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

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.

Observation of Edge Solitons in Topological Trimer Arrays

“…Edge solitons may also form in waveguide arraybased valley Hall systems [40][41][42][43]; they were observed in truncated photonic graphene lattice induced in atomic vapors [44]. Recently nonlinear corner states were demonstrated in higher-order 2D topological photonic insulators [45,46]. Among the simplest models admitting the formation of the 1D edge solitons bifurcating from linear edge states are dimerized Su-Schrieffer-Heeger lattices [47].…”

Nonlinear topological valley Hall edge states arising from type-II Dirac cones

“…22,32,75 We believe that our results may prove relevant to other type-II systems such as nonlinear effects and high-frequency rectification in type-II topological semimetals 76 and may also enlighten new ideas in nonlinear non-Hermitian topological systems. 77 Moreover, there is still a plethora of interesting topics yet to be explored in nonlinear systems that could involve type-II Dirac points, including higher-order topological phases, 73,75,78 new physics arising from engineered longitudinal modulation, 79,80 synthetic dimensions, 81 and even the innovation of topological semiconductor laser technologies. [17][18][19][20] Thus, our work on nonlinear VHE states in engineered type-II lattices will surely stimulate further interest in topological photonics-an area that will continue to grow in the next decade.…”

“…1(c) but with a judiciously controlled writing process). [71][72][73] The technique relies on writing the waveguides site-by-site in a 10-mm-long nonlinear photorefractive crystal (SBN:61 with cerium doping: 0.002% CeO 2 ). The experimental setup (more details about the setup can be found in the Supplementary Material) involves a continuous wave laser beam (λ ¼ 532 nm) to illuminate a spatial light modulator, which creates a quasinon-diffracting writing beam with variable input positions.…”

“…Of course, the probe beam can locally change the index structure of the lattices due to its self-action during nonlinear propagation-the ingredient needed to study the nonlinear effects experimentally. 72,73 To appreciate the formation of nonlinear VHE states presented in Fig. 3(e), two out-of-phase elliptical Gaussian beams (due to the property of the VHE state that has a staggered phase structure along the y axis) are superimposed as a probe beam with an input power of only 3 μW, whose position is marked by the white dashed oval in Fig.…”

Realization of Second-Order Photonic Square-Root Topological Insulators

“…A key feature of the topological insulators is the existence of gapless edge states, which exhibit robust unidirectional transport without backscattering, even in the presence of defects or disorders. − According to the normal bulk-boundary correspondence, a conventional d -dimensional topological insulator supports ( d -1)-dimensional boundary states. However, the newly discovered higher-order topological insulators (HOTIs) can support not only ( d -1) but also ( d - n )-dimensional boundary states (with n ≥ 2; a typical example is the 0D corner states in a 2D system). − Thus far, HOTIs have been experimentally demonstrated in condensed matter systems as well as a variety of other synthetic platforms ranging from electric circuits − to acoustics − and photonics. − In addition to the fundamental interest, HOTIs are highly tested and touted for novel applications in robust photonic crystal nanocavities and low-threshold topological corner state lasing. , Indeed, research activities on HOTIs have blossomed, , from linear to nonlinear regimes, − from real to synthetic dimensions, and from Hermitian to non-Hermitian systems …”