmesh,ymesh]=polarmesh([0,screensize/10,nptsr],[0 2*pi nptstheta],'lin');

-domain(:,:,1)=rmesh; domain(:,:,2)=thetamesh;

-zout_magn=recompose(domain,'lg',coeffs,[q,lambda,accuracy]);

-figure(3)

-title('recomposed');

-h=pcolor(xmesh,ymesh,abs(zout_magn).^2); set(h,'edgecolor','none'); axis square; colorbar; drawnow; shg;

-

-

-