$\mathcal{PT}$对称复杂晶体中的Talbot自成像
Talbot self-imaging in $\mathcal{PT}$-symmetric complex crystals
摘要：
Talbot效应是周期波在近场衍射中的自成像特性，是具有连续平移不变性的傍轴系统中的一种显著干涉现象。在晶体中，即具有离散平移不变性的系统中，自成像一直被认为是一种罕见的效应，仅限于特定的初始场分布。在这里，它表明，在一类无间隙的$\mathcal{PT}$对称复杂的晶体在对称性破缺阈值Talbot复兴可以出现几乎任何初始周期波分布，这是相称的晶格周期。一个可能的实验实现相称的泰伯自成像的光脉冲在复杂的“时间”晶体，实现在一个光色散光纤环的振幅和相位调制器，简要讨论。
英文摘要：
The Talbot effect, i.e. the self-imaging property of a periodic wave in near-field diffraction, is a remarkable interference phenomenon in paraxial systems with continuous translational invariance. In crystals, i.e. systems with discrete translational invariance, self-imaging has been regarded so far as a seldom effect, restricted to special sets of initial field distributions. Here it is shown that in a class of gapless $\mathcal{PT}$-symmetric complex crystals at the symmetry breaking threshold Talbot revivals can arise for almost any initial periodic wave distribution which is commensurate with the lattice period. A possible experimental realization of commensurate Talbot self-imaging for light pulses in complex 'temporal' crystals, realized in an optical dispersive fiber loop with amplitude and phase modulators, is briefly discussed.
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