Space–time light structuring has emerged as a very powerful tool for controlling the propagation dynamics of pulsed beams. The ability to manipulate and generate space–time distributions of light has been remarkably enhanced in past few years, letting us envision applications across the entire spectrum of optics. Space–time invariant optical wavepackets manipulated up to now are usually two-dimensional objects (one space dimension and time) whose mode-resolved spectra lie in a conical section. Using simple symmetry and invariance principles, we show that such wavepackets are particular cases of more general three-dimensional structures whose space–time frequencies lie on quadric surfaces. Our proposed framework allows classifying invariant space–time wavepackets localized in all dimensions in any group velocity dispersion regime, both in bulk and waveguides. Particular emphasis is placed on longitudinal orbital angular momentum-carrying space–time wavepackets. This unprecedented theoretical approach paves the way for versatile synthesizing of space–time optics.

中文翻译：

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构造不变时空波包的二次曲线

时空光结构化已成为控制脉冲光束传播动力学的非常强大的工具。在过去的几年里，操纵和产生光的时空分布的能力得到了显着增强，让我们可以设想在整个光学光谱中的应用。到目前为止，操作的时空不变光波包通常是二维物体（一个空间维和时间），其模式分辨光谱位于锥形截面中。使用简单的对称性和不变性原理，我们表明这种波包是更一般的三维结构的特例，其时空频率位于二次曲面上。我们提出的框架允许在任何群速度色散机制中对位于所有维度的不变时空波包进行分类，无论是散装还是波导。特别强调了携带纵向轨道角动量的时空波包。这种前所未有的理论方法为时空光学的多功能合成铺平了道路。