Electromagnetic field enhancement in a subwavelength rectangular open cavity

Gao, Yixian; Li, Peijun; Yuan, Xianfeng

doi:10.1007/s42985-021-00108-5

Cited by 2 publications

(1 citation statement)

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“…Bonnetier and Triki [7] developed a BIE method to study resonances in a perfectly conducting half plane with a subwavelength cavity and firstly obtained asymptotic formulae for the resonances. Subsequently, Babadjian et al [3] used this method to study resonances by two interacting subwavelength cavities, Lin and Zhang developed a simplified BIE method to study resonances in a slab with a single slit [26], periodic slits [27,28], or a periodic array of two subwavelength slits [25], Gao et al [14] studied resonances by a rectangular cavity of mixed conducting parts. Using the MA methods, Joly and Tordeux [19][20][21] and Clausel et al [11] studied resonances by thin slots, Holley and Schnitzer [17] studied resonances in a slab with a single slit, and Brandão et al [8] studied resonances in a slab of finite conductivity with a single slit or periodic slits.…”

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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