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<p>We study the scattering of time-harmonic scalar waves by a periodic array of penetrable, high-contrast obstacles with small period, confined to a bounded Lipschitz domain. The strong contrast between the obstacles and the background induces subwavelength resonances. We derive a frequency-dependent effective model in the vanishing-period limit and prove quantitative convergence of the scattered waves in the original heterogeneous setup to those in the effective model. We also identify the limiting set of scattering resonances and establish the convergence rates. Finally, we establish the convergence rates for the far-field pattern of the scattered waves in the heterogeneous setting to that of the effective model.</p>

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Homogenization of the Scattered Wave and Scattering Resonances for Periodic High-Contrast Subwavelength Resonators

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Yuxin Du,
  • Xin Fu,
  • Wenjia Jing

摘要

We study the scattering of time-harmonic scalar waves by a periodic array of penetrable, high-contrast obstacles with small period, confined to a bounded Lipschitz domain. The strong contrast between the obstacles and the background induces subwavelength resonances. We derive a frequency-dependent effective model in the vanishing-period limit and prove quantitative convergence of the scattered waves in the original heterogeneous setup to those in the effective model. We also identify the limiting set of scattering resonances and establish the convergence rates. Finally, we establish the convergence rates for the far-field pattern of the scattered waves in the heterogeneous setting to that of the effective model.