Voicu R C, Sandu T
Research Centre for Integrated Systems, Nanotechnologies, and Carbon Based Materials, National Institute for Research and Development in Microtechnologies-IMT, 126A, Erou Iancu Nicolae Street, Bucharest, Romania.
Proc Math Phys Eng Sci. 2017 Mar;473(2199):20160796. doi: 10.1098/rspa.2016.0796. Epub 2017 Mar 15.
The boundary integral equation (BIE) method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of the Laplace equation can be used to calculate the full set of eigenvalues and eigenfunctions of the electrostatic operator for shapes and shells described by separable coordinate systems. These results not only unify and generalize many existing studies, but also offer us the opportunity to expand the study of phenomena such as cloaking by anomalous localized resonance. Hence, we calculate the eigenvalues and eigenfunctions of elliptic and circular cylinders. We illustrate the benefits of using the BIE method to interpret recent experiments involving localized surface phonon polariton resonances and the size scaling of plasmon resonances in graphene nanodiscs. Finally, symmetry-based operator analysis can be extended from the electrostatic to the full-wave regime. Thus, bound states of light in the continuum can be studied for shapes beyond spherical configurations.
边界积分方程（BIE）方法确定了局域表面声子和等离激元极化激元共振与其相关静电算符的本征值之间的明确关系。我们表明，拉普拉斯方程的群论分析可用于计算由可分离坐标系描述的形状和壳的静电算符的全套本征值和本征函数。这些结果不仅统一和推广了许多现有研究，还为我们提供了扩展对诸如异常局域共振隐身等现象研究的机会。因此，我们计算了椭圆和圆柱的本征值和本征函数。我们说明了使用BIE方法来解释最近涉及局域表面声子极化激元共振以及石墨烯纳米盘中等离激元共振尺寸缩放的实验的好处。最后，基于对称性的算符分析可以从静电领域扩展到全波领域。因此，可以研究超出球形构型的形状的连续统中的光束缚态。
