Topological Bulk Lasing Modes Using an Imaginary Gauge Field

Topological edge modes, which are robust against disorders, have been used to enhance the spatial stability of lasers. Recently, it was revealed that topological lasers can be further stabilized using a novel topological phase in non-Hermitian photonic topological insulators. Here we propose a procedure to realize topologically protected modes extended over a d-dimensional bulk by introducing an imaginary gauge field. This generalizes the idea of zero-energy extended modes in the one-dimensional Su-Schrieffer-Heeger lattice into higher dimensional lattices allowing a d-dimensional bulky mode that is topologically protected. Furthermore, we numerically demonstrate that the topological bulk lasing mode can achieve high temporal stability superior to topological edge mode lasers. In the exemplified topological extended mode in the kagome lattice, we show that large regions of stability exist in its parameter space.