自由空间中含角色散光波包群速度的极限。第二部分：不可微角色散：教程
Limits on the free-space group velocity of optical wave packets incorporating angular dispersion. Part~II, non-differentiable angular dispersion: tutorial
- 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）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本教程第二部分提出不可微角色散概念，可在傍轴区域实现光波包群速度显著偏离光速且无高阶色散，并统一了传播不变时空波包的理论框架。
AI中文摘要：
在本教程的第一部分中，我们展示了将角色散（AD）引入准直光脉冲可以实现对波包在自由空间中群速度的调谐。原则上，群速度可以取任意值，无论是超光速、亚光速，甚至是负值。然而，群速度相对于$c$（真空中的光速）的任何显著偏离，都要求脉冲在非傍轴区域中以相对于光轴的大角度传播。在本教程的第二部分中，我们描述了最近发现的一种新形式的角色散，我们称之为“不可微角色散”，它规避了传统（可微）角色散所施加的限制。不可微角色散\textit{并不}指不连续、含有拐点或具有奇异性的角色散分布。相反，不可微角色散分布是连续、光滑的，并且除一个波长外处处可微，在该波长处导数不存在。我们表明，这种不可微性对于调谐自由空间中脉冲光束的群速度带来了有益的特性；即，在傍轴区域内可以实现群速度相对于$c$的显著偏离，同时保持无群速度色散和所有高阶色散效应。本教程概述了这些通过不可微角色散调谐波包群速度的最新结果，并将其与第一部分中概述的传统角色散的相关结果联系起来。此外，我们表明，不可微角色散支撑了传播不变时空波包的独特特性，从而将大量结果统一在一个单一的概念框架中。
英文摘要：
In Part~I of this tutorial, we showed that introducing angular dispersion (AD) into a collimated optical pulse allows for tuning the wave packet group velocity in free space. In principle, the group velocity can take on arbitrary values, whether superluminal, subluminal, or even negative. However, any significant deviation of the group velocity from $c$ (the speed of light in vacuum) necessitates propagation at large angles with respect to the optical axis in the non-paraxial regime. In Part~II of this tutorial, we describe the recent discovery of a new form of AD we refer to as `non-differentiable AD', which circumvents the limits imposed by conventional (differentiable) AD. Non-differentiable AD does \textit{not} refer to an AD profile that is discontinuous, contains a kink, or features a singularity. Rather, a non-differentiable AD profile is continuous, smooth, and is differentiable everywhere except for one wavelength at which the derivative is not defined. We show that salutary features follow from this non-differentiability with respect to tuning the group velocity of a pulsed beam in free space; namely, significant deviations in the group velocity away from $c$ are achievable in the paraxial regime while remaining free of group-velocity dispersion and all higher-order dispersive effects. This tutorial presents an outline of these recent results for tuning the group velocity of a wave packet via non-differentiable AD, connecting them with the corresponding results associated with conventional AD -- as outlined in Part~I. Moreover, we show that non-differentiable AD undergirds the unique characteristics of propagation-invariant space-time wave packets, thus unifying a large swathe of results in a single conceptual framework.
