Theory of Topological Corner State Laser in Kagome Waveguide Arrays

TL;DR

This paper demonstrates a topological corner state laser in a Kagome waveguide array, showing stable lasing with low thresholds in second-order topological insulators, and explores the effects of gain placement and nonlinear absorption.

Contribution

It introduces a novel corner state laser based on second-order topological insulators in Kagome waveguide arrays, expanding topological laser concepts beyond first-order systems.

Findings

Stable lasing achieved in corner states with lowest thresholds.

Lasing in other regions requires higher thresholds and shows instabilities.

Two-photon absorption stabilizes nonlinear lasing states.

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.