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# Generation of extreme ultraviolet rays with time-varying orbital angular momentum

## Pulses with Twist and Torque

Structured light rays can serve as eddy beams with optical angular momentum and have been used to improve optical communication and imaging. Rego et al. generated dynamic vortex pulses through the interference of two time-delayed vortex beams with different orbital angular momentum through the process of generating high harmonics. A controlled time delay between pulses allowed the high-harmonic ultraviolet vortex beam to have a time-dependent angular momentum called self-torque. Such dynamic vortex pulses could potentially be used to manipulate nanostructures and atoms on ultrafast time scales.

Science this edition, S. eaaw9486

## Structured Summary

### INTRODUCTION

Light rays carry both energy and momentum, which can exert a small but detectable pressure on illuminated objects. In 1992, it was recognized that light can have an angular momentum (OAM) even when the spatial shape of the light beam rotates (or twists) about its own axis. Although not visible to the naked eye, the presence of OAM can be revealed when the light beam interacts with matter. OAM beams enable new applications in the fields of optical communication, microscopy, quantum optics and microparticle manipulation. So far, however, were all OAM rays – also known as vortex rays – static. That is, the OAM does not change in time. Here we introduce a new property of light rays and validate them experimentally, which manifests itself as a time-variable OAM along the light pulse. we call this property the self-torque of light.

### RATIONALE

Although self-torque can be found in various physical systems (eg, electrodynamics and general relativity), it has not been recognized that light could have such a property where no external forces are involved. The self-torque is an inherent property of light and is different from the mechanical torque exerted by static OAM rays on the matter. Ultraviolet (EUV) self-timed radiation naturally arises when the extreme non-linear process of high harmonic generation (HHG) is driven by two ultrafast laser pulses with different OAM and time delay to each other. HHG imposes a time-varying OAM along the EUV pulses with all subsequent OAM components physically present. This new class of dynamic OAM rays could be used in the future to manipulate the fastest nanoscale magnetic, topological, molecular, and quantum excitations.

### RESULTS

Self-aligned beams are generated by HHG, a method in which an ultrafast laser pulse is coherently upconverted to the EUV and X-ray regions of the spectrum. By driving the HHG process with two time-delayed, infrared vortex pulses with different OAM

$ℓ 1$

and

$ℓ 2$

the generated high harmonics arise as EUV rays with a Self-torque

$– ξ q ≃ ℏ q ( ℓ 2 – ℓ 1 19659029]) / t d$

this depends on the characteristics of the driving fields, ie their OAM content and relative time delay ( t d ) – and to the harmonic order ( q ). Remarkably, the self-torque of light also manifests as a frequency chirp along its azimuth coordinate, allowing for its experimental characterization. This ultrafast, continuous temporal OAM variation extending from

$q 1$

to

$q 2$

is much smaller than the driving laser pulse duration and changes to femtoseconds (10 -15 s) and even sub-femtosecond timescales for high values ​​of self-torque. The presence of intrinsic torque in the experimentally generated EUV beams is confirmed by measuring their azimuthal frequency chirp, which is controlled by adjusting the time delay between the drive pulses. Moreover, the large amount of frequency chirp, when driven by pulses of few cycles, results in a supercontinuum EUV spectrum.

### CONCLUSION

We have theoretically predicted and experimentally generated light rays with a new property, which we call the self-momentum of light, in which the OAM content changes extremely fast along the pulse over time. This inherent property of light provides additional ways of producing patterned light rays. Because the OAM value changes on femtosecond timescales and the wavelengths are much shorter than that of visible light, self-centered HHG beams can be exceptional tools for manipulating laser material at attosecond time and nanometer scale scales.

## Abstract

Light Fields The OAM (Carrying Orbital Angular Momentum) provides powerful features for applications in the fields of optical communication, microscopy, quantum optics, and microparticle manipulation. Number of light rays appearing as lines to manifest a natural OAM variation along a momentum: the self-momentum of light. Although self-torque is found in various physical systems (i.e., electrodynamics and general relativity), it was not recognized that light could have such a property. We show that extremely ultraviolet self-aligned beams occur in the generation of high harmonics driven by time-delayed pulses of varying OAM. We monitor the momentum of extreme ultraviolet rays through their azimuthal frequency chirp. This class of dynamic OAM rays offers the opportunity to control magnetic, topological, and quantum excitations, and to manipulate molecules and nanostructures on their natural time and length scales.