Sparsifying preconditioner for the time-harmonic Maxwell's equations

Liu, Fei; Ying, Lexing

doi:10.1016/j.jcp.2018.10.004

Cited by 5 publications

(5 citation statements)

References 23 publications

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“…where 𝐹 (r) = 𝑘 2 [𝜖 𝑟 (r) − 1]/(4𝜋) and 𝐸 (r) is the total field given by the sum of the scattered field and the incident field 𝐸 𝑖 (r), which we assume is a plane wave of the form 𝑒 𝑖k 𝑖 •r . A similar expression can be obtained for the full electromagnetic vector field [37,44], but here we only consider the scalar form. In the far field approximation, the Green's function reduces to…”

Section: Approachmentioning

confidence: 99%

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Inverse Design of Invisibility Cloaks using the Optical Theorem

Slovick¹,

Hellhake²

2021

Preprint

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We develop and apply an optimization method to design invisibility cloaks. Our method is based on minimizing the forward scattering amplitude of the cloaked object, which by the optical theorem, is equivalent to the total cross section. The use of the optical theorem circumvents the need to evaluate and integrate the scattering amplitude over angle at each iteration, and thus provides a simpler, more computationally efficient objective function for optimizing structures. We implement the approach using gradient descent optimization and present several gradient-permittivity cloaks that reduce scatter by metallic targets of different size and shape.

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Section: Approachmentioning

confidence: 99%

“…where 𝐹 is a diagonal matrix and ℎ 3 has been absorbed into the definition of 𝐺. This matrix equation can be solved to obtain the total field as [37,44,45]…”

Section: Approachmentioning

confidence: 99%

Inverse Design of Invisibility Cloaks using the Optical Theorem

Slovick¹,

Hellhake²

2021

Preprint

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“…, µ, and σ are scalars. With this notation, the time-harmonic Maxwell's equation for the electric field in an inhomogeneous medium is [29][30][31]…”

Section: Arxiv:190907798v1 [Physicsoptics] 14 Sep 2019mentioning

confidence: 99%

“…Following the notations in Refs. [29][30][31], let (x) be the electric permittivity, µ = µ 0 be the magnetic permeability, and σ(x) be the electric conductivity, where (x) = 0 outside a compact region Ω. We also assume isotropic media, i.e.…”

Section: Approachmentioning

confidence: 99%

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Poles of the scattering matrix: an inverse method for designing photonic resonators

Slovick¹,

Matlin²

2020

Opt. Express

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We develop and implement a new mathematical and computational framework for designing photonic elements with one or more high-Q scattering resonances. The approach relies on solving for the poles of the scattering matrix, which mathematically amounts to minimizing the determinant of the Fredholm integral operator of the electric field with respect to the permittivity profile of the scattering element. We apply the method to design subwavelength gradient-permittivity structures with multiple scattering resonances and quality factors exceeding 500. We also find the spectral scattering cross sections are consistent with Fano lineshapes. The compact form and computational efficiency of our formalism suggest it can be a useful tool for designing Fano-resonant structures with multiple high-Q resonances for applications such as frequency mixing and conversion.

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