Tunable terahertz topological edge and corner states in designer surface plasmon crystals.

In this work, we study topological edge and corner states in two-dimensional (2D) Su-Schrieffer-Heeger lattices from designer surface plasmon crystals (DSPCs), where the vertical confinement of the designer surface plasmons enables signal detection without the need of additional covers for the sample. In particular, the formation of higher-order topological insulator can be determined by the two-dimensional Zak phase, and the zero-dimensional subwavelength corner states are found in the designed DSPCs at the terahertz (THz) frequency band together with the edge states. Moreover, the corner state frequency can be tuned by modifying the defect strength, i.e., the location or diameter of the corner pillars. This work may provide a new approach for confining THz waves in DSPCs, which is promising for the development of THz topological photonic integrated devices with high compactness, robustness and tunability.

Dynamically Emerging Topological Phase Transitions in Nonlinear Interacting Soliton Lattices.

We demonstrate dynamical topological phase transitions in evolving Su-Schrieffer-Heeger lattices made of interacting soliton arrays, which are entirely driven by nonlinearity and thereby exemplify an emergent nonlinear topological phenomenon. The phase transitions occur from the topologically trivial-to-nontrivial phase in periodic succession with crossovers from the topologically nontrivial-to-trivial regime. The signature of phase transition is the gap-closing and reopening point, where two extended states are pulled from the bands into the gap to become localized topological edge states. Crossovers occur via decoupling of the edge states from the bulk of the lattice.

Nonlinear control of photonic higher-order topological bound states in the continuum.

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to the HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states that are also BICs in a laser-written second-order topological lattice and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.