On plasmon modes in multi‐layer structures
Xiaoping Fang, Youjun Deng
Abstract
In this paper, we consider the plasmon resonance in multi‐layer structures. We show that the plasmon mode is equivalent to the eigenvalue problem of a matrix, whose order is the same to the number of layers. For any number of layers, the exact characteristic polynomial is derived by a conjecture and is verified by using induction. It is shown that all the roots to the characteristic polynomial are real and exist in the span , when the background field is uniform in . Numerical examples are presented for finding all the plasmon modes, and it is surprisingly to find out that such multi‐layer structures may induce so called surface‐plasmon‐resonance‐like band.
Topics & Concepts
Eigenvalues and eigenvectorsMathematicsPlasmonSurface plasmon resonanceResonance (particle physics)Surface plasmonPolynomialConjectureField (mathematics)Layer (electronics)Mathematical analysisSpan (engineering)Pure mathematicsOpticsPhysicsQuantum mechanicsMaterials scienceNanoparticleComposite materialCivil engineeringEngineeringPhotonic Crystals and ApplicationsElectromagnetic Scattering and AnalysisPlasmonic and Surface Plasmon Research