Scattering resonances for a three-dimensional subwavelength hole

Fatima, Maryam; Lin, Junshan

doi:10.1007/s42985-021-00111-w

Cited by 2 publications

(2 citation statements)

References 27 publications

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“…Nevertheless, much fewer theories have been developed so far to rigorously study resonances in 3D structures. Resonances of acoustic waves in a three-dimensional slab of tiny circular or square holes have been studied in [13,22].…”

Section: Introductionmentioning

confidence: 99%

A Fourier Matching Method for Analyzing Resonances in a Sound-Hard Slab with Subwavelength Holes

Wangtao Lu,

Wei Wang,

Jiaxin Zhou

2024

CSIAM-AM

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This paper presents a Fourier matching method to rigorously study resonances in a sound-hard slab with a finite number of narrow cylindrical holes. The cross sections of the holes, of diameters O(h) for h ≪ 1, can be arbitrarily shaped. Outside the slab, a sound field can be represented in terms of its normal derivatives on the apertures of the holes. Inside each hole, the field can be represented in terms of a countable Fourier basis due to the zero Neumann boundary condition on the side surface. The countably infinite Fourier coefficients for all the holes constitute the unknowns. Matching the two field representatives leads to a countable-dimensional linear system governing the unknowns. Due to the invertibility of a principal submatrix of the infinite-dimensional coefficient matrix, we reduce the linear system to a finitedimensional one. Resonances are those when the finite-dimensional linear system becomes singular. We derive asymptotic formulae for the resonances in the subwavelength structure for h ≪ 1. They reveal that a sound field with its real frequency close to a resonance frequency can be enhanced by a magnitude O(h −2 ). Numerical experiments are carried out to validate the proposed resonance formulae.

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Section: Introductionmentioning

confidence: 99%

A Fourier Matching Method for Analyzing Resonances in a Sound-Hard Slab with Subwavelength Holes

Wangtao Lu,

Wei Wang,

Jiaxin Zhou

2024

CSIAM-AM

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“…The matched asymptotic expansion techniques have also been applied to construct the solution of the slit scattering problem in [22,23,24]. The generalization of the above techniques to the studies of the acoustic wave resonances in three-dimensional subwavelength holes can be found in [16,28,34]. We would also like to refer readers to [1,2,3,4] and references therein for the mathematical studies of other type of subwavelength resonances, such as Helmholtz resonators and nanoparticles, etc.…”

Section: Introductionmentioning

confidence: 99%

Mathematical theory for electromagnetic scattering resonances and field enhancement in a subwavelength annular gap

Lin¹,

Lu²,

Zhang³

2022

Preprint

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This work presents a mathematical theory for electromagnetic scattering resonances in a subwavelength annular hole embedded in a metallic slab, with the annulus width h1. The model is representative among many 3D subwavelength hole structures, which are able to induce resonant scattering of electromagnetic wave and the so-called extraordinary optical transmission. We develop a multiscale framework for the underlying scattering problem based upon a combination of the integral equation in the exterior domain and the waveguide mode expansion inside the tiny hole. The matching of the electromagnetic field over the hole aperture leads to a sequence of decoupled infinite systems, which are used to set up the resonance conditions for the scattering problem. By performing rigorous analysis for the infinite systems and the resonance conditions, we characterize all the resonances in a bounded domain over the complex plane. It is shown that the resonances are associated with the TE and TEM waveguide modes in the annular hole, and they are close to the real axis with the imaginary parts of order O(h). We also investigate the resonant scattering when an incident wave is present. It is proved that the electromagnetic field is amplified with order O(1/h) at the resonant frequencies that are associated with the TE modes in the annular hole. On the other hand, one particular resonance associated with the TEM mode can not be excited by a plane wave but can be excited with a near-field electric dipole source, leading to field enhancement of order O(1/h).

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Scattering resonances for a three-dimensional subwavelength hole

Cited by 2 publications

References 27 publications

A Fourier Matching Method for Analyzing Resonances in a Sound-Hard Slab with Subwavelength Holes

A Fourier Matching Method for Analyzing Resonances in a Sound-Hard Slab with Subwavelength Holes

Mathematical theory for electromagnetic scattering resonances and field enhancement in a subwavelength annular gap

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