Summing Pauli asymptotic series to solve the wedge problem

Area of Science:

• Electromagnetics
• Wave Propagation
• Computational Physics

Background:

• The wedge diffraction problem is a fundamental challenge in electromagnetics.
• Pauli's asymptotic treatment (1938) provides a foundational method for analyzing this problem.
• Traditional methods may struggle with accuracy in near-field regions.

Purpose of the Study:

• To re-evaluate and enhance Pauli's asymptotic treatment for wedge diffraction.
• To develop a robust computational tool for electromagnetic field retrieval.
• To accurately determine the total electromagnetic field, particularly in the near zone.

Main Methods:

• The study revisits Pauli's asymptotic treatment.
• The factorial divergent nature of the Pauli series is mathematically proven.
• The Weniger transformation, a nonlinear resummation technique, is employed to sum the series.
• Numerical simulations are performed to validate the approach.

Main Results:

• The Pauli series is confirmed to have a factorial divergent character.
• The Weniger transformation effectively sums the divergent Pauli series.
• The enhanced method accurately retrieves the total electromagnetic field in the near zone.
• Numerical results demonstrate the approach's accuracy and effectiveness.

Conclusions:

• The revisited Pauli asymptotic treatment, combined with the Weniger transformation, offers a powerful computational tool.
• This approach significantly improves the accuracy of electromagnetic field calculations in near-field regions.
• The method provides an effective solution for the wedge diffraction problem.