自由空间中包含角色散的光波包群速度极限。第一部分，常规角色散：教程
Limits on the free-space group velocity of optical wave packets incorporating angular dispersion. Part~I, conventional angular dispersion: tutorial
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- University of Central Florida（中佛罗里达大学）
- Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
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中文总结 AI 辅助
本文通过时空结构化脉冲光束，证明自由空间中可实现任意群速度，突破传统直觉限制，并系统分析了常规角色散引起的群速度偏差及其色散影响。
中文摘要 AI 辅助
平面波光脉冲在自由空间中沿其传播轴测量的群速度为 $c$（真空中的光速）。有时人们认为，在自由空间中对场进行空间结构化会使其群速度低于 $c$，因为直观上，构成波包的倾斜波矢会增加平均群延迟。在此，我们表明，对脉冲光束（或波包）进行时空结构化，原则上可以在自由空间中产生任意群速度，这与上述常见直觉相反。我们在此关注具有角色散（AD）的脉冲，其中传播角依赖于波长。这类波包特别重要，因为它们的群速度在横向场分布和传播轴上都是恒定的，从而产生明确的群延迟。然而，自由空间中AD引起的群速度与 $c$ 的显著偏差不可避免地需要大的数值孔径，这深处于非傍轴区域，并且此类波包会经历AD引起的群速度色散。本文提出的公式涵盖了一系列广泛的结果，并将它们统一在一个框架中。在本教程的第二部分，我们描述了最近发现的“不可微角色散”（与传播不变时空波包相关），它有助于规避本文所述的常规（可微）角色散相关的极限。
英文摘要
A plane-wave optical pulse travels in free space at a group velocity $c$ (the speed of light in vacuum) measured along its propagation axis. It is sometimes thought that spatially structuring the field in free space reduces the group velocity below $c$ because -- intuitively -- the oblique wave vectors undergirding the wave packet increase the average group delay. Here we show that spatiotemporally structuring a pulsed optical beam (or wave packet) can yield -- in principle -- arbitrary group velocities in free space in contradistinction to this commonly held intuition. We devote our attention here to pulses endowed with angular dispersion (AD) where the propagation angle is wavelength dependent. This class of wave packets is particularly pertinent because their group velocity is constant over the transverse field profile and along the propagation axis, thereby yielding an unambiguous group delay. However, significant deviation of the AD-induced group velocity in free space from~$c$ inevitably requires a large numerical aperture that lies deep in the non-paraxial regime, and such wave packets experience AD-induced group-velocity dispersion. The formulation presented here captures a broad range of results, connecting them in a single framework. In Part~II of this tutorial, we describe recently identified `non-differentiable AD' (associated with propagation-invariant space-time wave packets) that helps circumvent the limits associated with conventional (differentiable) AD as outlined here.
