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Differential theory: application to highly conducting gratings.
Evgeny Popov1, Boris Chernov, Michel Nevière
1Institut Fresnel, Unité Mixte de Recherche Associée au Centre National de la Recherche Scientifique, Faculté des Sciences et Techniques de St.-Jérôme, Marseille Cedex 20, France. e.popov@fresnel.fr
Summary
The fast Fourier factorization method shows numerical instability for low-loss metallic gratings. Modifications to the differential theory of gratings improve stability for analyzing silver and gold gratings.
Area of Science:
- Optics
- Materials Science
- Computational Physics
Background:
- The fast Fourier factorization method enhances the differential theory of gratings.
- Numerical instability arises in metallic gratings with low refractive index real parts (e.g., Ag, Au in IR).
- Li's inverse rule and matrix condition numbers explain this instability.
Purpose of the Study:
- To address numerical instability in the fast Fourier factorization method for metallic gratings.
- To improve the convergence of differential theory and rigorous coupled-wave methods.
- To enable accurate analysis of infrared silver and gold gratings.
Main Methods:
- Investigating matrix condition numbers related to Li's inverse rule.
- Applying additional truncation to matrices in the differential system.
- Introducing lossier material within the grating bulk, creating a thin metallic layer.
Main Results:
- Truncation of matrices partially mitigates numerical problems.
- Using a thin layer of highly conducting metal significantly improves convergence.
- Optical properties remain unchanged if the metallic layer is sufficiently thick.
Conclusions:
- The fast Fourier factorization method requires modifications for low-loss metallic gratings.
- Matrix truncation and thin-layer metal approaches enhance numerical stability.
- These methods improve the applicability of differential theory for various grating profiles.