Past exam of the laser science and quantum information processing course of the University of Oxford / 2022 / 2 / c

The source optical resonator has Rayleigh rangeThe symmetric target optical resonator has its fundamental Gaussian beam beam waist halfway between the mirrors. At distance $\ell =L_2/2$ from that beam waist, wavefront curvature is $R_2=\ell +z_B^2/\ell$. ThusHere $f^2=2.25{\mathrm{m}}^2>z_A{z}_B=0.866025{\mathrm{m}}^2$, so b gives two real branches:Only the first branch has the target beam waist downstream of the optical lens. It is also geometrically accessible: the optical lens is $u-L_1\simeq 0.62642\mathrm{m}$ beyond the source output mirror, and the target input mirror is $v-L_2/2\simeq 7.44786\mathrm{m}$ beyond the optical lens. The total separation between beam waists is $u+v\simeq 14.07428\mathrm{m}$.