On plasmon modes in multi-layer structures

TL;DR

This paper analyzes plasmon resonance in multi-layer structures, deriving the eigenvalue problem and characteristic polynomial, revealing real roots within a specific interval, and discovering surface-plasmon-resonance-like bands through numerical examples.

Contribution

It introduces a novel eigenvalue framework for plasmon modes in multi-layer structures and derives an exact characteristic polynomial for any number of layers.

Findings

All roots of the characteristic polynomial are real within [-1, 2]

Multi-layer structures can induce surface-plasmon-resonance-like bands

Numerical methods effectively find all plasmon modes

Abstract

In this paper, we consider the plasmon resonance in multi-layer structures. The conductivity problem associated with uniformly distributed background field is considered. 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 [-1, 2]. 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.