Statistical and coherence effects in nonlinear optical parametric up conversion. I - Coherent interaction. II - Incoherent interaction

After establishing the distinction between coherent and incoherent nonlinear optical interactions, parametric up-conversion (PUC) by coherent nonlinear optical mixing of strong, pumping radiation with weak input radiation is considered from the viewpoint of generating radiation. PUC efficiency is calculated by the conserved statistics method, and is shown to depend on the strong pumping radiation's photon statistics alone, so as to decrease with increasing fluctuation level in the pumping radiation. The fourth-order statistics of generated sum-frequency radiation are calculated in the first approximation of the iterative solution, and the statistics of both generating radiations are projected onto the statistical distribution of the resulting sum-frequency radiation in the same way as at the beginning of the process.