一种时态元表面的能量保存机制
An Energy Conserving Mechanism for Temporal Metasurfaces
摘要：
当波传播通过时空超材料时，改变时空超材料的微结构特性通常需要增加或去除能量，这取决于调制类型可以是指数形式。这限制了时空超材料的实现和应用。我们解决了这个问题，通过引入一种新的机制，在非线性设置的时间元表面上保存能量。首先通过考虑在一维弹簧和质量链的离散介质中传播的波包来证明这个想法，其中使用我们的能量守恒机制，我们表明弹簧刚度可以在几个时间界面处增加，并且能量仍然守恒。然后，我们考虑一个有趣的应用程序的时间反演成像在1-d和2-d弹簧质量系统与一个波包旅行的均匀制度。我们的数值模拟表明，在1-d，当波包击中时间界面产生两组波，一个在时间上向前传播，另一个向后传播。时间反演的波重新汇聚在源的位置，我们观察到它的再生。在二维中，我们使用更复杂的初始形状，即使这样，我们也可以观察到原始图像或源的再生。因此，我们在非线性系统中实现了具有能量守恒的时间反演成像。能量守恒机制可以很容易地推广到连续介质。
英文摘要：
Changing the microstructure properties of a space-time metamaterial while a wave is propagating through it, in general requires addition or removal of energy, which can be of exponential form depending on the type of modulation. This limits the realization and application of space-time metamaterials. We resolve this issue by introducing a novel mechanism of conserving energy at temporal metasurfaces in a non-linear setting. The idea is first demonstrated by considering a wave-packet propagating in a discrete medium of 1-d chain of springs and masses, where using our energy conserving mechanism we show that the spring stiffness can be incremented at several time interfaces and the energy will still be conserved. We then consider an interesting application of time-reversed imaging in 1-d and 2-d spring-mass systems with a wave packet traveling in the homogenized regime. Our numerical simulations show that, in 1-d, when the wave packet hits the time-interface two sets of waves are generated, one traveling forward in time and the other traveling backward. The time-reversed waves re-converge at the location of the source and we observe its regeneration. In 2-d, we use more complicated initial shapes and, even then, we observe regeneration of the original image or source. Thus, we achieve time-reversed imaging with conservation of energy in a non-linear system. The energy conserving mechanism can be easily extended to continuum media.
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