Constant adiabatic geometric phase in three-wave mixing under different depletion levels

An adiabatic geometric phase (AGP) can be accumulated through circular rotation of the quasi-phase-matching (QPM) parameters in the χ⁽²⁾ nonlinear process. When the weak idler and signal are coupled by a strong pump, the AGP can be well predicted. However, once the intensities of the signal and idler become comparable to that of the pump, the AGP accumulated via the same circular rotation as that of the QPM parameter deviates from the prediction and strongly depends on the intensities of the input waves. This deviation brings great uncertainty in the precise creation of AGPs via these nonlinear processes. In this paper, we successfully find a constant geometric phase, which is almost independent of the intensity of the pump, under a typical modulation pattern of the nonlinear crystal. This finding effectively suppresses the uncertainty in creating the AGP in the nonlinear frequency conversion.