A complete phase diagram for dark-bright coupled plasmonic systems: applicability of Fano's formula

Although coupled plasmonic systems have been extensively studied in the past decades, their theoretical understanding is still far from satisfactory. Here, based on experimental and numerical studies on a series of symmetry-broken nano-patch plasmonic resonators, we found that Fano's formula, widely used in modeling such systems previously, works well for one polarization but completely fails for another polarization. In contrast, a two-mode coupled-mode theory (CMT) can interpret all experimental results well. This motivated us to employ the CMT to establish a complete phase diagram for such coupled plasmonic systems, which not only revealed the diversified effects and their governing physics in different phase regions, but more importantly, also justifies the applicabilities of two simplified models (including Fano's formula) derived previously. Our results present a unified picture for the distinct effects discovered in such systems, which can facilitate people's understanding of the governing physics and can design functional devices facing requests for diversified applications.