In the Wigner formalism, after giving a general description of a light beam, the theory of parametric down-conversion is developed to second-order in the coupling constant. We then describe the detection process by calculating the auto-correlation and cross-correlations of the signal and idler beams. Four recent experiments are analyzed in detail: interference on a screen, Franson's experiments ͓Phys.

Ozone generation in pure oxygen using a wire-to-cylinder corona discharge reactor is experimentally and numerically investigated. Ozone concentration is determined by means of direct UV spectroscopy and the effects of Joule heating and ozone decomposition on the electrodes are analysed for different discharge gaps. The numerical model combines the physical processes in the corona discharge with the chemistry of ozone formation and destruction. The chemical kinetics model and the electrical model are coupled through Poisson's equation, and the current–voltage (CV) characteristic measured in experiments is used as input data to the numerical simulation. The numerical model is able to predict the radial distributions of electrons, ions, atoms and molecules for each applied voltage of the CV characteristic. In particular, the evolution of ozone density inside the discharge cell has been investigated as a function of current intensity and applied voltage.

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The spatial distribution of the species generated in a wire-cylinder positive corona discharge in pure oxygen has been computed using a plasma chemistry model that includes the most significant reactions between electrons, ions, atoms and molecules. The plasma chemistry model is included in the continuity equations of each species, which are coupled with Poisson's equation for the electric field and the energy conservation equation for the gas temperature. The current–voltage characteristic measured in the experiments has been used as an input data to the numerical simulation. The numerical model is able to reproduce the basic structure of the positive corona discharge and highlights the importance of Joule heating on ozone generation. The average ozone density has been computed as a function of current intensity and compared with the experimental measurements of ozone concentration determined by UV absorption spectroscopy.

We extend the Wigner function formalism for parametric down-conversion experiments presented in a previous paper ͓Phys. Rev. A 55 3879 ͑1997͔͒ to experiments involving propagation through a dispersive medium ͓Steinberg et al., Phys. Rev. A 45, 6659 ͑1992͔͒, and polarization ͓Kwiat et al., Phys. Rev. A 45, 7729 ͑1992͔͒. ͓S1050-2947͑97͒02009-X͔ PACS number͑s͒: 42.50.Ar, 03.65.Sq, 42.50.Lc