Sebastiano Cominelli, Benjamin Vial, Sébastien Guenneau, Richard V. Craster
{"title":"Isospectral open cavities and gratings","authors":"Sebastiano Cominelli, Benjamin Vial, Sébastien Guenneau, Richard V. Craster","doi":"10.1098/rspa.2023.0853","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","FirstCategoryId":"103","ListUrlMain":"https://doi.org/10.1098/rspa.2023.0853","RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
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.
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.