Rigorous calculation of the nonlinear Kerr coefficient for a waveguide using power-dependent dispersion modification

Area of Science:

• Nonlinear optics
• Waveguide theory
• Computational electromagnetics

Background:

• Nonlinear Kerr coefficient is crucial for understanding light-matter interactions in optical waveguides.
• Existing formulas for Kerr coefficient calculation often lack rigor or are limited in scope.
• Accurate determination of nonlinear properties is essential for designing advanced photonic devices.

Purpose of the Study:

• To propose a direct and rigorous method for calculating the nonlinear Kerr coefficient of waveguides.
• To validate the proposed method by comparing results with existing literature.
• To demonstrate the method's applicability to different waveguide geometries.

Main Methods:

• Utilizing effective power-dependent permittivity for direct dispersion calculation.
• Employing tensor permittivity to fully account for the electric field's vectorial nature.
• Implementing the approach with standard mode solvers for computational convenience.

Main Results:

• The direct calculation method provides a rigorous determination of the nonlinear Kerr coefficient.
• Calculated Kerr coefficients for nonlinear slab and wire waveguides show good agreement with literature values.
• The proposed approach is shown to be computationally efficient and versatile.

Conclusions:

• The effective power-dependent permittivity method offers a robust approach for nonlinear waveguide analysis.
• This technique simplifies the accurate characterization of nonlinear optical properties.
• The findings facilitate the design and optimization of nonlinear photonic devices.