Small mode volume topological photonic states in one-dimensional lattices with dipole--quadrupole interactions

TL;DR

This paper investigates topological photonic states in one-dimensional lattices with dipole and quadrupole interactions, revealing new edge states with smaller mode volumes and potential for robust light confinement.

Contribution

It introduces the role of quadrupole moments in topological photonic states and characterizes their impact on edge states and mode localization in 1D lattices.

Findings

Quadrupolar edge states coexist with dipolar states at the same energy.

Quadrupolar edge states have shorter localization lengths and smaller mode volumes.

Quadrupole moments significantly influence the band topology and edge state properties.

Abstract

We study the topological photonic states in one-dimensional (1-D) lattices analogue to the Su-Schrieffer-Heeger (SSH) model beyond the dipole approximation. The electromagnetic resonances of the lattices supported by near-field interactions between the plasmonic nanoparticles are studied analytically with coupled dipole--quadrupole method. The topological phase transition in the bipartite lattices is determined by the change of Zak phase. Our results reveal the contribution of quadrupole moments to the near-field interactions and the band topology. It is found that the topological edge states in non-trivial lattices have both dipolar and quadrupolar nature. The quadrupolar edge states are not only orthogonal to the dipolar edge states, but also spatially localized at different sublattices. Furthermore, the quadrupolar topological edge states, which coexist at the same energy with the quadrupolar flat band have shorter localization length and hence smaller mode volume than the conventional dipolar edge states. The findings deepen our understanding in topological systems that involve higher-order multipoles, or in analogy to the wave functions in quantum systems with higher-orbital angular momentum, and may be useful in designing topological systems for confining light robustly and enhancing light-matter interactions.