Spatiotemporal optical vortices with controllable radial and azimuthal quantum numbers

TL;DR

This paper explores the creation and control of complex 3D spatiotemporal optical vortices with specific quantum numbers, demonstrating mode conversion techniques and potential applications in quantum information and nonlinear optics.

Contribution

It introduces a new class of spatiotemporal Laguerre-Gaussian wavepackets with controllable quantum numbers and demonstrates mode conversion with Hermite-Gaussian wavepackets.

Findings

Spatiotemporal Laguerre-Gaussian wavepackets exhibit phase singularities and multi-ring topology.

Mode conversion between STLG and ST Hermite-Gaussian wavepackets is achieved via spatiotemporal astigmatism.

The study offers insights into high-dimensional quantum information and photonic topology.

Abstract

Optical spatiotemporal vortices with transverse photon orbital angular momentum (OAM) have recently become a focal point of research. In this work we theoretically and experimentally investigate optical spatiotemporal vortices with radial and azimuthal quantum numbers, known as spatiotemporal Laguerre-Gaussian (STLG) wavepackets. These 3D wavepackets exhibit phase singularities and cylinder-shaped edge dislocations, resulting in a multi-ring topology in its spatiotemporal profile. Unlike conventional ST optical vortices, STLG wavepackets with non-zero p and l values carry a composite transverse OAM consisting of two directionally opposite components. We further demonstrate mode conversion between an STLG wavepacket and an ST Hermite-Gaussian wavepacket through the application of strong spatiotemporal astigmatism. The converted STHG wavepacket is de-coupled in intensity in space-time domain that can be utilized to implement the efficient and accurate recognition of ultrafast STLG wavepackets carried various p and l. This study may offer new insights into high-dimensional quantum information, photonic topology, and nonlinear optics, while promising potential applications in other wave phenomena such as acoustics and electron waves.