Quadrics for Structuring Invariant Space–Time Wavepackets
Pierre Béjot, Bertrand Kibler
Abstract
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.