On plasmon modes in multi‐layer structures

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.