Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution

Granet, Gérard

doi:10.1364/josaa.16.002510

Cited by 143 publications

(85 citation statements)

References 7 publications

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“…Our first test case is the metallic grating already analyzed in several research papers [6,16]. The lamellar grating normalized pitch d/λ is set to 1, the normalized line width f is 0.5 and the normalized line height h/λ is 1.…”

Section: Metallic Gratingsmentioning

confidence: 99%

“…The values of reference R ref are taken from Table 1 of the Granet's adaptive implementation [16] using 201 basis functions. Up to the first five significant digits, the considered exact values are 0.73428 and 0.84848 for the TE and TM polarization respectively.…”

Section: Metallic Gratingsmentioning

confidence: 99%

“…This test case has already been used in Ref. [16]. The incidence and geometrical parameters are: θ = 29 • , ε 21 = 1, ε 22 = 25, d/λ = 1, f = 0.4.…”

Section: Dielectric Gratingsmentioning

confidence: 99%

See 2 more Smart Citations

Modal Method Based on Spline Expansion for the Electromagnetic Analysis of the Lamellar Grating

Armeanu

Edee²,

Granet³

et al. 2010

PIER

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Abstract-This paper reports an exact and explicit representation of the differential operators from Maxwell's equations. In order to solve these equations, the spline basis functions with compact support are used. We describe the electromagnetic analysis of the lamellar grating as an eigenvalues problem. We choose the second degree spline as basis functions. The basis functions are projected onto a set of test functions. We use and compare several test functions namely: Dirac, Pulse and Spline. We show that the choice of the basis and test functions has a great influence on the convergence speed. The outcomes are compared with those obtained by implementing the Finite-Difference Modal Method which is used as a reference. In order to improve the numerical results an adaptive spatial resolution is used. Compared to the reference method, we show a significantly improved convergence when using the spline expansion projected onto spline test functions.

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Section: Metallic Gratingsmentioning

confidence: 99%

Section: Metallic Gratingsmentioning

confidence: 99%

See 1 more Smart Citation

Modal Method Based on Spline Expansion for the Electromagnetic Analysis of the Lamellar Grating

Armeanu

Edee²,

Granet³

et al. 2010

PIER

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“…In the past decades the method has matured due to fundamental studies and improvements to its stability (Moharam et al, 1995b;Li, 1996a) and convergence (Granet and Guizal, 1996;Lalanne and Morris, 1996;Li, 1996b). Other important contributions to the evolution of the method are the techniques of adaptive spatial resolution (Granet, 1999) and normal vector fields Nevière, 2000, 2001;Schuster et al, 2007). Ref.…”

Section: Introductionmentioning

confidence: 99%

Efficient solution of Maxwell’s equations for geometries with repeating patterns by an exchange of discretization directions in the aperiodic Fourier modal method

Pisarenco

Maubach

Setija

et al. 2012

Journal of Computational Physics

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“…The method has a history of more than three decades marked by considerable improvements on stability [4] and convergence [5,6,7]. The monograph [8] gives an overview of the evolution and the implementation of Fourier modal methods.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for the Solution of Time-Harmonic Maxwell Equations for Two-Dimensional Scatterers

Pisarenco

Maubach

Setija³

et al. 2010

AIP Conference Proceedings

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Abstract. The Fourier modal method (FMM) is a method for efficiently solving Maxwell equations with periodic boundary conditions. In a recent paper [1] the extension of the FMM to non-periodic structures has been demonstrated for a simple two-dimensional rectangular scatterer illuminated by TE-polarized light with a wavevector normal to the third (invariant) dimension. In this paper we present a generalized version of the aperiodic Fourier modal method in contrast-field formulation (aFMM-CFF) which allows arbitrary profiles of the scatterer as well as arbitrary angles of incidence of light.

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Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution

Cited by 143 publications

References 7 publications

Modal Method Based on Spline Expansion for the Electromagnetic Analysis of the Lamellar Grating

Modal Method Based on Spline Expansion for the Electromagnetic Analysis of the Lamellar Grating

Efficient solution of Maxwell’s equations for geometries with repeating patterns by an exchange of discretization directions in the aperiodic Fourier modal method

A Numerical Method for the Solution of Time-Harmonic Maxwell Equations for Two-Dimensional Scatterers

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