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Fast semi-analytical solution of Maxwell's equations in Born approximation for periodic structures
Summary
We introduce a rapid semi-analytical method using Fourier modal method (FMM) for Maxwell
Area of Science:
- Computational electromagnetics
- Wave propagation modeling
Background:
- Solving Maxwell's equations is crucial for understanding wave phenomena.
- Existing numerical methods can be computationally intensive.
Purpose of the Study:
- To develop a faster semi-analytical approach for Maxwell's equations.
- To leverage Born approximation within the Fourier modal method (FMM).
Main Methods:
- Utilizing the Fourier modal method (FMM) under Born approximation.
- Exploiting matrix diagonalization for computational efficiency.
- Employing analytical solutions in the vertical direction.
Main Results:
- Reduced computational complexity from cubic to linear.
- Wavelength-independent degrees of freedom in the vertical direction.
- Applicability to 2D periodic geometries with planar illumination.
Conclusions:
- The proposed method offers significant computational speed-up.
- Enables efficient simulation of electromagnetic wave interactions.
- Suitable for analyzing periodic nanophotonic structures.
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