Analysis of the Rigorous Coupled Wave Approach for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e669" altimg="si2.svg"><mml:mi>s</mml:mi></mml:math>-polarized light in gratings

Civiletti, Benjamin J.; Lakhtakia, Akhlesh; Monk, Peter

doi:10.1016/j.cam.2019.112478

Cited by 7 publications

(1 citation statement)

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“…The first part of this assumption has been proved in Theorem 3.3 of [10], in case that ( ) is piecewise constant and inequalities (2.2) hold true. The assumption that is independent of can be proved, for example, if the grating is non-trapping [6]. In addition, by following the arguments in Theorem 2.1 of [13], it is possible to show that is independent of when is small enough.…”

Section: S511mentioning

confidence: 99%

An asymptotic model based on matching far and near field expansions for thin gratings problems

et al. 2021

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In this paper, we devise an asymptotic model for calculating electromagnetic diffraction and absorption in planar multilayered structures with a shallow surface-relief grating. Far from the grating, we assume that the solution can be written as a power series in terms of the grating thickness δ , the coefficients of this expansion being smooth up to the grating. However, the expansion approximates the solution only sufficiently far from the grating (far field approximation). Near the grating, we assume that there exists another expansion in powers of δ (near field approximation). Moreover, there is an overlapping zone where both expansion are valid. The proposed model is based on matching the two expansions on this overlapping domain. Then, by truncating terms of order δ 2 or higher, we obtain explicitly the equations satisfied by the lowest order terms in the power series. Under appropriate assumptions, we prove second order convergence of the error with respect to δ . Finally, an alternative form, more convenient for implementation, is derived and discretized with finite elements to perform some numerical tests.

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Section: S511mentioning

confidence: 99%