Theorie der parametrischen Vier-Photonen-Wechselwirkung. III. Verstärkung und Oszillation bei Berücksichtigung der Rückwirkung auf die Pumpwelle

The processes of parametric amplification and oscillation in a medium with cubic polarization are investigated theoretically taking into consideration the depletion of the pump wave. We suppose that phase-matching is realized exactly (a possible nonlinear detuning of the exact phase-matching should be compensated by a suitable subsequent adjustment of the frequencies). A consequence of linear losses is the appearance of a threshold for the parametric amplification. There exist a maximum length, a minimum length and an optimum length of the nonlinear medium for the process of parametric amplification. The threshold intensity, the optimum length of the nonlinear medium and the optimum reflection coefficient for outcoupling are determined for two arrangements of the double resonant parametric four-photon oscillator (ring resonator, FABRY -PEROT resonator). It is shown that for the above mentioned arrangements of the single resonant and the double resonant four-photon oscillator the efficiency is a monotonous function of the threshold excess. On the contrary in case of the three-photon oscillator there exists an optimum value of the threshold excess.