From 6fc1edd2abd1102e8875ccd434ce028a5ec1fc2b Mon Sep 17 00:00:00 2001 From: Eugeniy Mikhailov Date: Tue, 13 May 2014 16:54:56 -0400 Subject: init --- Readme | 7 +++ gauss_on_aperture.m | 122 ++++++++++++++++++++++++++++++++++++++++++++++++++++ init.m | 2 + 3 files changed, 131 insertions(+) create mode 100644 Readme create mode 100644 gauss_on_aperture.m create mode 100644 init.m diff --git a/Readme b/Readme new file mode 100644 index 0000000..40e23dd --- /dev/null +++ b/Readme @@ -0,0 +1,7 @@ + +This code uses optics_toolkit code which can be obtained from +http://mercury.pr.erau.edu/~greta9a1/downloads/index.html + +the older version is also available at mathwork web site +http://www.mathworks.com/matlabcentral/fileexchange/15459-basic-paraxial-optics-toolkit + diff --git a/gauss_on_aperture.m b/gauss_on_aperture.m new file mode 100644 index 0000000..4523c73 --- /dev/null +++ b/gauss_on_aperture.m @@ -0,0 +1,122 @@ +% 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; + + + diff --git a/init.m b/init.m new file mode 100644 index 0000000..5a40352 --- /dev/null +++ b/init.m @@ -0,0 +1,2 @@ +addpath( genpath( '../optics_toolkit/') ); + -- cgit v1.2.3