Isospectral open cavities and gratings

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-05-15 DOI:10.1098/rspa.2023.0853
Sebastiano Cominelli, Benjamin Vial, Sébastien Guenneau, Richard V. Craster
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Abstract

Open cavities are often an essential component in the design of ultra-thin subwavelength metasurfaces and a typical requirement is that cavities have precise, often low frequency, resonances while simultaneously being physically compact. To aid this design challenge, we develop a methodology to allow isospectral twinning of reference cavities with either smaller or larger ones, enforcing their spectra to coincide so that open resonators are identical in terms of their complex eigenfrequencies. For open systems, the spectrum is not purely discrete and real, and we pay special attention to the accurate twinning of leaky modes associated with complex-valued eigenfrequencies with an imaginary part orders of magnitude lower than the real part. We further consider twinning of two-dimensional gratings, and model these with Floquet–Bloch conditions along one direction and perfectly matched layers in the other one; complex eigenfrequencies of special interest are located in the vicinity of the positive real line and further depend upon the Bloch wavenumber. The isospectral behaviour is illustrated, and quantified, throughout by numerical simulation using finite-element analysis.

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等谱开腔和光栅
开腔通常是超薄亚波长元表面设计中的重要组成部分,其典型要求是开腔具有精确(通常是低频)的共振,同时物理结构紧凑。为了应对这一设计挑战,我们开发了一种方法,允许参考空腔与较小或较大的空腔等谱孪生,强制它们的频谱重合,从而使开放式谐振器的复特征频率相同。对于开放系统,频谱并非纯粹离散和实数,我们特别关注与复值特征频率相关的泄漏模式的精确孪生,其虚部比实部低几个数量级。我们进一步考虑了二维光栅的孪生问题,并利用沿一个方向的 Floquet-Bloch 条件和另一个方向的完全匹配层对其进行建模;特别关注的复值特征频率位于正实线附近,并进一步取决于 Bloch 波长。利用有限元分析进行的数值模拟说明并量化了整个等谱行为。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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