Spatial evolution of wave amplitudes, stability of solutions, and bifurcations in sum and difference frequency generation processes under two-photon resonance conditions

An investigation is made of four-photon sum and difference frequency generation under two-photon resonance conditions allowing for population migration accompanying incoherent processes and for the possibility of a one-photon quasiresonance with the emitted radiation in inverted and uninverted media. A study is made of parametric bleaching of the medium and phase locking of the interacting waves, their stability, and influence on the conversion quantum efficiency η. It is established that resonant parametric processes have a larger region of stability than nonresonant ones. An analysis is made of bifurcation, typical of resonant processes, that strongly influences η. Accurate analytic expressions are derived for the maximum attainable values of η and it is shown that there is an optimum frequency detuning from a one-photon resonance.