Photonic quadrupole topological insulator using orbital-induced synthetic flux

Photonic Molecule Approach to Multiorbital Topology

The concepts of topology provide a powerful tool to tailor the propagation and localization of the waves. While electrons have only two available spin states, engineered degeneracies of photonic modes provide novel opportunities resembling spin degrees of freedom in condensed matter. Here, we tailor such degeneracies for the array of femtosecond laser written waveguides in the optical range exploiting the idea of photonic molecules: clusters of strongly coupled waveguides. In our experiments, we observe unconventional topological modes protected by the Z3 invariant arising due to the interplay of interorbital coupling and geometric dimerization mechanism. We track multiple topological transitions in the system with the change in the lattice spacings and excitation wavelength. This strategy opens an avenue for designing novel types of photonic topological phases and states.

Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators

We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological phases. We find a fine-grained categorization of Chern insulators, their band topologies characterized by identical Chern numbers are completely different. Furthermore, we prove that different topologies cause zeros in their Bloch wave function overlaps, which imprint the band gap closing and appear at the degenerate points of topological phase transition. The Bloch wave function overlaps predict the reflection and refraction at a topological time boundary, and the overlap zeros ensure the existence of vanishing revival amplitude at critical times even though different topologies before and after the time boundary have identical Chern numbers. Our findings create new opportunities for topological metamaterials, uncover the topological feature hidden in the time boundary effect as a probe of topology, and open a venue for the exploration of the rich physics originating from the long-range couplings.

Acoustic Higher-Order Topological Insulators Induced by Orbital-Interactions

The discovery of higher-order topological insulator metamaterials, in analogy with their condensed-matter counterparts, has enabled various breakthroughs in photonics, mechanics, and acoustics. A common way of inducing higher-order topological wave phenomena is through pseudo-spins, which mimic the electron spins as a symmetry-breaking degree of freedom. Here, this work exploits degenerate orbitals in acoustic resonant cavities to demonstrate versatile, orbital-selective, higher-order topological corner states. Type-II corner states are theoretically investigated and experimentally demonstrated based on tailored orbital interactions, without the need for long-range hoppings that has so far served as a key ingredient for Type-II corner states in single-orbital systems. Due to the orthogonal nature of the degenerate p orbitals, this work also introduces a universal strategy to realize orbital-dependent edge modes, featuring high-Q edge states identified in bulk bands. These findings provide an understanding of the interplay between acoustic orbitals and topology, shedding light on orbital-related topological wave physics, as well as its applications for acoustic sensing and trapping.

Dynamical Detection of Topological Spectral Density

Local density of states (LDOS) is emerging as powerful means of exploring classical-wave topological phases. However, the current LDOS detection method remains rare and merely works for static situations. Here, we introduce a generic dynamical method to detect both the static and Floquet LDOS, based on an elegant connection between dynamics of chiral density and local spectral densities. Moreover, we find that the Floquet LDOS allows to measure out Floquet quasienergy spectra and identify topological π modes. As an example, we demonstrate that both the static and Floquet higher-order topological phase can be universally identified via LDOS detection, regardless of whether the topological corner modes are in energy gaps, bands, or continuous energy spectra without band gaps. Our study opens a new avenue utilizing dynamics to detect topological spectral densities and provides a universal approach of identifying static and Floquet topological phases.

Quadrupole topological phases and filling anomaly in all-dielectric Lieb lattice photonic crystals

While higher-order photonic topological corner states typically are created in systems with nontrivial bulk dipole polarization, they could also be created in systems with vanishing dipole polarization but with nontrivial quadrupole topology, which though is less explored. In this work, we show that simple all-dielectric photonic crystals in the Lieb lattice can host a topologically nontrivial quadrupole bandgap. Through a combination of symmetry analysis of the eigenmodes and explicit calculations of the Wannier bands and their polarization using the Wilson loop method, we demonstrate that the Lieb photonic crystals can have a bandgap with vanishing dipole polarization but with nontrivial quadrupole topology. The nontrivial bulk quadrupole moment could result in edge-localized polarization and topological corner states in systems with open edges. Interestingly, the indices of the corner states show an unusual "3+1" pattern compared to previously known "2+2" pattern, and this new pattern leads to unusual filling anomaly when the corner states are filled. Our work could not only deepen our understanding about quadrupole topology in simple all-dielectric photonic crystals but could also offer new opportunities for practical applications in integrated photonic devices.

Photonic Möbius topological insulator from projective symmetry in multiorbital waveguides

The gauge fields dramatically alter the algebraic structure of spatial symmetries and make them projectively represented, giving rise to novel topological phases. Here, we propose a photonic Möbius topological insulator enabled by projective translation symmetry in multiorbital waveguide arrays, where the artificial π gauge flux is aroused by the inter-orbital coupling between the first (s) and third (d) order modes. In the presence of π flux, the two translation symmetries of rectangular lattices anti-commute with each other. By tuning the spatial spacing between two waveguides to break the translation symmetry, a topological insulator is created with two Möbius twisted edge bands appearing in the bandgap and featuring 4π periodicity. Importantly, the Möbius twists are accompanied by discrete diffraction in beam propagation, which exhibit directional transport by tuning the initial phase of the beam envelope according to the eigenvalues of translation operators. This work manifests the significance of gauge fields in topology and provides an efficient approach to steering the direction of beam transmission.