Full-mode characterization of correlated photon pairs generated in spontaneous downconversion

Spontaneous parametric downconversion is the primary source to generate entangled photon pairs in quantum photonics laboratories. Depending on experimental design, generated can be correlated frequency spectrum, polarisation, position-momentum, and spatial modes. Exploring modes' correlation has hitherto been limited polar coordinates' azimuthal angle, a few attempts study Walsh modes radial states. Here, we full-mode correlation, Laguerre-Gauss basis, between type-I crystal. Furthermore, explore effect of structured pump beam possessing different onto bi-photon correlation. Finally, use capability project over arbitrary mode superpositions perform state's full tomography 16-dimensional subspace.