Fourier modal method with spatial adaptive resolution for structures comprising homogeneous layers

Area of Science:

• Computational physics
• Numerical methods
• Electromagnetics

Background:

• The Fourier modal method (FMM) is a powerful technique for analyzing periodic structures.
• Adaptive spatial resolution can improve the accuracy and efficiency of numerical methods.
• Solving eigenvalue problems is computationally intensive in many physics simulations.

Purpose of the Study:

• To introduce a numerical improvement to the Fourier modal method using adaptive spatial resolution.
• To demonstrate a simplified approach for solving eigenvalue problems within the FMM framework.
• To quantify the computational time savings achieved by the proposed method.

Main Methods:

• Implementation of adaptive spatial resolution within the Fourier modal method.
• Development of a strategy to deduce solutions of multiple eigenvalue problems from a single one.
• Numerical simulations to validate the method and assess performance.

Main Results:

• A significant numerical improvement in the Fourier modal method was achieved.
• A straightforward method to solve all relevant eigenvalue problems from one solution was established.
• Substantial computation time savings were demonstrated through numerical examples.

Conclusions:

• The proposed adaptive spatial resolution enhances the efficiency of the Fourier modal method.
• The simplified eigenvalue problem solving reduces computational burden.
• This approach offers practical advantages for electromagnetic simulations requiring FMM.