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Register a new userNonlinear control of photonic higher-order topological bound states in the continuum
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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 a 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 demonstrate the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states which, serendipitously, are also BICs in a laser-written second-order topological lattice. We further demonstrate nonlinear coupling with edge states at a low nonlinearity, transitioning to solitons at a high nonlinearity. Theoretically, we calculate the analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by both focusing and defocusing nonlinearities. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.
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We show that lattices with higher-order topology can support corner-localized bound states in the continuum (BICs). We propose a method for the direct identification of BICs in condensed matter settings and use it to demonstrate the existence of BICs in a concrete lattice model. Although the onset for these states is given by corner-induced filling anomalies in certain topological crystalline phases, additional symmetries are required to protect the BICs from hybridizing with their degenerate bulk states. We demonstrate the protection mechanism for BICs in this model and show how breaking this mechanism transforms the BICs into higher-order topological resonances. Our work shows that topological states arising from the bulk-boundary correspondence in topological phases are more robust than previously expected, expanding the search space for crystalline topological phases to include those with boundary-localized BICs or resonances.
Higher-order topological insulators are a recently discovered class of materials that can possess zero-dimensional localized states regardless of the dimension of the lattice. Here, we experimentally demonstrate that the topological corner-localized modes of higher-order topological insulators can be symmetry protected bound states in the continuum; these states do not hybridize with the surrounding bulk states of the lattice even in the absence of a bulk bandgap. As such, this class of structures has potential applications in confining and controlling light in systems that do not support a complete photonic bandgap.
Bound states in the continuum (BICs) are radiationless localized states embedded in the part of the parameter space that otherwise corresponds to radiative modes. Many decades after their original prediction and early observations in acoustic systems, such states have been demonstrated recently in photonic structures with engineered geometries. Here, we put forward a mechanism, based on waveguiding structures that contain anisotropic birefringent materials, that affords the existence of BICs with fundamentally new properties. In particular, anisotropy-induced BICs may exist in symmetric as well as in asymmetric geometries; they form in tunable angular propagation directions; their polarization may be pure transverse electric, pure transverse magnetic or full vector with tunable polarization hybridity; and they may be the only possible bound states of properly designed structures, and thus appear as a discrete, isolated bound state embedded in a whole sea of radiative states.
Recently, high-order topological insulators (HOTIs), accompanied by topologically nontrivial boundary states with codimension larger than one, have been extensively explored because of unconventional bulk-boundary correspondences. As a novel type of HOTIs, very recent works have explored the square-root HOTIs, where the topological nontrivial nature of bulk bands stems from the square of the Hamiltonian. In this paper, we experimentally demonstrate 2D square-root HOTIs in photonic waveguide arrays written in glass using femtosecond laser direct-write techniques. Edge and corner states are clearly observed through visible light spectra. The dynamical evolutions of topological boundary states are experimentally demonstrated, which further verify the existence of in-gap edge and corner states. The robustness of these edge and corner states is revealed by introducing defects and disorders into the bulk structures. Our studies provide an extended platform for realizing light manipulation and stable photonic devices.
Higher-order topological insulators (HOTI) are a novel topological phase beyond the framework of the conventional bulk-boundary correspondence. In these peculiar systems, the topologically nontrivial boundary modes are characterized by a co-dimension of at least two. Despite several promising preliminary considerations regarding the impact of nonlinearity in such systems, the flourishing field of experimental HOTI research has thus far been confined to the linear evolution of topological states. As such, the observation of the interplay between nonlinearity and the dynamics of higher-order topological phases in conservative systems remains elusive. In our work, we experimentally demonstrate nonlinear higher-order topological corner states. Our photonic platform enables us to observe nonlinear topological corner states as well as the formation of solitons in such topological structures. Our work paves the way towards the exploration of topological properties of matter in the nonlinear regime, and may herald a new class of compact devices that harnesses the intriguing features of topology in an on-demand fashion.
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