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Analysis of the rigorous coupled wave approach for \(p\)-polarized light in gratings. (English) Zbl 1470.78002

The authors consider an electromagnetic scattering problem for a periodic grating where the incident field is given by a p-polarized plane wave. For the solution of this problem, they study the “rigorous coupled wave approach”, where the periodicity properties of the solution allow the use of the Fourier series for the expansion of the scattered fields. In particular, the scattering problem is approximated by replacing the relative permittivity with a piecewise constant function in the direction perpendicular to the periodicity of the grating and expressing the problem in terms of the Fourier coefficients of the magnetic field. The authors show the convergence of the method when the discretization step in the approximation of the relative permittivity tends to zero, and when the number of Fourier coefficients in the approximation of the magnetic field tends to infinity. The paper concludes with some concrete examples giving a numerical evidence of the convergence results.

MSC:

78A45 Diffraction, scattering
78A40 Waves and radiation in optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
35Q61 Maxwell equations
35B20 Perturbations in context of PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

Software:

S4; NGSolve; Solcore
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Full Text: DOI arXiv

References:

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