Hamiltonian approach for optimization of phase-sensitive double-pumped parametric amplifiers

Area of Science:

• Nonlinear optics
• Quantum optics
• Fiber optics

Background:

• Nonlinear four-wave mixing (NFW) is crucial for optical signal processing.
• Phase-sensitive parametric amplifiers are vital for signal amplification.
• Pump depletion in amplifiers complicates theoretical analysis.

Purpose of the Study:

• To simplify the complex equations governing nonlinear four-wave mixing.
• To analyze signal amplification in phase-sensitive parametric amplifiers under pump depletion.
• To optimize amplifier parameters for maximum signal gain.

Main Methods:

• Applied Hamiltonian formalism to reduce NFW equations.
• Utilized a one-degree-of-freedom Hamiltonian system.
• Analyzed phase portraits and trajectories of the Hamiltonian system.
• Investigated the role of the separatrix for optimal wave interaction.

Main Results:

• Theoretical maximum gain identified on extremal trajectories in symmetric cases.
• The separatrix trajectory was proposed as optimal for reduced nonlinear interaction.
• Derived analytical expressions for maximum amplification, optimal fiber length, and phase.
• Achieved optimized phase-sensitive parametric amplification across a wide wavelength range.

Conclusions:

• Hamiltonian formalism offers a simplified approach to NFW analysis.
• Optimal trajectory selection (separatrix) enhances signal amplification efficiency.
• The optimized amplifier design enables maximum signal gain in phase-sensitive systems.