Influence of walk-off, dispersion, and diffraction on the coherence of parametric fluorescence

We consider the basic problem of spontaneous parametric generation from quantum noise fluctuations in the presence of a continuous plane-wave pump. We show, both numerically and analytically, that the walk-off between the down-converted fields is the key ingredient that leads to the generation of coherent fields in the parametric process. Along these lines, our theory reveals that, in the absence of walk-off, diffraction and chromatic dispersion in usual quadratically nonlinear materials only lead to incoherent erratic dynamics. Moreover, a two-dimensional study shows that, when the walk-off is exclusively temporal (or spatial), the parametric process is not able to yield the generation of spatially (or temporally) coherent fields. This study sheds light on the problem of coherence in parametric fluorescence and, in particular, allows us to explain various recent experimental observations.