Adiabatic geometric phase in fully nonlinear three-wave mixing

Yongyao Li*, Ofir Yesharim, Inbar Hurvitz, Aviv Karnieli, Shenhe Fu, Gil Porat, Ady Arie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In a nonlinear three-wave mixing process, the interacting waves can accumulate an adiabatic geometric phase (AGP) if the nonlinear coefficient of the crystal is modulated in a proper manner along the nonlinear crystal. This concept was studied so far only for the case in which the pump wave is much stronger than the two other waves, hence can be assumed to be constant. Here we extend this analysis for the fully nonlinear process, in which all three waves can be depleted and we show that the sign and magnitude of the AGP can be controlled by the period, phase, and duty cycle of the nonlinear modulation pattern. In this fully nonlinear interaction, all the states of the system can be mapped onto a closed surface. Specifically, we study a process in which the eigenstate of the system follows a circular rotation on the surface. Our analysis reveals that the AGP equals to the difference between the total phase accumulated along the circular trajectory and that along its vertical projection, which is universal for the undepleted (linear) and depleted (nonlinear) cases. Moreover, the analysis reveals that the AGPs in the processes of sum-frequency generation and difference-frequency generation have opposite chirality. Finally, we utilize the AGP in the fully nonlinear case for splitting the beam into different diffraction orders in the far field.

Original languageEnglish
Article number033807
JournalPhysical Review A
Issue number3
StatePublished - Mar 2020


FundersFunder number
National Natural Science Foundation of China11575063, 11974146, 11874112
Natural Science Foundation of Guangdong Province2017B030306009
Israel Science Foundation1415/17
China Scholarship Council201808440001


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