Simple parameterized coordinate transformation method for deep- and smooth-profile gratings

Xu, Xihong; Li, Lifeng

doi:10.1364/ol.39.006644

Cited by 10 publications

(5 citation statements)

References 7 publications

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“…The differential formalism can handle both shallow and deep structures; however, we need to adopt local coordinate distortion instead of the global coordinate translation as studied in a series of studies [182][183][184][185][186][187][188][189][190][191]. That is because the local transformation affects only a bounded region near the structured surface and enables us to apply a simple criterion to select the incoming and outgoing fields.…”

Section: Chaptermentioning

confidence: 99%

“…gA > 1), large matrix elements do not localise near the diagonal elements any longer. This phenomenon occurs even in the conventional grating calculation handled by the differential formalism [182][183][184][185][186][187][188][189][190][191][192][193] as mentioned at the beginning of this chapter. In that regime, we have to adopt local coordinate distortion instead of the global coordinate translation (7.1).…”

Section: Numerical Implementationmentioning

confidence: 99%

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Dynamical metasurfaces: electromagnetic properties and instabilities

Oue¹

2021

Preprint

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In this thesis, I analyse the electromagnetic properties of dynamical metasurfaces and find two critical phenomena. The first is the Casimir-induced instability of a deformable metallic film.In general, two charge-neutral interfaces attract with or repel each other due to the contribution from the zero-point fluctuation of the electromagnetic field between them, namely, the Casimir effect. The effects of perturbative interface corrugation on the Casimir energy in the film system is studied by the proximity force approximation with dispersion correction. If the corrugation period exceeds a critical value, the Casimir effect dominates the surface tension and brings about structural instability. The second is Čerebkov radiation in the vacuum from a timevarying, corrugated surface. Travelling faster than light brings about electromagnetic shockThe copyright of this thesis rests with the author. Unless otherwise indicated, its contents are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International Licence (CC BY NC-SA).

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Section: Chaptermentioning

confidence: 99%

Section: Numerical Implementationmentioning

confidence: 99%

Dynamical metasurfaces: electromagnetic properties and instabilities

Oue¹

2021

Preprint

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“…This wall manifests as poor matrix conditioning when writing boundary conditions at the surface of the grating, rendering inversions impossible. Various methods have been developed to overcome these challenges, such as analytical regularization [4], or increasing the calculation precision, using a parametric coordinate system [5], or working with multi-precision [6] [7] [8].…”

Section: Introductionmentioning

confidence: 99%

Diffraction by gratings: from the C-method to the stochastic C-method

Chandezon,

Granet

2024

J. Opt. Soc. Am. A

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The Chandezon, or C-method, is an efficient and versatile numerical method for modeling diffraction problems involving smooth surface relief gratings. For some grating profiles, the C-method is limited when the height-to-period ratio exceeds a factor of 3. This is due to the formation of ill-conditioned matrices for inversion. Here, the Stochastic C-method (SCM) is introduced as a solution which leverages stochastic differential equations to overcome these numerical difficulties. The SCM is developed by altering the physical model of the grating profile function to include an additive Brownian noise component. The inclusion of noise, dramatically expands the applicability of the C-method and enriches the physical model. Numerical experiments show that the SCM achieves a precision on the order of 10 −5 for diffracted/transmitted amplitudes on sinusoidal profiles with height-to-period ratios as high as 72. These results are in agreement with those obtained using multi-precision and the Rigorous Coupled Wave Analysis (RCWA).

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“…14,15 Recently, by using a simple parameterization scheme we enabled the C method to converge for gratings of smooth profiles with groove depth-to-period ratios up to or greater than 10 and made its aforementioned convergence range practically unlimited. 16 Our parameterization function in that work consisted of two straight line segments joined together at x = d/2:…”

Section: Introductionmentioning

confidence: 99%

Enlarging applicability domain of the C method with piecewise linear parameterization: gratings of deep and smooth profiles

2015

SPIE Proceedings

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We present two piecewise linear parameterization schemes for the parameterized coordinate transformation method (the C method) to enable it to model gratings of deep and smooth grooves. This work generalizes and elaborates our previous work [Opt. Lett. 39(23), 6644 (2014)]. The previous bilinear transformation is replaced with a general multi-linear transformation. This gives us flexibility to handle more general grating profiles while retaining the simplicity of the linear transformation. We give some general, simple, and empirical rules on composing the piecewise linear transformation function. Both enlarged convergence range and increased groove depth-to-period ratio, which can be at least 10, are achieved with the parameterized C method for a wide class of smooth grating profiles.

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Simple parameterized coordinate transformation method for deep- and smooth-profile gratings

Cited by 10 publications

References 7 publications

Dynamical metasurfaces: electromagnetic properties and instabilities

Dynamical metasurfaces: electromagnetic properties and instabilities

Diffraction by gratings: from the C-method to the stochastic C-method

Enlarging applicability domain of the C method with piecewise linear parameterization: gratings of deep and smooth profiles

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