Theoretical study of diatomic plasmonic chains : Zak phase and spatial-temporal symmetries

Abstract

Being small and compact, plasmonic chains and arrays of metal nanoparticles have been of great interest for decades, as they were proven to support electro-magnetic energy transfer via coupled plasmon modes. In this thesis, we studied plasmonic chains with two nanoparticles in a unit cell, namely diatomic plasmonic chains. This simple dimmerization enriched plasmonic chains with many possibilities. We presented diatomic plasmonic chains with alternative separations to mimic the Su-Schrieffer-Heeger model, a simple model which is able to have topological non-trivial phase. In this case, the inverse polarizabily and the coupled dipole equation play the roles of the eigen-energy and the Hamiltonian matrix with respectively. When two diatomic plasmonic chains with different Zak phases are connected together, topologically protected edge states will be formed. We also proposed a magnetized diatomic plasmonic chain to obtain non-reciprocal dispersion relations. By hybridizing with free photons modes, such structure supports one-way propagating coupled plasmon modes over a small range of frequencies. The relationship between the crucial rotation-time-reversal symmetry and the spectral reciprocity in this structure was discussed and demonstrated. Finally, we introduced the zero extinction property induced by inversion-time-reversal (PT) symmetry, and studied the relationship between the Zak phase and the PT symmetry. The Zak phase was found remained quantized for a 2-band PT symmetric system, provided in the unbroken PT phase and a modification on the Bloch's function. Coated diatomic plasmonic chain with gain-loss-balanced shells is given as an example, which supports edge states with complex frequencies when the Zak phase is π. Our results pave the way to achieve various optical components based on plasmonic chains in the future.