Adiabatic geometric phase in fully nonlinear three-wave mixing

Abstract

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.

arXiv comment9 pages, 36 references, 7 figures. Published on Physical Review A

References in corpus (14)

• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Berry Phase Effects on Electronic Properties
• Observation of Berry's Phase in a Solid State Qubit
• An Ultra-high Numerical Aperture Metalens at Visible Wavelengths
• Adiabatic Theory of Nonlinear Evolution of Quantum States
• Spin-to-orbital angular momentum conversion in dielectric metasurfaces
• Geometrical Representation of Sum Frequency Generation and Adiabatic Frequency Conversion
• Guiding light via geometric phases
• Optical manipulation of Berry phase in a solid-state spin qubit
• Adiabatic Geometric Phase for a General Quantum States
• Efficient, Broadband and Robust Frequency Conversion by Fully Nonlinear Adiabatic Three Wave Mixing
• Adiabatic geometric phase in fully nonlinear three-wave mixing
• Non-reciprocal geometric phase in nonlinear frequency conversion
• Broadband and robust adiabatic second-harmonic generation by a temperature gradient in birefringently phase-matched lithium triborate crystal

Cited by in corpus (6)

• Adiabatic geometric phase in fully nonlinear three-wave mixing
• Semidiscrete optical vortex droplets in quasi-phase-matched photonic crystals
• Geometric phase with full-wedge and half-wedge rotation in nonlinear frequency conversion
• Geometric representation of adiabatic distributed-Bragg-reflectors and broadening the photonic bandgap
• Complete and robust energy conversion by sum frequency generation based on Invariant Engineering
• Observation of geometric phase for unpolarized and partially polarized light fields