Temporal uniaxial crystal in a dispersion-modulated lattice model

Time reflection and refraction, as temporal analogs to spatial phenomena, provide a degree of freedom for manipulating wave dynamics within the temporal domain. In this study, we investigate the dynamics of Gaussian wave packets at time interfaces within one-dimensional lattice models, providing insights into generalized temporal refraction and dispersion control. By redefining time reflection as temporal negative refraction, we propose a generalized temporal Snell's law based on the equivalent refractive index, which effectively predicts both temporal positive and negative refraction. Furthermore, we introduce a “temporal uniaxial crystal” by extending our investigation to a three-band model without symmetry constraints, characterized by double temporal positive and negative refraction. Our approach not only deepens the understanding of time refraction but also offers a versatile tool for studying complex wave behaviors in time-variant systems.