光子时间晶体中的非线性波动力学
Nonlinear wave dynamics in photonic time crystals
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中文总结 AI 辅助
该研究通过解析简化麦克斯韦方程得到非线性马蒂厄方程，推导同宿分界线等参数，揭示时空带隙孤子成核可产生动量空间超连续谱，建立了非线性光子时间晶体中相关动力学的直接联系。
中文摘要 AI 辅助
针对空间单色波，存在立方非线性项和周期性时变折射率（即光子时间晶体）的麦克斯韦波动方程可简化为非线性马蒂厄方程。在主动量带隙附近，该方程存在自治二维简化形式，其完整哈密顿相图可通过解析方法获得。我们推导了对应时间局域动量带隙孤子的两条同宿分界线，确定了非线性中心和临界哈密顿值H_c，并计算了最大线性参量增益点。随后我们研究了空间局域脉冲，展示了多时空带隙孤子的成核如何在动量空间产生宽超连续谱；对于更强的种子，瞬态极端非线性局域会伴随该动量谱的突然额外展宽。这些结果建立了非线性光子时间晶体中弗洛凯放大、非线性饱和、同宿动力学与动量空间光谱展宽之间的直接联系。
英文摘要
Maxwell's wave equation in the presence of a cubic nonlinearity and a periodically time-varying refractive index (a photonic time crystal) is reduced, for spatially monochromatic waves, to a nonlinear Mathieu equation. Near the principal momentum gap this equation admits an autonomous two-dimensional reduction whose complete Hamiltonian phase portrait can be obtained analytically. We derive the two homoclinic separatrices corresponding to temporally localised momentum gap solitons, identify the nonlinear centres and the critical Hamiltonian value $H_c$, and calculate the point of maximum linear parametric gain. We then consider spatially localised pulses and show how the nucleation of multiple spatiotemporal gap solitons can produce a broad supercontinuum in momentum space; for stronger seeds, transient extreme nonlinear localisation can accompany an abrupt additional broadening of this momentum spectrum. These results establish a direct connection between Floquet amplification, nonlinear saturation, homoclinic dynamics, and momentum space spectral broadening in nonlinear photonic time crystals.
