A subwavelength metallic particle supports localized surface plasmons for some negative permittivity values, which are eigenvalues of the self-adjoint quasi-static plasmonic eigenvalue problem (PEP). This work investigates the existence of complex plasmonic resonances for a 2D particle whose boundary is smooth except for one straight corner. These resonances are defined using the multivalued nature of some solutions of the corner dispersion relations and they are shown to be eigenvalues of a PEP that is complex-scaled at the corner, the finite element discretization of which yields a linear generalized eigenvalue problem. Numerical results show that the complex scaling deforms the essential spectrum (associated with the corner) so as to unveil both embedded plasmonic eigenvalues and complex plasmonic resonances. The later are analogous to complex scattering resonances with the local behavior at the corner playing the role of the behavior at infinity. These results corroborate the study of Li and Shipman (J. Integral Equ. Appl. 31(4), 2019), which proved the existence of embedded plasmonic eigenvalues and discussed the construction of particles that exhibit complex plasmonic resonances.

亚波长金属粒子为某些负介电常数值提供了局部表面等离振子，这是自伴准静态等离激元本征值问题（PEP）的本征值。这项工作研究了一个二维粒子的复等离子体激元共振的存在，该粒子的边界是一个平直的角，除了一个直角。这些共振是使用角扩散关系的某些解的多值性质来定义的，它们显示为在角处复杂缩放的PEP的特征值，其有限元离散化产生线性广义特征值问题。数值结果表明，复杂的标度使基本谱（与角相关）变形，从而揭示了嵌入的等离子体特征值和复杂的等离子体共振。后者类似于复杂的散射共振，在拐角处的局部行为起着无穷大行为的作用。这些结果证实了Li和Shipman的研究（J.Integral Equ.Appl.31（4），2019），该研究证明了嵌入的等离激元特征值的存在，并讨论了表现出复杂等离激元共振的粒子的构造。