Theory of parametric four-photon interaction. III. Amplification and oscillation with consideration of the depletion of the pump wave

NILOY KUMAR DUTTA

J. Frahm, Randolf Fischer

Abstract 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.

G. G. Adonts, L. M. Kocharyan, N. V. Shakhnazaryan

J. Frahm, Reiner Fischer

Abstract The processes of parametric amplification and oscillation in a medium with cubic polarization is investigated in parametric approximation. For the case of amplification the threshold power of the pump wave is calculated. The influence of a finite phase mismatching and of the initial phases on the amplification process is discussed. For larger values of mismatching a periodical change between amplification and depletion may appear. For the cases of a single resonant oscillator (for the signal wave only), a double resonant oscillator (for both signal and idler wave) and a double resonant oscillator with the pump wave reflected at the second mirror the threshold power of the pump wave and the rise time are calculated. Characteristic differences between four‐photon and three‐photon parametric oscillators are discussed. A numerical estimation of the threshold power for some media with nonlinear susceptibilities known from literature leads to the conclusion that the realization of a four‐photon parametric oscillator should be possible. In the appendix we discuss the influence of diffraction, focussing, birefrigence, nonstationarity and depletion of the pump wave on the studied process as well as the conditions under which these effects can be neglected.

Hisashi Matsuoka, Atsushi Okamoto, Mototsugu Takamura +1 more

We analyze the phase-conjugate reflectivity and the amplification property of cross-polarized four-wave mixing with a photorefractive BaTiO3 crystal in consideration of the pump-beam depletion. The coupled-wave equations of cross-polarized four-wave mixing with ordinary writing beams and an extraordinary reading beam are derived and solved with the grating-integral method. The results of calculations of the reflectivity and the amplification factors will be compared with the result under the undepleted-pumps approximation. In addition, to achieve high conversion efficiency, the optimum conditions for the intensity ratio and the angle configurations of the probe and pump beams are also discussed.

W. R. Garrett, Roger C. Hart, M. G. Payne +2 more