Optical parametric amplification from quantum noise

The propagation problem of optical parametric interaction is examined using a quantum theoretical treatment, and the total signal intensity is calculated as if the parametric amplification starts from quantum noise, while the pump wave is described classically. By neglecting pump wave depletion and assuming an exact matchint of the wave vector components perpendicular to the propagation direction in each case, it is shown that only two parametric modes (signal and idler modes) couple during the amplification process. The corresponding set of differential equations is solved analytically. The overall signal intensity is provided by the integration of all modes (amplification linewidth and solid angle). By interpreting thy result in terms of the classical theory, an expression for the virtual initial intensity is obtained if the amplification starts from quantum noise.