Efficient cascade quasi-synchronous parametric generation with up-conversion

We report efficient cascade up-conversion generation due to two simultaneous quasi-synchronous processes of parametric decay ω₃→ω₁+ ω₂ of pump quanta at the frequency ω₃ and up-conversion of one of the generated waves ω₁+ω₃→ω₄>ω₃ at the frequency ω₁ in a medium with a quadratic nonlinearity. It is found that the necessary condition for this generation is the requirement |γ₁|²>(ω₂/ω₁)|γ₂|², where γ_1,2 are the averaged constants of the nonlinear coupling for the processes ω₁+ω_2,3→ω_3,4, respectively. If this requirement is fulfilled, the plane monochromatic pump wave is completely depleted, while the limiting (the noise seed intensity is I_10,20→0 at the input) efficiency of the energy conversion into radiation at the frequency ω₄ is independent of I_10,20 and determined only by the relations between |γ_1,2|² and the frequencies of the interacting waves.