Nondegenerate Four Wave Mixing in Rare-Earth Doped Fiber Under the Influence of Coherent Population Trapping

By applying a strong coupling field between a lower state and the upper state of an allowed transition to ground, an enhancement of nondegenerate four wave mixing (NDFWM) with a resonantly enhanced third-order nonlinear susceptibility in a rare-earth doped fiber can be obtained. We have derived an expression for the third-order non-linear susceptibility using quantum theory and discussed the conversion efficiency for NDFWM. The theoretical result shows that the conversion efficiency has a maximum value while the third-order nonlinear susceptibility shows constructive interference at the Rabi frequency Ω₂₃ =±√Г₂Г₃. On account of phase-mismatch, the frequency conversion efficiency has a maximum value over a certain small range of frequency separation (such as 0 < Δf < 30 GHz at the wavelength λ_c = 1.55 μm), and the frequency conversion range increases with increase of the third-order nonlinear susceptibility.