Photonic topological subspace-induced bound states in the continuum.

Bound states in the continuum (BICs) are intriguing localized states that possess eigenvalues embedded within the continuum of extended states. Recently, a combination of topological band theory and BIC physics has given rise to a novel form of topological matter known as topological BICs. In this work, we experimentally demonstrate the photonic topological subspace-induced BICs. By using femtosecond-laser writing, we experimentally establish a photonic nontrivial three-leg ladder lattice, thereby directly observe the localized propagation of two kinds of topological edge states which exist at different boundaries. Interestingly, such edge states appear in the continuum of the bulk modes, and the topological properties are inherited from its independent subspace Hamiltonian which contains a celebrated Su-Schrieffer-Heeger lattice. This work not only presents a novel, to the best of our knowledge, platform for investigating topological physics in optics, but also unveils exciting prospects for future exploration of other remarkable BICs.

Topological edge states in photonic decorated trimer lattices.

In recent years, topological insulators have been extensively studied in one-dimensional periodic systems, such as Su-Schrieffer-Heeger and trimer lattices. The remarkable feature of these one-dimensional models is that they support topological edge states, which are protected by lattice symmetry. To further study the role of lattice symmetry in one-dimensional topological insulators, here we design a modified version of the conventional trimer lattices, i.e., decorated trimer lattices. Using the femtosecond laser writing technique, we experimentally establish a series of one-dimensional photonic decorated trimer lattices with and without inversion symmetry, thereby directly observing three kinds of topological edge state. Interestingly, we demonstrate that the additional vertical intracell coupling strength in our model can change the energy band spectrum, thereby generating unconventional topological edge states with a longer localization length in another boundary. This work offers novel insight into topological insulators in one-dimensional photonic lattices.

Square-root higher-order topological insulators in a photonic decorated SSH lattice.

Recently, there has been a surge of interest in square-root higher-order topological insulators (HOTIs) due to their unique topological properties inherited from their squared Hamiltonian. Different from conventional HOTIs, square-root HOTIs support paired corner states that exist in different bandgaps. In this work, we experimentally establish a series of two-dimensional photonic decorated Su-Schrieffer-Heeger (SSH) lattices by using the femtosecond-laser writing technique and thereby directly observe paired topological corner states. Interestingly, the higher-order topological properties of such square-root HOTIs are inherited from the parent Hamiltonian, which contains the celebrated 2D SSH lattice. The dynamic evolution of square-root corner states indicates that they exist in different bandgaps. This work not only provides a new platform to study higher-order topology in optics, it also brings about new possibilities for future studies of other novel HOTIs.

Observation of higher-order topological corner states in photonic two-dimensional trimer lattices.

We demonstrate the first, to the best of our knowledge, experimental observation of higher-order topological corner states in the photonic two-dimensional (2D) trimer lattices. Using a femtosecond laser direct writing technology, we experimentally fabricate a series of 2D trimer lattices with different open boundary conditions and thereby observe two kinds of 0D topological corner states, i.e., topological corner states and topological defect corner states. Interestingly, these corner states and defect corner states can not only exist in the bandgap but also coexist with the bulk states and show obvious localization properties. This work provides fresh perspectives on higher-order topology in artificial microstructures.

Observation of topological Anderson phase in laser-written quasi-periodic waveguide arrays.

We report on the experimental observation of the topological Anderson phase in one-dimensional quasi-periodical waveguide arrays produced by femtosecond laser writing. The evanescently coupled waveguides are with alternating coupling constants, constructing photonic lattices analogous to the Su-Schrieffer-Heeger model. Dynamic tuning of the interdimer hopping amplitudes of the waveguide array generates the quasi-periodic disorder of the coupling constants for the model. As light propagates in the corresponding photonic waveguides, it exhibits different modes depending on the magnitude of the disorder. The topological Anderson phase is observed as the disorder is sufficiently strong, which corresponds to the zero-energy mode in its spectrum. The experimental results are consistent with the theoretical simulations, confirming the existence of the disorder-driven topological phase from a trivial band in the photonic lattice.