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1. Dynamics of Dissipative Cavity Solitons in a Lattice Trap

   https://doi.org/10.1002/lpor.202500257  

   Taheri, Hossein; Matsko, Andrey B; Wiesenfeld, Kurt A (May 2025, Laser & Photonics Reviews)

   Dichromatic coherent pumping of optical microresonators possessing broadband Kerr nonlinearity reveals a rich variety of nonlinear and critical phenomena, including time‐translation symmetry breaking, multistability, and chaos. This pumping scheme has garnered significant interest owing to its practical applications arising from optical‐to‐microwave frequency stability transfer and frequency‐division phase noise reduction. In this work, a generalized analytical model is developed to elucidate the dynamics of dissipative Kerr cavity solitons as particles in dual‐frequency pumped Kerr cavities. The model offers quantitative and intuitive insight into the behavior of the system both within and beyond the locking range wherein solitons synchronize to the two driving lasers. It also predicts new phenomena and expounds hitherto unexplained experimental observations covering bistability, hysteresis, and Arnold tongues. The unified framework simultaneously delineates the parameter space for the existence of dissipative discrete time crystals recently reported in dually pumped optical solitons. Bridging a fundamental study with practical applications, this work offers valuable understanding of two‐point injection‐locked microcombs for realizing chip‐scale optical clocks and superior microwave photonic oscillators. 

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2. On the Temporal Tweezing of Cavity Solitons

   https://doi.org/10.1007/s44198-024-00193-1  

   Rossi, Julia; Chandramouli, Sathyanarayanan; Carretero-González, Ricardo; Kevrekidis, Panayotis_G (July 2024, Journal of Nonlinear Mathematical Physics)

   Abstract Motivated by the work of Jang et al., Nat Commun 6:7370 (2015), where the authors experimentally tweeze cavity solitons in a passive loop of optical fiber, we study the amenability to tweezing of cavity solitons as the properties of a localized tweezer are varied. The system is modeled by the Lugiato-Lefever equation, a variant of the complex Ginzburg-Landau equation. We produce an effective, localized, trapping tweezer potential by assuming a Gaussian phase-modulation of the holding beam. The potential for tweezing is then assessed as the total (temporal) displacement and speed of the tweezer are varied, and corresponding phase diagrams are presented. As the relative speed of the tweezer is increased we find two possible dynamical scenarios: successful tweezing and release of the cavity soliton. We also deploy a non-conservative variational approximation (NCVA) based on a Lagrangian description which reduces the original dissipative partial differential equation to a set of coupled ordinary differential equations for the cavity soliton parameters. We illustrate the ability of the NCVA to accurately predict the separatrix between successful and failed tweezing. This showcases the versatility of the NCVA to provide a low-dimensional description of the experimental realization of the temporal tweezing. 

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3. Fabrication of Arrays of Topological Solitons in Patterned Chiral Liquid Crystals for Real‐Time Observation of Morphogenesis

   https://doi.org/10.1002/adma.202201749  

   Park, Geonhyeong; Suh, Ahram; Zhao, Hanqing; Lee, Changjae; Choi, Yun‐Seok; Smalyukh, Ivan_I; Yoon, Dong_Ki (June 2022, Advanced Materials)

   Abstract Topological solitons have knotted continuous field configurations embedded in a uniform background, and occur in cosmology, biology, and electromagnetism. However, real‐time observation of their morphogenesis and dynamics is still challenging because their size and timescale are enormously large or tiny. Liquid crystal (LC) structures are promising candidates for a model‐system to study the morphogenesis of topological solitons, enabling direct visualization due to the proper size and timescale. Here, a new way is found to rationalize the real‐time observation of the generation and transformation of topological solitons using cholesteric LCs confined in patterned substrates. The experimental demonstration shows the topologically protected structures arise via the transformation of topological defects. Numerical modeling based on minimization of free energy closely reconstructs the experimental findings. The fundamental insights obtained from the direct observations pose new theoretical challenges in understanding the morphogenesis of different types of topological solitons within a broad range of scales. 

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4. Weakly nonlinear topological gap solitons in Su–Schrieffer–Heeger photonic lattices

   https://doi.org/10.1364/OL.411102  

   Guo, Min; Xia, Shiqi; Wang, Nan; Song, Daohong; Chen, Zhigang; Yang, Jianke (November 2020, Optics Letters)

   We study both theoretically and experimentally the effect of nonlinearity on topologically protected linear interface modes in a photonic Su–Schrieffer–Heeger (SSH) lattice. It is shown that under either focusing or defocusing nonlinearity, this linear topological mode of the SSH lattice turns into a family of topological gap solitons. These solitons are stable. However, they exhibit only a low amplitude and power and are thus weakly nonlinear, even when the bandgap of the SSH lattice is wide. As a consequence, if the initial beam has modest or high power, it will either delocalize, or evolve into a soliton not belonging to the family of topological gap solitons. These theoretical predictions are observed in our experiments with optically induced SSH-type photorefractive lattices. 

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5. Magnetic skyrmions and domain walls for logical and neuromorphic computing

   https://doi.org/10.1088/2634-4386/acc6e8  

   Hu, Xuan; Cui, Can; Liu, Samuel; Garcia-Sanchez, Felipe; Brigner, Wesley H; Walker, Benjamin W; Edwards, Alexander J; Xiao, T Patrick; Bennett, Christopher H; Hassan, Naimul; et al (May 2023, Neuromorphic Computing and Engineering)

   Abstract Topological solitons are exciting candidates for the physical implementation of next-generation computing systems. As these solitons are nanoscale and can be controlled with minimal energy consumption, they are ideal to fulfill emerging needs for computing in the era of big data processing and storage. Magnetic domain walls (DWs) and magnetic skyrmions are two types of topological solitons that are particularly exciting for next-generation computing systems in light of their non-volatility, scalability, rich physical interactions, and ability to exhibit non-linear behaviors. Here we summarize the development of computing systems based on magnetic topological solitons, highlighting logical and neuromorphic computing with magnetic DWs and skyrmions. 

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