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Overlap of LaguerreGaussianE(n,0, ...) with itself was equal to 0.5
For example
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screensize=0.125;
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=0.008;
R=-1e3;
lambda=0.795e-6;
q=q_(w,R,lambda);
z1=LaguerreGaussianE([0,0,q_(w,R,lambda),lambda],xmesh,ymesh,'cart');
z2=LaguerreGaussianE([0,0,q_(w,R,lambda),lambda],xmesh,ymesh,'cart');
a=overlap(z1,conj(z2),domain,rmesh)
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a use to be 0.5 instead of 1
As result decomposition -> composition cycle was not producing the same beam
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