具有任意复兴间距的精确自成像
Exact Self-Imaging with Arbitrary Revival Spacings
AI总结：
通过规范相空间几何揭示自成像的隐藏自由度，实现沿传播轴加速、减速及多项式、指数、正弦轨迹的Talbot地毯。
摘要：
自成像是近轴波演化的核心特征；然而，在过去的两个世纪中，尽管有许多实现和推广，但沿传播轴的复现平面的均匀性一直被认为是基本的。在这里，我们在规范相空间几何的自然框架内重新表述自成像的一般现象，揭示了一个隐藏的规范坐标，其中所有精确自成像确实是均匀的，但不必对应于物理传播轴。这导致了一个自成像的一般定律，其中物理复现平面的间距可以通过初始横向相位结构的选择来规定。使用单个可编程空间光调制器，我们演示了以沿传播轴加速和减速的复现间距为特征的Talbot地毯的构建，以及那些遵循多项式、指数和正弦轴向轨迹的Talbot地毯。这些结果揭示了近轴波传播中隐藏的几何自由度：精确自成像在规范坐标中是刚性的，但在物理空间中是自由可编程的，允许定性的新型光学复现。
英文摘要：
Self-imaging represents a core hallmark of paraxial wave evolution; yet, across its many realizations and generalizations over the past two centuries, the uniformity of recurrence planes along the propagation axis has been considered fundamental. Here we reformulate the general phenomenon of self-imaging within the natural framework of canonical phase-space geometry, revealing a hidden canonical coordinate in which all exact self-imaging is indeed uniform, but which need not correspond to the physical propagation axis. This leads to a general law of self-imaging, in which the spacing of the physical recurrence planes can be prescribed through the choice of initial transverse phase structure. Using a single programmable spatial light modulator, we demonstrate the construction of Talbot carpets characterized by recurrence spacings that accelerate and decelerate along the propagation axis, as well as those that follow polynomial, exponential, and sinusoidal axial trajectories. These results reveal a hidden geometric freedom in paraxial wave propagation: exact self-imaging is rigid in canonical coordinates, but freely programmable in physical space, allowing for qualitatively new forms of optical recurrence.
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