Yessenov Murat, Bhaduri Basanta, Abouraddy Ayman F
J Opt Soc Am A Opt Image Sci Vis. 2021 Oct 1;38(10):1409-1422. doi: 10.1364/JOSAA.430105.
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, 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.
时空（ST）波包是具有精确时空结构的脉冲光束，凭借这一结构它们展现出诸如传播不变性和可调群速度等独特且有用的特性。我们在此处以及两篇相关论文中详细研究了ST波包在非色散、均匀且各向同性电介质的平面界面处的折射情况。我们制定了一条折射定律，该定律确定了由于一种新发现的我们称之为“光谱曲率”的光学折射不变量，ST波包群速度在这样一个界面处的变化。由于光谱曲率在空间和时间自由度可分离的传统光学场中消失，这些现象迄今尚未被观测到。我们推导了基带、波和边带ST波包的折射定律，这些定律揭示了引人入胜的折射现象，特别是对于前一类波包。我们在理论上进行了预测，并在相关论文中通过实验证实了诸如群速度不变性（群速度在界面处不发生变化的ST波包）、反常折射（在高折射率介质中群速度增加）、群速度反转（折射时群速度符号改变但大小不变）以及折射后的ST波包群速度对入射角的依赖性等折射现象。
