Abstract
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.
Highlights
In an attempt at ultimate control of the flow of light, photonic topological insulators (PTIs) [1] have enabled exciting devices such as unidirectional waveguides and topological lasers that are robust against perturbations and defects
We have shown a procedure to obtain topological modes extended over a d-dimensional bulk using an imaginary gauge field
We have demonstrated the existence of a topological extended mode in the kagome lattice in the rhombus geometry
Summary
In an attempt at ultimate control of the flow of light, photonic topological insulators (PTIs) [1] have enabled exciting devices such as unidirectional waveguides and topological lasers that are robust against perturbations and defects. The one-dimensional (1D) Su-Schrieffer-Heeger (SSH) model [19] has been utilized to generate edge states with gain and loss and implement topological lasing devices [11,12,13]. Topological bulk lasers have been proposed to achieve broad-area emission by using extended topological modes based solely on the parity symmetry at the point in a two-dimensional (2D) hexagonal cavity [17] or by using an imaginary gauge field in a 1D PT symmetric SSH lattice to delocalize the zero-energy boundary mode over the 1D bulk [18]. We demonstrate a topological extended mode on a 2D bulk by using a kagome lattice with a rhombus geometry and an imaginary gauge field.
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