1. Introduction

During the last decade, the scientific community has shown an increasing interest in the models of plasmon fields due to their potential applications, which occur practically in all branches of science and technology. In the present study, we emphasize the analysis of correlation trajectories on a metal surface with random structure. The resulting model offers applications to development of nano-antennas having the possibility of a tunable bandwidth [1]. This type of structure has applications in the synthesis of new light sources and the control of magnetic effects [2]. The tunable effects are controlled with the curvature parameter having applications in surface-enhanced Raman spectroscopy (SERS), also as the local excitation of quantum dots. Implementing the evanescent behavior of the plasmon field, the analysis is extended to the propagation of plasmon fields through a tandem array of metal films similar to photonic crystal structures [3, 4].

As a starting point, we describe the study of the electric field in the neighborhood of a nanoparticle using the electrostatic approximation [2]. The electric field corresponds to the plasmon particle. This model allowsthe description of the interaction between two plasmon particles. The interaction is extended to describe the plasmon fields propagating on a surface generating a wave behaviorsatisfying the Helmholtz equation where the wave number must have complex valuesin orderto recoverthe traditional surface plasmon models. Controlling the random distribution of nanoparticles, we

analyze the correlation effectsleading usto induce localization effects. Thislaststatement is obtained by masking thin metalsurface with two independent random array hole distributions. Controlling the scale factors, we modify the curvature of the correlation trajectory. The model isrelated with a speckle pattern emerging from a rough surface [5]. This configuration issimilarto the configuration proposed by Reatherfor the coupling of plasmon fields. Experimentalresults are shown.
