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Avoided resonance crossing [1] is a general phenomenon occurring in almost all physical interactions. It describes the splitting behavior in a coupled system. For example, in dielectric hexagonal dielectric resonators [2], the degenerated triangular resonant modes exhibit energy level and line-width anti-crossing by varying the height of one hexagonal edge. One of the modes leads to longer life time with higher quality factor. Whether the energy level or line-width exhibits either crossing or anti-crossing depends on the mechanism of interaction [1,2]. In this paper, we show that similar anti-resonance crossing behavior can be observed in plasmonic nanostructures due to either near field or far field coupling. Near field coupling in disk dimmer can lead to both energy and line-width anti-crossing. This anti-crossing phenomena can also be explained by simple Hamiltonian model [1,2] and we show the corresponding phenomena for both vertically and horizontally aligned two disks. By varying the size of one disk as the hetero-dimer approaching homo-dimer, the anti-crossing in both energy and linewidth appears. The Hamiltonian model also predicts the energy crossing and linewidth anticrossing for far field coupling. However, there is little literature discussion on the avoided crossing by far field coupling in plasmonic structure.
In this work we found that far field coupling in double layered disk array with gap size close to Fabry-Perot (FP) resonant condition leads to line-width anti-crossing but energy crossing by varying either the gap size or the diameter of one disk. Asymmetric reflection and absorption spectra from different side of the double layered disk arrays with asymmetric disk arrays (or disk arrays without mirror system) show the disappearing of Fabry-Perot resonant mode and non-reciprocal perfect absorption properties. This nearly perfect absorption is fundamentally connected to the anti-crossing phenomena in asymmetric disk arrays. We use a simple frequency-selective surface (FSS) model to represent the individual disk array and use the FP model to connect the tow arrays. This simple FSS-FP model matches well with the full wave finite-different time-domain modeling. This model can also explain the perfect absorption properties for ultra-thin metamaterial surface observed in literature. The observed avoided resonance crossings and nonreciprocal absorption in plasmonic nanostructure would lead to many photonics applications such as high Q resonators for future sensing applications.
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