Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms.

Area of Science:

• Computational Electromagnetics
• Optics and Photonics
• Numerical Methods

Background:

• Solving Maxwell's equations for large-scale structures presents significant computational challenges.
• Existing methods may struggle with the complexity and scale of electromagnetic field simulations.
• Efficient computation of electromagnetic fields is crucial for designing advanced optical components.

Purpose of the Study:

• To introduce a novel Domain Decomposition Spectral Method (DDSM) for frequency-domain Maxwell's equations.
• To demonstrate the application of DDSM within the Aperiodic Fourier Modal Method (AFMM) framework.
• To enable the simulation of electromagnetic fields diffracted by large-scale surfaces under arbitrary excitation.

Main Methods:

• Decomposition of large surfaces into smaller, manageable square sub-cells.
• Definition of a projector linking large-scale problem eigenvectors to sub-cell eigenfunctions.
• Independent computation of electromagnetic field spectra on each sub-cell, facilitating parallel processing.

Main Results:

• The DDSM successfully associates the electromagnetic field spectrum of a large domain with its sub-cell footprint.
• The method is suitable for parallel computing, enhancing simulation efficiency.
• Demonstrated ability to simulate both near and far fields of full 3D structures.

Conclusions:

• The DDSM provides an effective solution for simulating large-scale electromagnetic problems.
• The method allows for the design of large-area diffractive metalenses on conventional personal computers.
• DDSM offers a computationally efficient and scalable approach for advanced optical component design.