Anomalous topological phases, unpaired dirac cones, and weak antilocalization in helical photonic lattices

摘要

Topologically nontrivial photonic lattices can reveal topological effects inaccessible in condensed matter systems, and have promising applications including unidirectional light propagation robust against disorder. The first design scalable to optical frequencies employed the Floquet photonic topological insulator concept, in which a time periodic Floquet Hamiltonian was emulated by a helical waveguide array. While unidirectional edge modes were observed, other interesting effects associated with Floquet topological phases were inaccessible due to the lack of tunable phase transitions and high bending losses in this design. We show that the above limitations can be overcome using a class of staggered helical photonic lattices, employing a novel numerical method to compute their Floquet bandstructure. Topological phase transitions between conventional, Chern, and anomalous Floquet insulating phases can be observed via the simple tuning of a continuous lattice parameter such as its period or refractive index contrast. The anomalous Floquet phase, never before observed in an optical frequency photonic topological insulator, hosts protected edge states despite a vanishing Chern number. The low losses of this design combined with the ability to tune between different phases raises the exciting possibility of nonlinear or actively-controllable photonic lattices with topological protection. At phase boundaries the Floquet bandstructure hosts a single unpaired Dirac cone reminiscent of the surface states of 3D topological insulators and in contrast to the paired cones occurring in conventional lattices such as the honeycomb. The intrinsic chirality of an unpaired cone and the periodicity of the Floquet bandstructure enable the observation of a novel “discrete” conical diffraction. Wave propagation at Dirac cones is intrinsically robust against disorder, with backscattering and localization suppressed by weak antilocalization. Here the weak antilocalization is immune to intervalley scattering processes occurring in conventional paired Dirac bandstructures, and hence it can be observed even under short-ranged, uncorrelated disorder.