Minas Kouroublakis;Nikolaos L. Tsitsas;George Fikioris
{"title":"用双激发源辅助源法计算介质波导的特征值","authors":"Minas Kouroublakis;Nikolaos L. Tsitsas;George Fikioris","doi":"10.1109/JMMCT.2022.3176203","DOIUrl":null,"url":null,"abstract":"The Method of Auxiliary Sources with an Excitation Source (MAS-ES) has been successfully employed to compute the eigenvalues of arbitrarily-shaped, simply and multiply-connected hollow waveguides with perfectly electric conducting (PEC) walls. The main advantages of this method are its simplicity, and that it is free of spurious eigenvalues, in contrast to the standard MAS approach. In this paper, we demonstrate that the MAS-ES is also effective in computing the propagation constants (eigenvalues) \n<inline-formula><tex-math>$\\beta$</tex-math></inline-formula>\n of a cylindrical dielectric waveguide with core of arbitrary cross section. It is emphasized that two excitation sources (an electric and a magnetic current filament lying within the core) are required to excite hybrid modes of the dielectric waveguide; a hollow PEC waveguide requires only one source. The modified method, thus obtained, is named MAS with Two Excitation Sources (MAS-TES). The fact that the propagating modes are localized in the vicinity of the core allows us to determine the eigenvalues by measuring the response of the core to the excitation sources. This is performed by employing a response function \n<inline-formula><tex-math>$F(\\beta)$</tex-math></inline-formula>\n which is maximized when a standing wave is formed in the core. Plotting \n<inline-formula><tex-math>$F(\\beta)$</tex-math></inline-formula>\n for a dense set of \n<inline-formula><tex-math>$\\beta$</tex-math></inline-formula>\n results in a response curve the peaks of which correspond to the waveguide’s eigenvalues. The method is tested for several dielectric waveguides’ geometries, including two multimode cases, and it is shown to be free from discrete and continuous spurious solutions. All the MAS-TES results are compared with those obtained by an FEM-based commercial software and an excellent agreement is exhibited.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2022-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Computing Eigenvalues of Dielectric Waveguides by a Method of Auxiliary Sources With Two Excitation Sources\",\"authors\":\"Minas Kouroublakis;Nikolaos L. 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The modified method, thus obtained, is named MAS with Two Excitation Sources (MAS-TES). The fact that the propagating modes are localized in the vicinity of the core allows us to determine the eigenvalues by measuring the response of the core to the excitation sources. This is performed by employing a response function \\n<inline-formula><tex-math>$F(\\\\beta)$</tex-math></inline-formula>\\n which is maximized when a standing wave is formed in the core. Plotting \\n<inline-formula><tex-math>$F(\\\\beta)$</tex-math></inline-formula>\\n for a dense set of \\n<inline-formula><tex-math>$\\\\beta$</tex-math></inline-formula>\\n results in a response curve the peaks of which correspond to the waveguide’s eigenvalues. The method is tested for several dielectric waveguides’ geometries, including two multimode cases, and it is shown to be free from discrete and continuous spurious solutions. 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引用次数: 1
摘要
本文成功地利用带激励源的辅助源方法(MAS-ES)计算了具有完全导电(PEC)壁的任意形状、简单连接和多重连接的空心波导的特征值。与标准MAS方法相比,该方法的主要优点是简单,并且没有虚假特征值。在本文中,我们证明了MAS-ES在计算具有任意截面的圆柱形介质波导的传播常数(特征值)$\beta$时也是有效的。强调需要两个激发源(位于核心内的电电流和磁电流灯丝)来激发介电波导的混合模式;空心PEC波导只需要一个源。由此得到的改进方法被命名为MAS with Two Excitation Sources (MAS- tes)。传播模式在磁芯附近的局域化使得我们可以通过测量磁芯对激励源的响应来确定本征值。这是通过使用响应函数F(\beta)来实现的,当驻波在核心形成时,响应函数F(\beta)达到最大值。绘制$F(\beta)$作为$\beta$的密集集合得到响应曲线,其峰值对应于波导的特征值。该方法对几种介质波导的几何形状进行了测试,包括两种多模情况,结果表明该方法不存在离散和连续的杂散解。所有的MAS-TES结果都与基于fem的商业软件得到的结果进行了比较,显示出很好的一致性。
Computing Eigenvalues of Dielectric Waveguides by a Method of Auxiliary Sources With Two Excitation Sources
The Method of Auxiliary Sources with an Excitation Source (MAS-ES) has been successfully employed to compute the eigenvalues of arbitrarily-shaped, simply and multiply-connected hollow waveguides with perfectly electric conducting (PEC) walls. The main advantages of this method are its simplicity, and that it is free of spurious eigenvalues, in contrast to the standard MAS approach. In this paper, we demonstrate that the MAS-ES is also effective in computing the propagation constants (eigenvalues)
$\beta$
of a cylindrical dielectric waveguide with core of arbitrary cross section. It is emphasized that two excitation sources (an electric and a magnetic current filament lying within the core) are required to excite hybrid modes of the dielectric waveguide; a hollow PEC waveguide requires only one source. The modified method, thus obtained, is named MAS with Two Excitation Sources (MAS-TES). The fact that the propagating modes are localized in the vicinity of the core allows us to determine the eigenvalues by measuring the response of the core to the excitation sources. This is performed by employing a response function
$F(\beta)$
which is maximized when a standing wave is formed in the core. Plotting
$F(\beta)$
for a dense set of
$\beta$
results in a response curve the peaks of which correspond to the waveguide’s eigenvalues. The method is tested for several dielectric waveguides’ geometries, including two multimode cases, and it is shown to be free from discrete and continuous spurious solutions. All the MAS-TES results are compared with those obtained by an FEM-based commercial software and an excellent agreement is exhibited.