Role of topological phase-defects in the parametric generation process

We show that topological phase-defects are spontaneously generated from noise fluctuations in the degenerate configuration of the parametric interaction. These localized coherent structures are shown to affect the coherence properties of the parametrically generated field. It is shown that the emergence of coherence in the fundamental field relies on a previously unrecognized process of mutual annihilation of pairs of neighboring phase-defects. More precisely, the density of phase-defects N  , and the time correlation τcτc of the generated field, are shown to exhibit a power-law behavior with the propagation length, i.e., τc∝z1/4,N∝z-1/4.