Numerical investigation of effective nonlinear coefficient model for coupled third harmonic generation

Area of Science:

• Nonlinear optics
• Materials science
• Crystallography

Background:

• Quasi-phase-matching (QPM) crystals are crucial for nonlinear optical processes.
• Coupled third harmonic generation (CTHG) requires precise control over nonlinear coefficients.
• Optimizing domain structures in aperiodically poled lithium niobate (APPLN) is challenging.

Purpose of the Study:

• To numerically investigate the optimal effective nonlinear coefficient for CTHG in QPM crystals.
• To develop a method for optimizing domain distributions in APPLN crystals.
• To determine upper bounds on effective nonlinear coefficients for various fundamental wavelengths.

Main Methods:

• Conversion of the CTHG effective nonlinear coefficient to an Ising model.
• Optimization of domain distributions for APPLN crystals (0.5 mm and 1 mm lengths).
• Application of semidefinite programming to calculate upper bounds on nonlinear coefficients.
• Development of a crystal domain poling weight curve reconstruction method.

Main Results:

• Identified optimal domain distributions for APPLN crystals across a range of fundamental wavelengths (1000–6000 nm).
• Proposed a method to reconstruct poling weight curves for coupled nonlinear processes.
• Demonstrated optimal conversion ratios along the crystal length for coupled nonlinear processes.
• Calculated upper bounds for effective nonlinear coefficients (deff).

Conclusions:

• The study provides a framework for optimizing nonlinear coefficients in QPM crystals for CTHG.
• The proposed method is applicable to other coupled dual χ(2) processes.
• This research deepens the understanding of coupled nonlinear interactions in QPM devices.