Journal ArticleDOI
Convergence of the coupled-wave method for metallic lamellar diffraction gratings
Lifeng Li,Charles W. Haggans +1 more
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TLDR
In this article, it was shown that the coupled-wave method converges slowly for metallic lamellar gratings in TM polarization, and the reason for the slow convergence was attributed to the use of Fourier expansions to represent the permittivity and the electromagnetic fields in the grating region.Abstract:
Numerical evidence is presented that shows that, for metallic lamellar gratings in TM polarization, the coupled-wave method formulated by Moharam and Gaylord [ J. Opt. Soc. Am. A3, 1780 ( 1986)] converges slowly. (In some cases, for achieving a relative error of less than 1% in diffraction efficiencies, the number of spatial harmonics retained in the computation must be much greater than 100.) By classification of the modal methods for analyzing diffraction gratings into two distinct categories, the cause for the slow convergence is analyzed and attributed to the use of Fourier expansions to represent the permittivity and the electromagnetic fields in the grating region. The eigenvalues and the eigenfunctions of the modal fields in the grating region, whose accurate determination is crucial to the success of the coupled-wave method, are shown to converge slowly as a result of the use of these Fourier expansions. Despite its versatility and simplicity, the coupled-wave method should be used with caution for metallic surface-relief gratings in TM polarization.read more
Citations
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Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings
TL;DR: In this paper, the authors presented a stable and efficient numerical implementation of the analysis technique for one-dimensional binary gratings for both TE and TM polarization and for the general case of conical diffraction.
Journal ArticleDOI
Use of Fourier series in the analysis of discontinuous periodic structures
TL;DR: The recent reformulation of the coupled-wave method by Lalanne and Morris as mentioned in this paper, which dramatically improves the convergence of the method for metallic gratings in TM polarization, is given a firm mathematical foundation in this paper.
Journal ArticleDOI
Photonic spin hall effect at metasurfaces
TL;DR: A strong photonic SHE resulting in a measured large splitting of polarized light at metasurfaces is reported, which may provide a route for exploiting the spin and orbit angular momentum of light for information processing and communication.
Journal ArticleDOI
New formulation of the Fourier modal method for crossed surface-relief gratings
TL;DR: In this paper, a new formulation of the Fourier modal method (FMM) that applies the correct rules of Fourier factorization for crossed surface-relief gratings is presented.
Journal ArticleDOI
Highly improved convergence of the coupled-wave method for TM polarization
TL;DR: In this article, Li and Haggans analyzed the convergence rate of the coupled-wave method for TM polarization of metallic lamellar gratings and provided numerical evidence that highly improved convergence rates similar to the TE polarization case can be obtained.
References
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Journal ArticleDOI
Diffraction analysis of dielectric surface-relief gratings
M. G. Moharam,Thomas K. Gaylord +1 more
TL;DR: In this article, a dielectric surface-relief grating is analyzed using rigorous coupled-wave theory and the analysis applies to arbitrary grating profiles, groove depths, angles of incidence, and wavelengths.
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Rigorous coupled-wave analysis of metallic surface-relief gratings
M. G. Moharam,Thomas K. Gaylord +1 more
TL;DR: In this paper, a rigorous coupled-wave analysis for metallic surface-relief gratings is presented for all diffracted orders as a function of period, groove depth, polarization, and angle of incidence.
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Three-dimensional vector coupled-wave analysis of planar-grating diffraction
M. G. Moharam,Thomas K. Gaylord +1 more
TL;DR: In this paper, a 3D vector coupled-wave analysis of an arbitrarily oriented planar grating with slanted fringes is presented, which applies to any sinusoidal or nonsinusoidal amplitude and/or phase grating, any plane-wave angle of incidence, and any linear polarization.
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The Dielectric Lamellar Diffraction Grating
TL;DR: In this paper, a modal theory describing the diffraction properties of a dielectric lamellar grating is presented and the numerical implementation is shown to be suited to modelling the behaviour of high refractive index gratings.
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Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves
TL;DR: In this article, the diffraction of light by deep rectangular-groove transmission phase gratings is treated by solving Maxwell's equations numerically, and results are given for the light diffracted into the zero order by gratings with grating constants d in the range λ < d < 5λ, aspect ratio b (= linewidth/d), 0 < b < 1, and grating depths a < 5 λ, assuming a refractive index n 0 = 1.