Reliable computation of scattering from metallic binary gratings using Fourier-based modal methods

Area of Science:

• Electromagnetics and Optics
• Computational Physics
• Materials Science

Background:

• Modal methods are widely used for analyzing gratings.
• Convergence problems in these methods are often linked to mode computation inaccuracies.
• However, convergence issues can persist even with accurate mode computations.

Purpose of the Study:

• To identify the root cause of persistent convergence problems in modal methods for TM polarized fields.
• To propose an improved numerical approach for enhanced convergence.
• To demonstrate the effectiveness of the proposed method.

Main Methods:

• Analysis of the truncation of infinite linear equations arising from field matching at interfaces.
• Implementation of a modified truncation strategy using rectangular matrices.
• Application of a minimum least squared error (MLSE) approach to solve the truncated system.

Main Results:

• Convergence problems in modal methods for TM polarized fields are demonstrated to stem from the truncation of the infinite set of linear equations using a square matrix.
• Significant improvements in convergence rates are achieved by truncating the system with a rectangular matrix.
• The MLSE solution further enhances convergence and accuracy.

Conclusions:

• The choice of matrix truncation in modal methods is critical for convergence, independent of mode computation accuracy.
• Employing rectangular matrices and MLSE offers a robust solution to convergence challenges in grating analysis.
• This approach enhances the reliability and efficiency of modal methods for electromagnetic simulations.