TY - JOUR

T1 - Adiabatic geometric phase in fully nonlinear three-wave mixing

AU - Li, Yongyao

AU - Yesharim, Ofir

AU - Hurvitz, Inbar

AU - Karnieli, Aviv

AU - Fu, Shenhe

AU - Porat, Gil

AU - Arie, Ady

N1 - Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/3

Y1 - 2020/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85082830506&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.101.033807

DO - 10.1103/PhysRevA.101.033807

M3 - מאמר

AN - SCOPUS:85082830506

VL - 101

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 3

M1 - 033807

ER -