Blackhole waves at corners of negative material

Publication type:
Online talk
MIT 2020 — Calculus of Variations, Homogenization and Disorder
In this talk, we consider electromagnetic waves in presence of materials which have, in a given frequency range, a dielectric permittivity with a very small imaginary part, that will be neglected, and a negative real part. This occurs for instance for metals (like gold or silver) at optical frequencies and for homogenized models of some metamaterials. For such materials, very unsual singular phenomena take place at corners. In particular, for some configurations, a part of the energy may be trapped by the corners: this is the so-called blackhole effect [1]. In this presentation, we first give a mathematical analysis of this blackhole phenomenon, based on a detailed description of the corner's singularities, in the 2D case. Then we show that this phenomenon leads to numerical instabilities of finite element simulations. The solution that we have found and validated is to introduce a complex scaling at the corners. Finally, we compute the plasmonic eigenvalues of a 2D subwavelength particle with a corner. While a smooth particle has a discrete sequence of eigenvalues, blackhole waves at the corner lead to the presence of an essential spectrum filling an interval. Numerical results show that the complex scaling deforms this essential spectrum, so as to unveil both embedded eigenvalues and complex plasmonic resonances. The later are analogous to well-known complex scattering resonances, with the local behavior at the corner playing the role of the behavior at infinity.
    title={Blackhole waves at corners of negative material },
    organization={MIT 2020 — Calculus of Variations, Homogenization and 
           Disorder },
    year={2020 },