Corner states of light in photonic waveguides

Abstract

The recently established paradigm of higher-order topological states of matter has shown that not only, as previously thought, edge and surface states but also states localised to corners can have robust and exotic properties. Here we report on the experimental realisation of novel corner states made out of classical light in three-dimensional photonic structures inscribed in glass samples using femtosecond (fs) laser technology. By creating and analysing waveguide arrays forming two-dimensional breathing kagome lattices in various sample geometries, we establish this as a platform for corner states exhibiting a remarkable degree of flexibility and control. In each sample geometry we measure eigenmodes that are localised at the corners in a finite frequency range in complete analogy with a theoretical model of the breathing kagome. Here, the measurements reveal that light can be "fractionalised", corresponding to simultaneous localisation to each corner of a triangular sample, even in the presence of defects. The fabrication method applied in this work exposes the advantage of using fs-laser writing for producing compact three-dimensional devices thus paving the way for technological applications by simulating novel higher-order states of matter. arXiv:1812.08185v3 [cond-mat.mes-hall]

Higher-order topological solitonic insulators

“…However, a higher-order, e.g., kth-order, topological insulator allows (n − k)-dimensional topological boundary states with 2 k n, which goes beyond the standard bulk-boundary correspondence and is characterized by the bulk topological index [5][6][7][8][9][10][11][12]. Interestingly, the experimental evidences of higher-order topological insulators (HO-TIs) were reported so far only in classical mechanical and electromagnetic metamaterials [13][14][15][16][17][18][19][20][21]. In terms of applications of HOTIs in spintronics, it is intriguing to ask if they can exist in magnetic system which is intrinsically, however nonlinear, in contrast to its phononic and photonic counterparts.…”

Higher‐Order Topological States in Surface‐Wave Photonic Crystals

“…After the submission of this work, we become aware of several independent works, which report on realization of higher‐order photonic topological states based on photonic crystals in a generalized Su‐Schrieffer‐Heeger model, or based on optical waveguide arrays in a breathing kagome lattice model, or realization of photonic topological quadrupole phases …”

“…c,d) Measured and simulated magnetic field intensity distribution |H z | 2 over the sample at 13.24 GHz (marked by the black dashed line in Figure 3b) excitation, respectively. a generalized Su-Schrieffer-Heeger model, [43][44][45] or based on optical waveguide arrays in a breathing kagome lattice model, [46] or realization of photonic topological quadrupole phases. [47]…”

Qubit-photon corner states in all dimensions

“…Then, by placing the emitter close to a corner of the photonic bath, its directional emission and the reflection in the boundary generates a high-dimensional BIC that we label as qubit-photon corner state. In contrast to the recently observed topological photon corner states [43][44][45][46][47][48][49][50], ours can inherit a strong non-linearity from the emitter, and do not require a topologically nontrivial bath. We characterize these states in two and tree dimensions using exact numerical techniques to take into account the retardation effects and the corrections in the ultra-strong coupling regime, where these states acquire a finite lifetime.…”