diff options
| -rw-r--r-- | gauss_diffraction_on_aperture.m | 157 | ||||
| -rw-r--r-- | gauss_transmission_after_aperture.m | 55 |
2 files changed, 212 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
+
diff --git a/gauss_transmission_after_aperture.m b/gauss_transmission_after_aperture.m new file mode 100644 index 0000000..7a5bbc3 --- /dev/null +++ b/gauss_transmission_after_aperture.m @@ -0,0 +1,55 @@ +% 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.
+
+
+clear domain
+screensize=0.0125;
+nptsr=1500;
+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;
+
+z_before_mask=LaguerreGaussianE([0,0,q_(w,R,lambda),lambda],xmesh+deltax,ymesh+deltay,'cart');
+
+Np = 1000;
+apR = linspace(0, 2, Np); % aperture ratio
+for i = Np:-1:1
+ mask_R = w*apR(i);
+ % disk
+ mask = 1.0*((xmesh.^2+ymesh.^2) > mask_R^2);
+ zout=mask.*z_before_mask;
+ a_disk(i)=overlap(zout,conj(zout),domain,rmesh);
+
+ % iris
+ mask = 1.0*((xmesh.^2+ymesh.^2) < mask_R^2);
+ zout=mask.*z_before_mask;
+ a_iris(i)=overlap(zout,conj(zout),domain,rmesh);
+end
+
+
+plot( a_disk, apR, 'k-', a_iris, apR, 'r-' );
+grid on;
+legend( ['disk'; 'iris'] );
+ylabel('Aperture radius R_a/w');
+xlabel('Transmitter power ratio')
+title( 'LG_{00} beam transmission after round disk or aperture');
+
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