Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization

Granet, Gérard; Guizal, Brahim

doi:10.1364/josaa.13.001019

Cited by 332 publications

(224 citation statements)

References 6 publications

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“…(26) and (27) we have used the modified factorization rule introduced in [44]. Of course, in order to exploit numerically the FMM, a truncation has to be made, limiting the number of diffraction orders taken into account.…”

Section: -3mentioning

confidence: 99%

Casimir-Lifshitz force out of thermal equilibrium between dielectric gratings

et al. 2014

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We calculate the Casimir-Lifshitz pressure in a system consisting of two different one-dimensional dielectric lamellar gratings having two different temperatures and immersed in an environment having a third temperature. The calculation of the pressure is based on the knowledge of the scattering operators, deduced using the Fourier modal method. The behavior of the pressure is characterized in detail as a function of the three temperatures of the system as well as the geometrical parameters of the two gratings. We show that the interplay between nonequilibrium effects and geometrical periodicity offers a rich scenario for the manipulation of the force. In particular, we find regimes where the force can be strongly reduced for large ranges of temperatures. Moreover, a repulsive pressure can be obtained, whose features can be tuned by controlling the degrees of freedom of the system. Remarkably, the transition distance between attraction and repulsion can be decreased with respect to the case of two slabs, implying an experimental interest for the observation of repulsion.

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Section: -3mentioning

confidence: 99%

Casimir-Lifshitz force out of thermal equilibrium between dielectric gratings

et al. 2014

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“…Using a plane wave ansatz e iλz for the z-dependence, we obtain a generalized eigenvalue problem with eigenvalue λ 2 . Historically, the TM case has been considerably more challenging because it involves discontinuities in the fields [10,11]. Therefore, we only focus on this case but would like to note that the TE case follows from the TM case by interchanging E ↔ −H and ε ↔ μ.…”

Section: One-dimensional Layersmentioning

confidence: 99%

B-spline modal method: A polynomial approach compared to the Fourier modal method

Walz¹,

Zebrowski²,

Küchenmeister³

et al. 2013

Opt. Express

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Abstract:A detailed analysis of the B-spline Modal Method (BMM) for one-and two-dimensional diffraction gratings and a comparison to the Fourier Modal Method (FMM) is presented. Owing to its intrinsic capability to accurately resolve discontinuities, BMM avoids the notorious problems of FMM that are associated with the Gibbs phenomenon. As a result, BMM facilitates significantly more efficient eigenmode computations. With regard to BMM-based transmission and reflection computations, it is demonstrated that a novel Galerkin approach (in conjunction with a scattering-matrix algorithm) allows for an improved field matching between different layers. This approach is superior relative to the traditional point-wise field matching. Moreover, only this novel Galerkin approach allows for an competitive extension of BMM to the case of two-dimensional diffraction gratings. These improvements will be very useful for high-accuracy grating computations in general and for the analysis of associated electromagnetic field profiles in particular.

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“…However, this explanation was not sufficient to provide a solution, at least till the works of Lalanne at el. [18] and Granet and Guizal [19] that proposed a fast convergence formulation for lamellar gratings, discussed later. The theoretical explanation of this fast convergence was made by Li [20,21] who challenged the validity of the well-known convolution rule of presenting the product of functions in a truncated Fourier basis.…”

Section: The Factorization Rulesmentioning

confidence: 99%

Differential theory of diffraction in cylindrical coordinates

Popov¹,

Bonod

2007

Physica Status Solidi (b)

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The principles of the differential theory of light diffraction are presented in cylindrical coordinates. Special attention is played to the factorisation rules necessary to obtain faster convergence with respect to the number of basic functions used in the field representation. A detailed description is given for diffracting objects having rotational symmetry and finite cylindrical length. Some properties of light diffracted by a single circular aperture piereced in a finitely conducting screen are discussed, including the excitation of surface plasmon wave and the enhanced beaming.

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Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization

Cited by 332 publications

References 6 publications

Casimir-Lifshitz force out of thermal equilibrium between dielectric gratings

Casimir-Lifshitz force out of thermal equilibrium between dielectric gratings

B-spline modal method: A polynomial approach compared to the Fourier modal method

Differential theory of diffraction in cylindrical coordinates

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