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Spontaneous parametric downconversion is the primary source to generateentangled photon pairs in quantum photonics laboratories. Depending on theexperimental design, the generated photon pairs can be correlated in thefrequency spectrum, polarisation, position-momentum, and spatial modes.Exploring the spatial modes' correlation has hitherto been limited to the polarcoordinates' azimuthal angle, and a few attempts to study Walsh modes radialstates. Here, we study the full-mode correlation, on a Laguerre-Gauss basis,between photon pairs generated in a type-I crystal. Furthermore, we explore theeffect of a structured pump beam possessing different spatial modes ontobi-photon spatial correlation. Finally, we use the capability to project overarbitrary spatial mode superpositions to perform the bi-photon state's fullquantum tomography in a 16-dimensional subspace.

Full-mode Characterisation of Correlated Photon Pairs Generated in Spontaneous Downconversion