Detailed analysis of the surface-plasmon waves guided by a thin metal film based in the transverse resonance method

In this paper, a detailed analysis of the surface plasmon waves guided by a thin metal film is presented. The method used is the transverse resonance method that groups, in one equation, the solutions of all modes that propagate in the structure. The structure analyzed is constituted by a thin metal film surrounded by media with dielectric constants ε₁ and ε₂. For symmetric structures (ε₁ = ε₂), there are two solutions, both related to the bounded modes, symmetric (s_b) and asymmetric (a_b). For asymmetric structures (ε₁ ≠ ε₂), there are four solutions, two related to the bounded modes [s_b, a_b] and other two related to the leaky modes [s₁/, a₁]. The symmetric bounded mode (s_b) has a cut off point and bellow it the mode changes and behaves like an unusual mode called growing mode.