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.

Collapse Dynamics of Vector Vortex Beams in Kerr Medium with Parity–Time-Symmetric Lattice Modulation

“…Recently, the concept of PT symmetry originated from the study of quantum mechanics and has been introduced into optical systems [20][21][22][23][24][25][26]. It is worth noting that the parity-Photonics 2024, 11, 345 2 of 13 time (PT)-symmetric lattice, as an interesting periodic structure, has been extensively studied in nonlinear optics and soliton physics [27][28][29][30]; in particular, the study of the stabilization mechanisms of various solitons in PT-symmetric systems has obtained fruitful achievements [31][32][33][34][35]. Many novel applications in linear and nonlinear PT symmetry optics systems have been demonstrated, such as the localization of light, unidirectional transmission, and information encryption [36][37][38][39][40].…”

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.…”

One-Dimensional Gap Soliton Molecules and Clusters in Optical Lattice-Trapped Coherently Atomic Ensembles via Electromagnetically Induced Transparency

“…Diverse localized modes (no matter the matter waves or classical waves), including fundamental solitons, gap solitons, and vortices, have been found with the help of periodic potentials and under nonlinear regimes [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]; the latter two modes combine the finite gap's strong localization and materials's nonlinearity, enabling the formation and control of robust localized gap modes. Recently, the localization of light and matters has been extended to a novel twisted structure named Moiré superlattices that can be tuned to periodic form under the Pythagorean angle and an aperiodic one for other angles [34][35][36][37][38][39][40][41]; particularly, soliton formation and gap solitons and vortical ones have been addressed in such settings [28,[39][40][41][42][43]. It is deserved to be emphasized that twisted structures such as Moiré optical lattices can be made easily in optics and condensed matter physics experiments, providing a new controllable (twisted angle) degree of freedom in studying the linear, nonlinear, and quantum properties of light and matter waves.…”