Reformulation of the eigenvalue problem in the Fourier modal method with spatial adaptive resolution

Area of Science:

• Computational electromagnetics
• Nanophotonics
• Numerical methods

Background:

• The classical Fourier Modal Method (FMM) struggles with spurious modes, especially for metallic structures.
• Metallic nanostructures present challenges in electromagnetic simulations due to their unique optical properties.
• Accurate simulation of light-matter interactions is crucial for designing nanophotonic devices.

Purpose of the Study:

• To investigate the inherent stability of the Fourier Modal Method with Adaptive Spatial Resolution (FMMASR) against spurious modes.
• To explore methods for further enhancing the numerical stability of FMMASR.
• To improve the reliability of FMMASR for simulating metallic nanostructures.

Main Methods:

• Implementation of the Fourier Modal Method with Adaptive Spatial Resolution (FMMASR).
• Analysis of spurious mode generation in metallic structures using FMMASR.
• Reformulation of the FMMASR eigenvalue problem for enhanced stability.

Main Results:

• FMMASR demonstrates superior natural stability compared to the classical FMM regarding spurious modes in metallic structures.
• The reformulated eigenvalue problem of FMMASR leads to a significant improvement in numerical stability.
• The enhanced stability allows for more accurate simulations of electromagnetic phenomena in metallic systems.

Conclusions:

• FMMASR provides a more robust numerical framework for simulating metallic nanostructures.
• Reformulating the eigenvalue problem is an effective strategy to further stabilize FMMASR.
• This improved stability is critical for advancing research and development in nanophotonics and plasmonics.