Theory of sum-frequency generation in two series-arranged nonlinear crystals

An analysis is made of sum-frequency generation in two series-arranged nonlinear crystals taking into account changes in the phases of the interacting waves both in the crystals and in the air gap between them. It is shown that by optimizing the parameters of the problem such as the crystal lengths, the phase mismatch, and the pump intensities, and by compensating for undesirable phase shifts of the interacting waves, it is possible to achieve a high conversion efficiency in series-arranged nonlinear crystals.