a more organized versions

1 files changed, 157 insertions, 0 deletions

diff --git a/gauss_diffraction_on_aperture.m b/gauss_diffraction_on_aperture.m
new file mode 100644
index 0000000..6f72e85
--- /dev/null
+++ b/gauss_diffraction_on_aperture.m
@@ -0,0 +1,157 @@
+% 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

+