Multiband topological heterojunctions on the surface nanoscale axial photonics platform.

Analogue Hamiltonian simulation (AHS) in photonic systems can be an enticing alternative to direct experimental study of complex Hamiltonian systems, leading to the emergence of the field of topological photonics. In this work, we leverage the ultra-low loss operation and sub-angstrom fabrication precision of the Surface Nanoscale Axial Photonics Platform to experimentally demonstrate the first topologically nontrivial SNAP devices by coupling adjacent SNAP microresonators to form Su-Schrieffer-Heeger (SSH) lattices. Each axial mode of the microresonator array manifests distinct topological band structures, enabling us to observe behavior close to and far from the topological-trivial phase transition. We further expand the scope of topological SNAP systems to junctions between higher-order, multiband lattices with dissimilar topological phases created by coupling up to 21 well-matched SNAP microresonators. Analyzing these previously unexplored "heterojunctions" necessitated our development of generalized topological polarization methods. We thus demonstrate the exceptional promise of the SNAP platform for AHS of topological insulators.