Modal spectrum in spontaneous parametric down-conversion with noncollinear phase matching

Abstract

We investigate the effect of the down-conversion angle between the signal and idler beams in spontaneous parametric down-conversion on the bandwidth of the modal spectrum (Schmidt number) of the down-converted quantum state. For this purpose, we consider both the full Schmidt number and the azimuthal Schmidt number in the Laguerre-Gaussian basis. For the full Schmidt number, we show that the approximation of the phase-matching function with a Gaussian function gives results that disagree significantly from those obtained with the more physical sinc-type phase-matching function. We found a drastic increase in both the Schmidt number and the azimuthal Schmidt number for small down-conversion angles, in agreement with recent experimental results.