Edge Solitons in Nonlinear Photonic Topological Insulators

Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal invariant topological insulators. Because of limitations imposed by nature, topologically non-trivial electronic order seems to be uncommon except in small-band-gap semiconductors with strong spin-orbit interactions. In this Article we show that artificial electromagnetic structures, known as metamaterials, provide an attractive platform for designing phot...

Topological theories have established a new set of rules that govern the transport properties in a wide variety of wave-mechanical settings. In a marked departure from the established approaches that induce Floquet topological phases by specifically tailored discrete coupling protocols or helical lattice motions, we introduce a new class of bimorphic Floquet topological insulators that leverage connective chains with periodically modulated on-site potentials to unlock new top...

The topic of photonic topological insulators and scattering-protected edge states bridges concepts from condensed matter physics and electromagnetics, and necessitates understanding the Berry potential and related concepts. These notes are an attempt at a moderately self-contained introduction to the topic, including two detailed photonic examples drawn from the literature. We made these notes in the process of trying to understand this topic ourselves, and we are posting thi...

Topological edge states form at the edges of periodic materials with specific degeneracies in their modal spectra, such as Dirac points, under the action of effects breaking certain symmetries of the system. In particular, in Floquet topological insulators unidirectional edge states appear upon breakup of the effective time-reversal symmetry due to dynamical modulations of the underlying lattice potential. However, such states are usually reported for certain simple lattice t...

Optical microcavities supporting exciton-polariton quasi-particles offer one of the most powerful platforms for investigation of rapidly developing area of topological photonics in general, and of photonic topological insulators in particular. Energy bands of the microcavity polariton graphene are readily controlled by magnetic field and influenced by the spin-orbit coupling effects, a combination leading to formation of linear unidirectional edge states in polariton topologi...

Much of the recent enthusiasm directed towards topological insulators as a new state of matter is motivated by their hallmark feature of protected chiral edge states. In fermionic systems, Kramers degeneracy gives rise to these entities in the presence of time-reversal symmetry (TRS). In contrast, bosonic systems obeying TRS are generally assumed to be fundamentally precluded from supporting edge states. In this work, we dispel this perception and experimentally demonstrate c...

Edge modes in topological insulators are known to be robust against defects. We investigate if this also holds true when the defect is not static, but varies in time. We study the influence of defects with time-dependent coupling on the robustness of the transport along the edge in a Floquet system of helically curved waveguides. Waveguide arrays are fabricated via direct laser writing in a negative tone photoresist. We find that single dynamic defects do not destroy the chir...

Topological insulators combine insulating properties in the bulk with scattering-free transport along edges, supporting dissipationless unidirectional energy and information flow even in the presence of defects and disorder. The feasibility of engineering quantum Hamiltonians with photonic tools, combined with the availability of entangled photons, raises the intriguing possibility of employing topologically protected entangled states in optical quantum computing and informat...

Topological photonics has attracted widespread research attention in the past decade due to its fundamental interest and unique manner in controlling light propagation for advanced applications. Paradigmatic approaches have been proposed to achieve topological phases including topological insulators in a variety of photonic systems. In particular, photonic lattices composed of evanescently coupled waveguide arrays have been employed conveniently to explore and investigate top...

The propagation of linear and nonlinear edge modes in bounded photonic honeycomb lattices formed by an array of rapidly varying helical waveguides is studied. These edge modes are found to exhibit strong transmission (reflection) around sharp corners when the dispersion relation is topologically nontrivial (trivial), and can also remain stationary. An asymptotic theory is developed that establishes the presence (absence) of edge states on all four sides, including in particul...