Quantum structures in traveling-wave spontaneous parametric down-conversion

We analyze theoretically spatial structures appearing in the far diraction zone of the electromagnetic field emitted in the cavityless parametric down-conversion. We investigate in detail the spatial correlation functions of intensity and demonstrate the existence of strong quantum correlations between the regions of the far field symmetrical with respect to the optical axis. Our simplied model allows us to obtain analytical results for some limiting cases. We demonstrate that in the limit of small direction and ideal quantum efficiency of photodetection the noise reduction in the photocurrent dierence between symmetrical regions in the far direction field becomes complete at zero frequency of photocurrent fluctuations.