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A construction guide to analytically generated meshes for the Fourier Modal Method.

Jens Küchenmeister¹, Thomas Zebrowski, Kurt Busch

¹Institut für Theoretische Festkörperphysik and DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany.

|October 6, 2012

Summary

Adaptive coordinates and adaptive spatial resolution improve Fourier Modal Method simulations for photonic structures. This study offers mesh design guidelines for better performance in metallo-dielectric systems.

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Area of Science:

Photonics and computational electromagnetics.
Numerical methods for optical simulations.

Background:

Fourier Modal Method (FMM) is a powerful technique for simulating periodic photonic structures.
Metallo-dielectric systems present unique challenges for FMM simulations.
Efficient meshing is crucial for FMM accuracy and convergence.

Purpose of the Study:

To enhance the performance of the Fourier Modal Method (FMM) for simulating periodic photonic structures.
To introduce adaptive coordinate transformations and adaptive spatial resolution for improved FMM simulations.
To provide guidelines for optimal mesh selection in FMM.

Main Methods:

Development of analytical coordinate transformations for adaptive meshing.
Application of adaptive spatial resolution to FMM simulations.
Analysis of mesh convergence characteristics for various structures.

Main Results:

Adaptive coordinates and resolution significantly improve FMM performance, particularly for metallo-dielectric systems.
Demonstration of multiple analytical coordinate transformation approaches.
Establishment of general guidelines for mesh type and parameter selection based on convergence analysis.

Conclusions:

Adaptive meshing strategies are essential for optimizing FMM simulations of complex photonic structures.
The presented coordinate transformations and guidelines facilitate more accurate and efficient FMM analysis.
This work advances the simulation capabilities for periodic optical devices.