= Confocal reciprocal-Rayleigh-range map
{title2=$z_Rz_R'=(L/2)^2$}
For two equal <mirrors> of radius $L$ separated by $L$, a Gaussian <beam waist>[waist] at the centre is reflected to another <beam waist>[waist] at the same plane. Putting $a=L/2$, the <mirror> maps $q=a+iz_R$ to $-a+ia^2/z_R$, so the reflected <Rayleigh range> is $a^2/z_R$. Both beams have equal spots on the <mirrors> although their <beam waist>[waist] radii differ. Equal <beam waist>[waist] sizes select $z_R=L/2$.
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