Refraction at the interface between two materials is fundamental to the interaction of light with photonic devices and to the propagation of light through the atmosphere at large¹. Underpinning the traditional rules for the refraction of an optical field is the tacit presumption of the separability of its spatial and temporal degrees of freedom. We show here that endowing a pulsed beam with precise spatiotemporal spectral correlations^2,3,4 unveils remarkable refractory phenomena, such as group-velocity invariance with respect to the refractive index, group-delay cancellation, anomalous group-velocity increase in higher-index materials, and tunable group velocity by varying the angle of incidence. A law of refraction for ‘spacetime’ (ST) wave packets^5,6,7,8,9,10 encompassing these effects is verified experimentally in a variety of optical materials. Spacetime refraction defies our expectations derived from Fermat’s principle and offers new opportunities for moulding the flow of light and other wave phenomena.

在两种材料之间的界面处的折射对于光与光子器件的相互作用以及光通过大气层¹的传播是至关重要的。隐含了其空间时空自由度可分离性的默认推论，是对光场折射的传统规则的基础。我们在这里表明，赋予脉冲束精确的时空光谱相关性^2,3,4揭示了显着的难熔现象，例如相对于折射率的群速度不变性，群延迟抵消，异常高群折射率的增加通过改变入射角来调整材料的速度和可调整的组速度。“时空”（ST）波包的折射定律^5,6,7,8,9,10在各种光学材料中，已通过实验验证了涵盖这些效应的因素。时空折射违反了我们从费马原理得出的期望，并为塑造光流和其他波动现象提供了新的机会。