  Spontaneous parametric down-conversion (SPDC) is a widely used source for
photonic entanglement. Years of focused research have led to a solid
understanding of the process, but a cohesive analytical description of the
paraxial biphoton state has yet to be achieved. We derive a general expression
for the spatio-temporal biphoton state that applies universally across common
experimental settings and correctly describes the non-separability of spatial
and spectral modes. We formulate a criterion on how to decrease the coupling of
the spatial from the spectral degree of freedom by taking into account the Gouy
phase of interacting beams. This work provides new insights into the role of
the Gouy phase in SPDC, and also into the preparation of engineered entangled
states for multidimensional quantum information processing.
