Complex-scaling method for the complex plasmonic resonances of planar subwavelength particles with corners

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 (2019) [35], which proved the existence of embedded plasmonic eigenvalues and discussed the construction of particles that exhibit complex plasmonic resonances. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The paper investigates the complex plasmonic resonances for a 2D particle with a smooth boundary except for one straight corner, showing that these resonances are defined by the multivalued nature of some solutions of the corner dispersion relations. Through numerical results, it is demonstrated that complex scaling deforms the essential spectrum to reveal embedded plasmonic eigenvalues and complex plasmonic resonances. These results validate the research by Li and Shipman (2019) on particles exhibiting complex plasmonic resonances.