Quadrics for Structuring Invariant Space-Time Wavepackets

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.

Automated summary

Space-time light structuring is a powerful tool for controlling the dynamics of pulsed beams. Recent advancements have greatly enhanced the ability to manipulate and generate space-time distributions of light, allowing for applications across the field of optics. This study proposes a framework to classify light wavepackets in all dimensions, with a focus on those carrying orbital angular momentum. This theoretical approach opens up possibilities for versatile synthesis of space-time optics.