Quasi-phase-matched parametric amplification of waves with low-frequency pumping

It is shown for the first time that consecutive three-frequency interactions of waves with multiple frequencies ω, 2ω, and 3ω in periodically inhomogeneous and quadratically nonlinear crystals, such as lithium niobate, can result in highly efficient conversion of the energy of a pump wave of frequency 2ω into the energy of a wave of frequency 3ω