Number-phase properties of correlated chaotic fields

We study the arrangement of two down-conversion crystals with aligned and p artially aligned idler beams in the quasimonochromatic approximation. Treat ing the signal fields as correlated chaotic modes, we arrive at a detailed description and illustration of their mathematically well defined state in terms of number and phase properties. We show it to be a mixed partial phas e-difference state. We derive the closed formulae for the phase-difference distributions in this state derived from the phase-space distributions rela ted to the normal, symmetrical and antinormal orderings of field operators and show that such distributions depend exclusively on measures of correlat ion which are variants of the modulus of the familiar degree of coherence. Quantum correlation influences fluctuations of photon-number sum, photon-nu mber difference and quantum phase difference. Starting from a quasidistribu tion which carries the same information as the statistical operator, we arr ive at the joint distributions of number sum and phase difference and the q uasidistribution of number difference and phase difference.