Abstract
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.
Highlights
Over the past decade, topological insulators have attracted tremendous attention across many disciplines of natural sciences[1,2], including photonics[3]
The wave dynamics in our higher-order topological insulators (HOTIs) system can be described by the continuous nonlinear Schrödinger-like equation (NLSE), typically used for simulating a light field with amplitude ψ(x, y, z) propagating along the longitudinal z-direction of the photorefractive photonic lattice[64]: i
Even though we used a specific type of optical nonlinearity in our study, the concept and scheme of nonlinear control of HOTI corner modes developed here are expected to hold in other platforms beyond photonics
Summary
Topological insulators have attracted tremendous attention across many disciplines of natural sciences[1,2], including photonics[3]. HOTIs are attractive because they are related to many intriguing phenomena, such as higher-order band topology in twisted Moiré superlattices[33], topological lattice disclinations[34], and Majorana bound states[35] and their nontrivial braiding[36]. Toward applications, they have been touted and tested for robust photonic crystal nanocavities[37] and low-threshold topological corner state lasing[29,38].
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