Research Article

Generation of extreme-ultraviolet beams with time-varying orbital angular momentum

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Science  28 Jun 2019:
Vol. 364, Issue 6447, eaaw9486
DOI: 10.1126/science.aaw9486

Pulses with a twist and torque

Structured light beams can serve as vortex beams carrying optical angular momentum and have been used to enhance optical communications and imaging. Rego et al. generated dynamic vortex pulses by interfering two incident time-delayed vortex beams with different orbital angular momenta through the process of high harmonic generation. A controlled time delay between the pulses allowed the high harmonic extreme-ultraviolet vortex beam to exhibit 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.

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Structured Abstract


Light beams carry both energy and momentum, which can exert a small but detectable pressure on objects they illuminate. In 1992, it was realized that light can also possess orbital angular momentum (OAM) when the spatial shape of the beam of light rotates (or twists) around 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 are enabling new applications in optical communications, microscopy, quantum optics, and microparticle manipulation. To date, however, all OAM beams—also known as vortex beams—have been static; that is, the OAM does not vary in time. Here we introduce and experimentally validate a new property of light beams, manifested as a time-varying OAM along the light pulse; we term this property the self-torque of light.


Although self-torque is found in diverse physical systems (e.g., electrodynamics and general relativity), to date it was not realized that light could possess such a property, where no external forces are involved. Self-torque is an inherent property of light, distinguished from the mechanical torque exerted on matter by static-OAM beams. Extreme-ultraviolet (EUV) self-torqued beams naturally arise when the extreme nonlinear process of high harmonic generation (HHG) is driven by two ultrafast laser pulses with different OAM and time delayed with respect to each other. HHG imprints a time-varying OAM along the EUV pulses, where all subsequent OAM components are physically present. In the future, this new class of dynamic-OAM beams could be used for manipulating the fastest magnetic, topological, molecular, and quantum excitations at the nanoscale.


Self-torqued beams are naturally produced by HHG, a process in which an ultrafast laser pulse is coherently upconverted into the EUV and x-ray regions of the spectrum. By driving the HHG process with two time-delayed, infrared vortex pulses possessing different OAM, 1 and 2, the generated high harmonics emerge as EUV beams with a self-torque, ξqq(21)/td, that depends on the properties of the driving fields—that is, their OAM content and their relative time delay (td)—and on the harmonic order (q). Notably, the self-torque of light also manifests as a frequency chirp along their azimuthal coordinate, which enables its experimental characterization. This ultrafast, continuous, temporal OAM variation that spans from q1 to q2 is much smaller than the driving laser pulse duration and changes on femtosecond (10−15 s) and even subfemtosecond time scales for high values of self-torque. The presence of self-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 driving pulses. In addition, if driven by few-cycle pulses, the large amount of frequency chirp results in a supercontinuum EUV spectrum.


We have theoretically predicted and experimentally generated light beams with a new property that we call the self-torque of light, where the OAM content varies extremely rapidly in time, along the pulse itself. This inherent property of light opens additional routes for creating structured light beams. In addition, because the OAM value is changing on femtosecond time scales, at wavelengths much shorter than those of visible light, self-torqued HHG beams can be extraordinary tools for laser-matter manipulation on attosecond time and nanometer spatial scales.

Generation of EUV beams with self-torque.

(A) Two time-delayed, femtosecond infrared (IR) pulses with different OAM are focused into a gas target to produce self-torqued EUV beams through HHG. The distinctive signature of self-torqued beams is their time-dependent OAM, as shown in (B) for the 17th harmonic (47 nm, with self-torque ξ17 = 1.32 fs−1). (C) The self-torque imprints an azimuthal frequency chirp, which enables its experimental measurement.


Light fields carrying orbital angular momentum (OAM) provide powerful capabilities for applications in optical communications, microscopy, quantum optics, and microparticle manipulation. We introduce a property of light beams, manifested as a temporal OAM variation along a pulse: the self-torque of light. Although self-torque is found in diverse physical systems (i.e., electrodynamics and general relativity), it was not realized that light could possess such a property. We demonstrate that extreme-ultraviolet self-torqued beams arise in high-harmonic generation driven by time-delayed pulses with different OAM. We monitor the self-torque of extreme-ultraviolet beams through their azimuthal frequency chirp. This class of dynamic-OAM beams provides the ability for controlling magnetic, topological, and quantum excitations and for manipulating molecules and nanostructures on their natural time and length scales.

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