Evaluation of diffraction catastrophes by using Weniger transformation

Area of Science:

• Optics and Photonics
• Computational Mathematics

Background:

• The Weniger transformation is a powerful nonlinear sequence transformation.
• It accelerates the convergence of slowly converging or divergent series.
• Diffraction catastrophes are essential for analyzing optical fields near singularities.

Purpose of the Study:

• To numerically investigate the Weniger transformation's effect on diffraction catastrophe series expansions.
• To explore its potential application in optical field calculations.

Main Methods:

• Numerical analysis of the Weniger transformation applied to power series of diffraction catastrophes.
• Specific focus on Airy and Pearcey functions.

Main Results:

• The Weniger transformation effectively accelerates the convergence of series representations for diffraction catastrophes.
• Demonstrated efficiency for Airy and Pearcey functions.

Conclusions:

• The Weniger transformation shows significant promise as a computational tool in optics.
• It can be valuable for summing various types of series expansions in optical research.