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Published on: August 12, 2013
Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings
1Clermont Université, Université Blaise Pascal, LASMEA, BP 10448, Clermont-Ferrand, France. kofi.edee@univ-bpclermont.fr
Summary
A new modal method using Gegenbauer polynomial expansion (MMGE1) accurately solves plane wave diffraction by lamellar gratings. This approach offers improved accuracy over traditional Fourier modal methods (FMM).
Area of Science:
- Electromagnetics
- Optics
- Computational Physics
Background:
- Modal methods are widely used for solving lamellar grating diffraction problems.
- The Fourier modal method (FMM) can suffer from poor convergence due to approximations in basis functions.
- The Wilbraham-Gibbs phenomenon is a potential cause for FMM convergence issues.
Purpose of the Study:
- Introduce a novel modal method by Gegenbauer polynomial expansion (MMGE1).
- Investigate alternative basis functions for more accurate field representation in gratings.
- Compare the accuracy of MMGE1 against existing modal methods like FMM.
Main Methods:
- The proposed method (MMGE1) divides the grating structure into homogeneous layers.
- Electromagnetic fields are expanded using Gegenbauer polynomials within each layer.
- Rigorous boundary conditions are applied between layers to derive an eigenvalue equation.
Main Results:
- The MMGE1 approach accurately describes the electromagnetic fields.
- Results demonstrate superior accuracy compared to classical and parametric FMM.
- The use of Gegenbauer polynomials enhances the representation of fields.
Conclusions:
- MMGE1 provides a more accurate solution for plane wave diffraction by lamellar gratings.
- This method overcomes limitations associated with FMM convergence.
- Gegenbauer polynomial expansion offers a promising alternative for grating analysis.
