Event Soliton Formation in Mixed Energy-Momentum Gaps of Nonlinear Spacetime Crystals

• URL: http://arxiv.org/abs/2503.16113v1
• Date: Thu, 20 Mar 2025 13:00:56 GMT
• Title: Event Soliton Formation in Mixed Energy-Momentum Gaps of Nonlinear Spacetime Crystals
• Authors: Liang Zhang, Zhiwei Fan, Yiming Pan,
• Abstract summary: We report the formation of a novel soliton, termed event soliton, in nonlinear photonic spacetime crystals.<n>Under nonlinearity, the event solitons emerge as fully localized entities in both spacetime energy andmomentum domains.
• Score: 3.7004243429570476
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We report the formation of a novel soliton, termed event soliton, in nonlinear photonic spacetime crystals (STCs). In these media, simultaneous spatiotemporal periodic modulation of the dielectric constant generates mixed frequency (${\omega}$) and wavevector (k) gaps. Under Kerr nonlinearity, the event solitons emerge as fully localized entities in both spacetime and energy-momentum domains, providing a tangible demonstration of the concept of event in relativity. The ${\omega}$k-gap mixture arises from the coexistence and competition between time reflected and Bragg reflected waves due to the spatiotemporal modulation. We propose a new partial differential equation to capture various spatiotemporal patterns and present numerical simulations to validate our theoretical predictions, reflecting a three-way balance among k-gap opening, ${\omega}$-gap opening, and nonlinearity. Our work opens avenues for fundamental studies and fosters experimental prospects for implementing spacetime crystals in both time-varying photonics and periodically driven condensed matter systems.

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