Active devices have drawn considerable attention owing to their powerful capabilities to manipulate electromagnetic waves. Fast and periodic modulation of material properties is one of the key obstacles to the practical implementation of active metamaterials and metasurfaces. In this study, to circumvent this limitation, we employ a cascaded phase-matching mechanism to amplify signals through spatiotemporal modulation of permittivity. Our results show that the energy of the amplified fundamental mode can be efficiently transferred to that of the high harmonic components if the spatiotemporal modulation travels at the same speed as the signals. This outstanding benefit enables a low-frequency pump to excite parametric amplification. The realization of cascaded parametric amplification is demonstrated by finite-difference time-domain (FDTD) simulations and analytical calculations based on the Bloch–Floquet theory. We find that the same lasing state can always be excited by an incidence at different harmonic frequencies. The spectral and temporal responses of the space-time modulated slab strongly depend on the modulation length, modulation strength, and modulation velocity. Furthermore, the cascaded parametric oscillators composed of a cavity formed by photonic crystals are presented. The lasing threshold is significantly reduced by the cavity resonance. Finally, the excitation of cascaded parametric amplification relying on the Si-waveguide platform is demonstrated. We believed that the proposed mechanism provides a promising opportunity for the practical implementation of intense amplification and coherent radiation based on active metamaterials.

中文翻译：

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基于时空调制的级联参量放大

有源器件由于其强大的电磁波操纵能力而备受关注。材料特性的快速和周期性调制是活性超材料和超表面实际应用的主要障碍之一。在这项研究中，为了规避这一限制，我们采用级联相位匹配机制通过介电常数的时空调制来放大信号。我们的结果表明，如果时空调制以与信号相同的速度传播，则放大基模的能量可以有效地转移到高次谐波分量的能量。这一显着优势使低频泵能够激发参量放大。基于 Bloch-Floquet 理论的时域有限差分 (FDTD) 模拟和解析计算证明了级联参数放大的实现。我们发现相同的激光态总是可以被不同谐波频率的入射激发。时空调制平板的光谱和时间响应在很大程度上取决于调制长度、调制强度和调制速度。此外，还介绍了由光子晶体形成的腔体组成的级联参量振荡器。腔共振显着降低了激光阈值。最后，展示了基于硅波导平台的级联参量放大的激发。