Shifted equivalent sources and FFT acceleration for periodic scattering problems, including Wood anomalies

Bruno, Oscar P.; Maas, Martín

doi:10.1016/j.jcp.2018.10.044

Cited by 5 publications

(11 citation statements)

References 28 publications

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“…60λ size range. With recent developments in fast electromagnetic solvers [50,51], one can anticipate applying this approach to devices orders of magnitude larger, with small and controllable errors, in the near future. The full-device optimizations enable us to overcome the efficiency losses and single-functionality limitations associated with assuming small, periodic unit cells, which are especially prominent at high NA.…”

Section: Introductionmentioning

confidence: 99%

High-NA achromatic metalenses by inverse design

Chung¹,

Miller²

2020

Opt. Express

216

151

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We use inverse design to discover metalens structures that exhibit broadband, achromatic focusing across low, moderate, and high numerical apertures. We show that standard unit-cell approaches cannot achieve high-efficiency high-NA focusing, even at a single frequency, due to the incompleteness of the unit-cell basis, and we provide computational upper bounds on their maximum efficiencies. At low NA, our devices exhibit the highest theoretical efficiencies to date. At high NA-of 0.9 with translation-invariant films and of 0.99 with "freeform" structures-our designs are the first to exhibit achromatic high-NA focusing. arXiv:1905.09213v1 [physics.optics]

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Section: Introductionmentioning

confidence: 99%

High-NA achromatic metalenses by inverse design

Chung¹,

Miller²

2020

Opt. Express

216

151

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“…The results presented in this section were produced on a MacBookPro with a 2.7 GHz Intel processor and 8Gb of RAM based on a MATLAB implementation of the DDM algorithm. We did not strive to optimize the code in order to harness the best sequential computational performance; this is certainly possible, and it has been done in [16,9] via fast methods based on equivalent sources. Instead, we wanted to illustrate that, within a DDM approach, the use of windowed Green function method combined with shifted Green functions leads to a computational method for scattering by periodic layered media that is accurate and robust at all frequencies, including the challenging Wood frequencies.…”

Section: Numerical Resultsmentioning

confidence: 99%

Domain Decomposition for Quasi-Periodic Scattering by Layered Media via Robust Boundary-Integral Equations at All Frequencies

Pérez‐Arancibia

Shipman

Turc

et al. 2019

CICP

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We develop a non-overlapping domain decomposition method (DDM) for scalar wave scattering by periodic layered media. Our approach relies on robust boundary-integral equation formulations of Robin-to-Robin (RtR) maps throughout the frequency spectrum, including cutoff (or Wood) frequencies. We overcome the obstacle of non-convergent quasi-periodic Green functions at these frequencies by incorporating newly introduced shifted Green functions. Using the latter in the definition of quasi-periodic boundary-integral operators leads to rigorously stable computations of RtR operators. We develop Nyström discretizations of the RtR maps that rely on trigonometric interpolation, singularity resolution, and fast convergent windowed quasi-periodic Green functions. We solve the tridiagonal DDM system via recursive Schur complements and establish rigorously that this procedure is always completed successfully. We present a variety of numerical results concerning Wood frequencies in two and three dimensions as well as large numbers of layers.In the technologically relevant case of piecewise constant periodic layered media, simulation methods based on boundary-integral equations (BIE) and quasi-periodic Green functions are attractive candidates. Radiation conditions are enforced automatically, and discretizations of material interfaces are much smaller than volumetric discretizations and do not suffer from the pollution effect. Quasi-periodic Green functions are infinite sums of free-space Green functions with periodically distributed monopole singularities. These double sums converge, although very slowly, for all but a discrete set of "cutoff" frequencies, for a given quasi-periodicity parameters (Bloch wavevector). These are cutoff frequencies at which a Rayleigh diffraction mode transitions between propagating and evanescent and the number of propagating directions jumps. Around these frequencies, the energy is rapidly redistributed along emerging new directions and is associated with anomalous scattering behavior. These frequencies are often referred to as Wood frequencies (or Wood configurations of wavevector and frequency) because their problematic association in the literature to Wood's anomaly; see the works [30,41,45,48],[39, Ch. 1] and references therein for discussions on this phenomenon. Popular methods for accelerating the slow convergence at non-Wood frequencies include Ewald summation [25] and lattice sums [37]. At very high frequencies, asymptotic methods help to accelerate computation; see for example [34].While the underlying scattering problems are, with regard to the PDE, generically stable at Wood configurations of wavevector and frequency, the latter pose a challenge to BIE for quasiperiodic problems. In three dimensions, they become increasingly close together at high frequency, and this puts the solution of quasi-periodic problems based on the quasi-periodic Green function out of reach. For periodic layered media with large numbers of layers, such as thin films used in photovoltaic cells, the probability ...

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“…The PDE problem under consideration is fully determined by equation (8) together with the boundary conditions…”

Section: Scattering Problemsmentioning

confidence: 99%

“…We will obtain α-quasi-periodic solutions of equation (8) by relying on integral equations and αquasi-periodic Green functions. The classical α-quasi-periodic Green function is introduced in the following section, which additionally describes the difficulties that arise at Rayleigh-Wood anomalies.…”

Section: Scattering Problemsmentioning

confidence: 99%

“…Wave-scattering by periodic media, including RW anomalous configurations, at which the quasiperiodic Green function ceases to exist, has continued to attract significant attention in the fields of optics [17,22,33,34,35,36,39,45,50] and computational electromagnetism [3,8,4,9,10,31,14,26,42,39,18]. Classical boundary integral equations methods [43,49,52] have relied on the quasi-periodic Green function (denoted throughout this work as G q κ ), which is defined in terms of a slowly converging infinite series (equation (27)).…”

Section: Introductionmentioning

confidence: 99%

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On the evaluation of quasi-periodic Green functions and wave-scattering at and around Rayleigh-Wood anomalies

Bruno

Fernandez-Lado

2020

Journal of Computational Physics

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Shifted equivalent sources and FFT acceleration for periodic scattering problems, including Wood anomalies

Abstract: Shifted equivalent sources and FFT acceleration for periodic scattering problems, including Wood anomalies,

Cited by 5 publications

References 28 publications

High-NA achromatic metalenses by inverse design

High-NA achromatic metalenses by inverse design

Domain Decomposition for Quasi-Periodic Scattering by Layered Media via Robust Boundary-Integral Equations at All Frequencies

On the evaluation of quasi-periodic Green functions and wave-scattering at and around Rayleigh-Wood anomalies

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