Nonlinear non-Hermitian higher-order topological laser

Abstract

Topological lasers are investigated in nonlinear, non-Hermitian, and topological lattice systems based on a quench dynamics starting from one site. Explicitly, we consider the topological laser in the Su-Schrieffer-Heeger model with two topological edge states and the second-order topological laser in the breathing kagome lattice with three topological corner states. Once we stimulate any one site, after some delay, all sites belonging to the topological edge or corner states are shown to emit stable laser light depending on the density of states, although no wave propagation is observed from the stimulated site. Thus the profile of topological edge or corner states is observable by measuring the intensity of lasing. The phenomenon occurs due to a combinational effect of linear non-Hermitian loss terms and nonlinear non-Hermitian gain terms in the presence of the topological edge or corner states. It is intriguing that the dynamics of topological edge or corner states are observed in real-time and real-space dynamics of the laser emission.