Quantum structures in traveling-wave spontaneous parametric down-conversion

We analyze theoretically spatial structures appearing in the far diffractio n zone of the electromagnetic field emitted in the cavityless parametric do wn-conversion. We investigate in detail the spatial correlation functions o f intensity and demonstrate the existence of strong: quantum correlations. between the regions of the far field symmetrical with respect to the optica l axis. Our simplified model allows us to obtain analytical results for som e limiting cases. We demonstrate that in the limit of small diffraction and ideal quantum efficiency of photodetection the noise reduction in the phot ocurrent difference between symmetrical regions in the far diffraction fiel d becomes complete at zero frequency of photocurrent fluctuations.