Multiband topological interfaces in 1D SNAP microresonator lattices

Analogue Hamiltonian simulation (AHS) in photonic systems can be an enticing alternative to direct experimental study of complex Hamiltonian systems such as simulating tight-binding models of the behavior of electrons within topological insulators to create forms of light with topological properties. In this work, we experimentally demonstrate topologically nontrivial Surface Nanoscale Axial Photonics (SNAP) devices by coupling together axial modes of adjacent SNAP microresonators to form Su-Schrieffer-Heeger (SSH) lattices. We fabricate topological SNAP systems to demonstrate higher-order generalizations of SSH lattices, and junctions between multiband lattices with dissimilar topological phases created from 21 frequency-matched SNAP microresonators. Such previously unexplored ``heterojunctions" between dissimilar multiband SSH models necessitated developing generalized topological polarization methods to analyze them. We thus demonstrate the exceptional promise of the SNAP platform for AHS of 1D topological insulators, and also open the door to the potential for simulating >2 dimensional systems by utilizing nonlinear interactions.