Topological Corner State Laser in Kagome Waveguide Arrays

In comparison with conventional lasers, whose stability may be affected by perturbations, such as defects and disorder, topological lasers may be remarkably stable when they lase in topologically protected edge states. In this work, we predict that corner laser can be implemented in a new continuous system, which is based on Kagome [1] waveguide arrays, where localized gain can be selectively provided in different waveguides, and where uniform losses, two-photon absorption, and focusing nonlinear interactions are present. Even though lasing in 0D corner states has been recently reported in photonic crystal cavities [2] - [4], this work suggests a new platform based on the continuous waveguide array in cavity-free configuration. We employ localized gain, which, when applied in different corners of our structure, offers unique advantage of highly selective excitation of bulk, edge, or corner nonlinear topological states in higher-order topological insulator. The possibility of such selective excitation in our truly two-dimensional system is a nontrivial result by itself taking into account complex spatial shape of the considered structure. We report on completely stable corner state lasing and bistability of the edge state lasing that can only be observed in the nonlinear medium. The detailed analysis of stability of lasing modes is provided for different values of linear gain and two-photon absorption coefficients.