Double-ring structure of metallic nano-particles for surface lattice resonance

Surface lattice resonances due to regular periodic array of metallic nanoparticles can be attributed to the mutual coupling between the localized surface plasmon resonance of different nanoparticles. As a result, when comparing the resonant effect of the single particle and the array, the resonance line width can be significantly reduced. In this paper, we extend the coupled dipole approximation to solve the electromagnetic characteristics of the particle ring structures with rotational symmetry, and the analytical model for the double ring array of metallic nano-particles are raised. Furthermore, we derive the general resonant condition of the double ring array and investigate some concrete illustrations in details. It shows that the full resonance of the whole array depends crucially on the structural parameters, whose enhancement factor can be extremely high. But a slight change on the structural parameters would result in a sharp reduce to the enhancement factor. We also found that the radiation field of the full resonance effect would be independent of the external field, which provides us a simple approach to produce a localized optical field with complex space distribution. This proposed structural can find potential applications in various fields such as metasurface, optoelectronics, optical manipulation, communication, biosensing and other applications.