Phaselike resonance behavior in optical transmission of sandwich coaxial square ring arrays

We studied the optical transmission through sandwich coaxial square ring arrays experimentally and theoretically. The hybridized mode of the localized surface-plasmons and surface-plasmon polaritons has been observed. This hybridized mode resembles the phase resonance mode in a compound grating structure and can be named as phaselike resonance mode. For the 0-phase resonance mode, energy can tunnel through the sample due to coherent constructive interference, forming a peak in the transmission spectrum. For the π-phase resonance mode, a dip appears instead. When the incident angle is increased, the π-phase resonance mode is split into two branches, one is redshifted while the other blueshifted.