Optimal conditions for parametric up-conversion in an externally excited nonlinear resonator

The approximation of a constant pump field is used to investigate a nonlinear resonator of the Fabry–Perot type with mirrors strongly reflecting at all three operating frequencies of a parametric frequency converter. The cases of phase matching and of a strong mismatch between the wave vectors are considered allowing for the dissipative losses and for external excitation of the resonator. Expressions are obtained for the optimal reflection coefficients of the entry mirror and the existence of the optimal length of the nonlinear crystal performing parametric conversion is demonstrated. The proposed system should ensure a higher conversion efficiency than that attainable in singly resonant and nonresonator systems.