arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2211.03224physics.opticsmath.AP
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全介质电磁超表面中的法诺共振

Fano resonances in all-dielectric electromagnetic metasurfaces

Habib Ammari, Bowen Li, Hongjie Li, Jun Zou

AI总结:

该工作为全介质超表面建立了严格的数学框架,分析亚波长共振及其渐近展开,证明实共振存在性,并利用群论与变分法揭示对称性破缺可引发法诺型反射和透射异常。

摘要:

我们关注由高折射率纳米粒子二维晶格构成的全介质超表面的共振电磁散射问题。在[Ammari et al., Trans. AMS, 376 (2023), 39-90]中,已证明单个高折射率纳米谐振器能与入射波耦合并表现出强磁偶极子响应。最近的物理实验揭示,当粒子按特定周期排列时,在宏观尺度上可能产生与单粒子情况不同的异常散射效应。在本工作中,我们将发展一个严格的数学框架来分析全介质超表面的共振行为。我们首先刻画这种周期设置下的亚波长散射共振及其关于纳米粒子折射率的渐近展开。然后我们证明,在周期麦克斯韦算子的本质谱之下总是存在实共振,并且它们是散射预解式的简单极点,具有指数衰减的共振模式。利用群论,我们讨论了超表面对称性对亚波长带函数及其相关本征函数的影响。对于法向入射的对称超表面,我们使用变分方法证明嵌入特征值(即嵌入连续辐射谱中的实亚波长共振)的存在性。此外,我们通过引入粒子的微小变形或略微偏离法向入射来打破构型对称性,并证明在这两种情况下都会出现法诺型反射和透射异常。

英文摘要:

We are interested in the resonant electromagnetic (EM) scattering by all-dielectric metasurfaces made of a two-dimensional lattice of nanoparticles with high refractive indices. In [Ammari et al., Trans. AMS, 376 (2023), 39-90], it has been shown that a single high-index nanoresonator can couple with the incident wave and exhibit a strong magnetic dipole response. Recent physics experiments reveal that when the particles are arranged in certain periodic configurations, they may have different anomalous scattering effects in the macroscopic scale, compared to the single-particle case. In this work, we shall develop a rigorous mathematical framework for analyzing the resonant behaviors of all-dielectric metasurfaces. We start with the characterization of subwavelength scattering resonances in such a periodic setting and their asymptotic expansions in terms of the refractive index of the nanoparticles. Then we show that real resonances always exist below the essential spectrum of the periodic Maxwell operator and that they are the simple poles of the scattering resolvent with the exponentially decaying resonant modes. By using group theory, we discuss the implications of the symmetry of the metasurface on the subwavelength band functions and their associated eigenfunctions. For the symmetric metasurfaces with the normal incidence, we use a variational method to show the existence of embedded eigenvalues (i.e., real subwavelength resonances embedded in the continuous radiation spectrum). Furthermore, we break the configuration symmetry either by introducing a small deformation of particles or by slightly deviating from the normal incidence and prove that Fano-type reflection and transmission anomalies can arise in both of these scenarios.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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