Engineering of functional topological transport in photonic waveguide arrays mimicking the extended Fock-state lattice

Topological edge pumping, as an efficient form of energy transfer protected by nontrivial topology, connects the topological characters of a modulated system with its transport behavior. It provides a powerful means to achieve robust wave manipulation between distant nodes and has been intensively investigated in quantum and optical systems. Here we propose to implement multiform energy transfers through the topological defect state in photonic waveguide arrays emulating the extended Fock state lattice (FSL). The FSL supports a topological defect state which enables efficient edge transfer and more complex transmission behavior due to phase transitions induced by on-site energies. By cross-linking two identical FSLs and modulating the linking strength, we construct a fast and robust topological beam splitter with tunable output ratios. When on-site energies are introduced on the occupied odd sites, the cross-linking FSL undergoes a series of phase transitions, after which the original defect channel state becomes a topological channel to transfers excitations from central site to different sites. In addition, we confirm that the multifunctional topological devices based on the defect state in the extended FSL chain manifests strong robustness against mild perturbations in coupling strengths and can be mapped to spatially modulated photonic waveguide arrays. This work verifies a promising route towards robust and multiform photonic excitation transports which may find applications in wave manipulation in integrated optics.