Theory of Topological Corner State Laser in Kagome Waveguide Arrays

Abstract

In comparison with conventional lasers, topological lasers are more robust and can be immune to disorder or de-fects if lasing occurs in topologically protected states. Previously reported topological lasers were almost exclu-sively based on the first-order photonic topological insulators. Here, we show that lasing can be achieved in the zero-dimensional corner state in a second-order photonic topological insulator, which is based on Kagome wave-guide array with a rhombic configuration. If gain is present in the corner of the structure, where topological corner state resides, stable lasing in this state is achieved, with lowest possible threshold, in the presence of uniform loss-es and two-photon absorption. When gain acts in other corners of the structure, lasing may occur in edge or bulk states, but it requires substantially larger thresholds and transition to stable lasing occurs over much larger propa-gation distances, sometimes due to instabilities, which are absent for lasing in corner states. We find that increasing two-photon absorption generally plays strong stabilizing action for nonlinear lasing states. The transition to stable lasing stimulated by noisy inputs is illustrated. Our work demonstrates the realistic setting for corner state laser based on higher-order topological insulator realised with waveguide arrays.

20 pages

References in corpus (9)

• Topological Photonics
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Direct observation of corner states in second-order topological photonic crystal slabs
• Photonic crystal nanocavity based on a topological corner state
• Low-threshold topological nanolasers based on second-order corner state
• Floquet topological insulator laser

Cited by in corpus (15)

• Nonlinear non-Hermitian higher-order topological laser
• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• Corner modes of the breathing kagome lattice: origin and robustness
• Observation of $\pi$ solitons in oscillating waveguide arrays
• Nonlinear photonic disclination states
• Single-mode lasing based on PT-breaking of two-dimensional photonic higher-order topological insulator
• Vector valley Hall edge solitons in superhoneycomb lattices
• Tunable two-dimensional laser arrays with zero-phase locking
• Non-Hermitian topological exciton-polariton corner modes
• Dirac cones and higher-order topology in quasi-continuous media
• Observation of topologically distinct corner states in "bearded" photonic Kagome lattices
• Polarization-independent second-order photonic topological corner states
• Observation of nonlinear topological corner states originating from different spectral charges
• Supersymmetric non-Hermitian topological interface laser
• $\pi$ mode lasing in the non-Hermitian Floquet topological system