基于逆采样角谱的切比雪夫自成像
Chebyshev self-imaging from inverse-sampled angular spectra
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中文总结 AI 辅助
该研究提出通过逆采样角谱实现可编程的切比雪夫自成像，将自由空间衍射转化为整数乘法结构的读出，观测到素幂阶梯状的自成像复兴。
中文摘要 AI 辅助
近两个世纪以来，传统自成像遵循单一规律：周期波会在固定距离处重现自身，与带宽无关。本文表明该规律可编程：按模式指数的逆幂采样角谱，可使各模式以自身整数周期重新相位同步，将精确复兴延迟至所有周期的最小公倍数：$z_{\text{rev}}=z_{\text{T}}\text{e}^{r\boldsymbol{\text{ψ}}(M)}$，其中$\boldsymbol{\text{ψ}}$为第二类切比雪夫函数。实验中在传播距离上观测到这些复兴呈素幂阶梯状，将自由空间衍射转化为整数乘法结构的读出。
英文摘要
For nearly two centuries, conventional self-imaging has obeyed a single rule: a periodic wave reconstructs itself at a fixed distance, independent of its bandwidth. Here we show this law is programmable. Sampling the angular spectrum in inverse powers of the mode index makes each mode rephase with its own integer period, deferring exact revival to the least common multiple of all periods: $z_{\mathrm{rev}}=z_{\mathrm{T}}\,e^{rψ(M)}$, with $ψ$ the second Chebyshev function. We observe these revivals optically as a prime-power staircase in propagation distance, turning free-space diffraction into a readout of the multiplicative structure of the integers.
