Coupled Mode Modeling To Interpret Hybrid Modes and Fano Resonances in Plasmonic Systems

By generalizing the concept of extinction cross-section to complex valued extinction cross-section we analyze the coupling between plasmon modes in metallic dimers or quadrumers. Identifying the phase information in the field scattered by subsets of the whole plasmonic system allows to infer the formation of subradiant or super-radiant hybrid modes. We also propose a phenomenological modeling based on the use of coupled mode equations to deduce from rigorous calculations a quantitative estimate of mutual coupling coefficients when only two modes interfere. These coefficients determine the spectral position of hybrid modes. This approach is applied to two interacting silver spheres; the parameters of the energetic diagram are calculated as a function of the gap between spheres. In the case of two identical spheres illuminated with a linearly polarized light parallel or perpendicular to the dimer, only one hybrid mode is excited. The phenomenological modeling is then applied to a four-particle system, where the interaction between the initial dipolar modes gives rise to Fano resonances. In a weak coupling regime of the system, the asymmetric line profile in the extinction spectra of the system emerges from the superposition of a broad super-radiant mode and a sharp subradiant mode. A strong coupling regime is characterized by a broadened subradiant mode and a larger Fano resonance. The sharpness of the Fano resonance in the weak coupling regime makes this structure well suited for sensing applications.