Modeling the power of an optical parametric generator by discrete mode summation

An analytical expression for calculating the signal output power of an optical parametric generator (OPG) configuration was developed. The model is based on Heisenberg equations in space and radiation mode theory. A simple analytical expression can be obtained by assuming that all modes within the gain bandwidth of the nonlinear crystal have the same gain and the same interaction length. Another derivation considers the gain and interaction length of each individual mode. The model predictions are in excellent agreement with the measured signal power of OPGs based on 25- and 35-mm periodically poled LiNbO₃ crystal (with effective quadratic nonlinearity of ∼14.5 pm/V) and 47-mm periodically poled LiTaO₃ crystal (with effective quadratic nonlinearity of ∼9 pm/V). In addition, a comparison was made between the summation over discrete modes approach and the traditional approach of continuous integration over the beam parameters and pump frequency. We have found that the first approach, which is developed in this paper, predicts more accurately the output power of the OPG.