Considering the quantum state produced in type I spontaneous parametric down-conversion with collinear, degenerate signal and idler beams, and a Gaussian pump, we show that the azimuthal Schmidt number in the Laguerre-Gaussian (LG) basis increases when the radial indices of the LG modes detected in the signal and idler beams are different. These observations are confirmed by the good agreement between theoretical and experimental results. The theoretical results are obtained by deriving expressions for the probability amplitude to detect LG modes with any combination of azimuthal and radial indices in a down-converted photonic quantum state.
We present a simple way of simulating Spontaneous parametric down-conversion (SPDC) by modulating a classical laser beam with two spatial light modulators (SLM) through a back projection setup. This system has the advantage of having very high photon count rates, it can simulate a large range of pump beam profiles simply by modifying the hologram on the SLM, and it can be easily converted to a SPDC setup by simply changing only two of its components without the need to perform realignment. This setup can be used to give an indication whether a SPDC experiment will be feasible in a very short amount of time.