Geometric representation and the adiabatic geometric phase in four-wave mixing processes

Area of Science:

• Nonlinear optics
• Quantum optics
• Photonics

Background:

• Adiabatic geometric phase (AGP) is crucial for developing all-optical devices.
• Nonlinear frequency conversion, specifically four-wave mixing (FWM), offers pathways for optical modulation.
• Quasi-phase matching is a key technique for controlling nonlinear optical processes.

Purpose of the Study:

• To develop canonical Hamilton equations and geometric representations for two FWM schemes.
• To precisely describe and calculate AGP in FWM processes.
• To investigate AGP in both undepleted and depleted pump regimes.

Main Methods:

• Development of canonical Hamilton equations for FWM.
• Geometric representation for analyzing AGP.
• Systematic study of AGP for idler and signal waves in two FWM schemes.
• Analysis considering both undepleted and depleted pump cases.

Main Results:

• Canonical Hamilton equations and geometric representations accurately describe AGP in FWM.
• The proposed methods for calculating AGP are universal across different pump depletion scenarios.
• Demonstrated systematic analysis of AGP for idler and signal waves.

Conclusions:

• The developed methods provide a universal approach to calculate AGP in FWM.
• This research facilitates the design of all-optical devices for phase modulation.
• Findings are applicable to all-optical shaping and encoding of ultrafast light pulses.