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Three-dimensional adaptive coordinate transformations for the Fourier modal method.

Jens Küchenmeister

|February 12, 2014

Summary

This study introduces 3D adaptive coordinates and spatial resolution for the Fourier Modal Method (FMM), enhancing convergence for complex photonic systems. The approach integrates seamlessly with existing FMM codes by transforming material tensors.

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Area of Science:

Photonics and Computational Electromagnetics
Numerical Methods for Wave Propagation

Background:

Adaptive coordinates and spatial resolution improve Fourier Modal Method (FMM) convergence, particularly for metallo-dielectric systems.
Previous applications were limited to two-dimensional adaptive coordinate transformations.

Purpose of the Study:

To systematically construct three-dimensional adaptive coordinate and adaptive spatial resolution transformations for FMM.
To enable enhanced convergence for complex 3D photonic structures using FMM.

Main Methods:

Development of 3D adaptive coordinate and spatial resolution transformations within the FMM framework.
Application to a periodic system featuring two layers of rotated metallic crosses.
Focus on transforming material tensors for compatibility with existing FMM solvers.

Main Results:

Successful implementation of the first systematic 3D adaptive transformations for FMM.
Demonstration of the method's applicability to complex 3D periodic structures.
Validation of the approach for integration with standard FMM eigenproblem solvers.

Conclusions:

The developed 3D adaptive transformations offer a significant advancement for FMM simulations.
This method enhances computational efficiency and accuracy for 3D photonic and plasmonic devices.
The approach provides a versatile tool for researchers using FMM for complex material systems.