Title: Non-Foster Photonic Time Crystals Show Chinese title

Title: 非福斯特光子时间晶体

Abstract: Photonic time crystals (PhTCs) are spatially uniform media whose material parameters vary periodically in time, opening momentum bandgaps within which the fields of electromagnetic modes can grow exponentially in time. To date, PhTCs have utilized only passive, lossless materials with "positive" dispersion (Foster materials), and a theoretical framework addressing active materials with "negative" dispersion (non-Foster materials) in PhTCs and their associated physical properties remains undeveloped. Here, we explore the two classes of isotropic PhTCs with embedded non-Foster inclusions: a bulk medium with periodically modulated negative permittivity, and a metasurface whose surface capacitance alternates between positive and negative values. Employing an analytical transfer-matrix formulation, we demonstrate that non-Foster permittivity modulation not only broadens momentum bandgaps without bounds but also provides a gain rate that increases linearly with momentum. Remarkably, the proposed isotropic PhTCs support exponential amplification down to zero frequency-a regime inaccessible in conventional isotropic PhTCs. These results open new avenues for ultra-broadband wave control, high-gain signal processing, and energy-harvesting devices that leverage the unique dispersion of active, time-modulated circuitry. Show Chinese abstract

Abstract: 光子时间晶体（PhTCs）是空间均匀的介质，其材料参数在时间上周期性变化，在其中电磁模式的场可以随时间指数增长。到目前为止，PhTCs仅使用了被动、无损耗的材料，具有“正”色散（Foster材料），而针对PhTCs中具有“负”色散（非Foster材料）的主动材料及其相关物理特性的理论框架尚未建立。在这里，我们研究了两种具有嵌入式非Foster包含物的各向同性PhTCs：一种是具有周期性调制负介电常数的体介质，另一种是表面电容在正负值之间交替变化的超表面。采用解析传递矩阵公式，我们证明非Foster介电常数调制不仅无限制地拓宽动量带隙，还提供一个与动量成线性增加的增益率。值得注意的是，所提出的各向同性PhTCs支持从零频率开始的指数放大——这一区域在传统各向同性PhTCs中是无法达到的。这些结果为超宽带波控制、高增益信号处理和利用主动时间调制电路独特色散的能量收集装置开辟了新的途径。