Scattering resonances for a three-dimensional subwavelength hole

Maryam Fatima () and Junshan Lin ()
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Maryam Fatima: Auburn University
Junshan Lin: Auburn University

Partial Differential Equations and Applications, 2021, vol. 2, issue 4, 1-25

Abstract: Abstract This work aims to investigate scattering resonances and the field amplification at resonant frequencies for a subwavelength hole of width $$\varepsilon $$ ε embedded in a sound hard slab. We apply the integral equation approach and asymptotic analysis to derive the asymptotic expansions of scattering resonances and quantitatively analyze the corresponding field amplifications. It is shown that the complex-valued scattering resonances attain imaginary parts of order $$O(\varepsilon ^2)$$ O ( ε 2 ) . The field enhancement inside the hole and in the far field is of order $$O({1/\varepsilon ^2})$$ O ( 1 / ε 2 ) at the resonant frequencies, which is much stronger the enhancement order in the two-dimensional subwavelengt hole of the same width.

Keywords: Scattering resonances; Subwavelength holes; Acoustic wave; Helmholtz equation; 35C20; 35P30; 35Q60 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00111-w

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