Gap solitons in parity–time symmetric moiré optical lattices
Xiuye Liu, Jianhua Zeng
Abstract
Parity–time ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m1"> <mml:mrow> <mml:mi mathvariant="script">PT</mml:mi> </mml:mrow> </mml:math> ) symmetric lattices have been widely studied in controlling the flow of waves, and recently, moiré superlattices, connecting the periodic and non-periodic potentials, have been introduced for exploring unconventional physical properties in physics, while the combination of both and nonlinear waves therein remains unclear. Here, we report a theoretical survey of nonlinear wave localizations in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m2"> <mml:mrow> <mml:mi mathvariant="script">PT</mml:mi> </mml:mrow> </mml:math> symmetric moiré optical lattices, with the aim of revealing localized gap modes of different types and their stabilization mechanism. We uncover the formation, properties, and dynamics of fundamental and higher-order gap solitons as well as vortical ones with topological charge, all residing in the finite bandgaps of the underlying linear-Bloch wave spectrum. The stability regions of localized gap modes are inspected in two numerical ways: linear-stability analysis and direct perturbance simulations. Our results provide an insightful understanding of soliton physics in combined versatile platforms of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m3"> <mml:mrow> <mml:mi mathvariant="script">PT</mml:mi> </mml:mrow> </mml:math> symmetric systems and moiré patterns.