Dimer nanoparticles in a sandwich structure exhibit a large electric-field intensity enhancement. The dispersion relation between the surface plasmon resonance (SPR) and particle size has not been reported yet, owing to the effects of the particle size, shape, materials, etc. A sandwich structure, which contains a nano-right-triangle dimer array, SiO2 spacer, and Au film, is proposed, with a significant electric-field intensity enhancement and polarization-changing properties. The dependence of the peak positions of the two localized surface plasmon resonance (LSPR) modes as a function of the triangle thicknesses is discussed; different trends are observed for the different LSPR modes. We introduce a concept on the rule for LSPR peak position change, which can contribute to a better understanding of the LSPR modes. In addition, centrosymmetric but not axisymmetric structures, which like in our study exhibit surface plasmon polaritons typically show different responses to a different polarization of the incident light. Here, we showed that our centrosymmetric but not axisymmetric structure can change the linearly polarized light into a circularly or elliptically polarized wave, by surface plasmon-induced polarization properties. Far-field distribution maps are used to study the properties of the surface plasmons-induced circular or elliptic polarization wave. These findings could be employed to better understand the surface plasmon-induced polarization properties showed in previous reports and near-field of surface plasmons. These findings could be employed to better understand the near-field of surface plasmons and polarization properties.