Space-time (ST) wave packets are pulsed optical beams endowed with precise spatio-temporal structure by virtue of which they exhibit unique and useful characteristics such as propagation invariance and tunable group velocity. We study in detail here, and in two accompanying papers, the refraction of ST wave packets at planar interfaces between non-dispersive, homogeneous, and isotropic dielectrics. We formulate a law of refraction that determines the change in the ST wave-packet group velocity across such an interface as a consequence of a newly identified optical refractive invariant that we call the “spectral curvature”. Because the spectral curvature vanishes in conventional optical fields where the spatial and temporal degrees of freedom are separable, these phenomena have not been observed to date. We derive the laws of refraction for baseband, ${X}$ wave, and sideband ST wave packets that reveal fascinating refractive phenomena, especially for the former class of wave packets. We predict theoretically, and confirm experimentally in the accompanying papers, refractive phenomena such as group-velocity invariance (ST wave packets whose group velocity does not change across the interface), anomalous refraction (group-velocity increase in higher-index media), group-velocity inversion (change in the sign of the group velocity upon refraction but not its magnitude), and the dependence of the group velocity of the refracted ST wave packet on the angle of incidence.

中文翻译：

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时空波包的折射：一、理论原理

时空 (ST) 波包是具有精确时空结构的脉冲光束，因此它们表现出独特而有用的特性，例如传播不变性和可调群速度。我们在此处以及随附的两篇论文中详细研究了 ST 波包在非色散、均质和各向同性电介质之间的平面界面处的折射。我们制定了一个折射定律，该定律确定了由于新发现的光学折射不变量（我们称为“光谱曲率”）而导致的跨这种界面的 ST 波包群速度的变化。由于光谱曲率在空间和时间自由度可分离的传统光场中消失，因此迄今为止尚未观察到这些现象。${X}$波和边带 ST 波包，揭示了迷人的折射现象，尤其是前一类波包。我们从理论上预测并在随附的论文中通过实验证实了折射现象，例如群速度不变性（ST 波包的群速度在界面上不会改变）、异常折射（高折射率介质中的群速度增加）、群-速度反演（折射时群速度的符号发生变化，但不改变其幅度），以及折射 ST 波包的群速度对入射角的依赖性。