Gap solitons in parity–time symmetric moiré optical lattices

Abstract

Parity–time ( PT ) 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 PT 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 PT symmetric systems and moiré patterns.

One-dimensional PT -symmetric eigenmodes in k-wave number Scarf II potential with defocusing nonlinearity

“…Gross-Pitaevskii equations with Wadati class of potentials have a special interest while studying the  -symmetric systems [16][17][18].  -symmetric soliton models with Kerr nonlinearity in single [19][20][21][22][23][24][25][26][27] and coupled systems [28][29][30][31][32] have been studied extensively. Apart from Kerr nonlinear system, different kinds of nonlinear models such as nonlocal [33,34], variable coefficient [35], parabolic law [36], cubic-quintic [37,38], cubic-quartic [39], quintic-septimal [40,41] and cubic-quintic-septimal [42] nonlinear Schrodinger equations leading to different types of soliton solutions have been studied.…”

Light gap bullets in defocusing media with optical lattices

“…Introduction.-It is a challenging issue to create stable three-dimensional (3D) localized modes (alias solitons) owning to the inherent supercritical wave collapse triggered by attractive cubic (Kerr) nonlinearity (critical wave collapse also exists in two-dimensional (2D) settings) [1][2][3][4][5][6][7][8][9]. To against such high-dimensional wave collapses in the soliton research field in diverse branches of science, it is therefore necessary to introduce extra physical effects, including synthetic periodic potentials [10][11][12][13][14][15][16][17][18][19][20], saturable absorber [21,22], optical cavity [23][24][25], semiconductor active [26] or quadratic nonlinear media [27], waveguide and fiber arrays [28][29][30][31], materials with nonlocal [32,33] or competing (focusing) cubic and (defocusing) quintic nonlinearities [34,35], linear spin-orbit coupling [36], etc.…”

“…Corresponds what with this is the 3D spatiotemporal solitons supported by 2D complex lattices were reported so far merely in the self-focusing (attractive, g < 0) nonlinearity regime. In particular, the periodic potentials have shown incomparable band-gap control engineering within where new localized states called localized gap modes like gap solitons and vortices were and still are warmly explored in both experimental and theoretical sides [10][11][12][13][14][15][16][17][18][19][20]. It is therefore a pronounced imagine is to reveal the formation of 3D spatiotemporal solitons in finite gaps of the 2D optical lattices and how and what their stabilization and dynamics configurations would look like.…”