High Power Laser Science and Engineering, (2017), Vol. 5, e3, 8 pages.
© The Author(s) 2017. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/
licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
doi:10.1017/hpl.2017.1
Attosecond twisted beams from high-order harmonic
generation driven by optical vortices
Carlos Hern
´
andez-Garc
´
ıa
1
, Laura Rego
1
, Julio San Rom
´
an
1
, Antonio Pic
´
on
1,2
, and Luis Plaja
1
1
Grupo de Investigaci
´
on en Aplicaciones del L
´
aser y Fot
´
onica, Departamento de F
´
ısica Aplicada, University of Salamanca,
E-37008, Salamanca, Spain
2
Argonne National Laboratory, Argonne, IL 60439, USA
(Received 29 June 2016; revised 21 December 2016; accepted 26 December 2016)
Abstract
Optical vortices are structures of the electromagnetic field with a spiral phase ramp about a point-phase singularity,
carrying orbital angular momentum (OAM). Recently, OAM has been imprinted to short-wavelength radiation through
high-order harmonic generation (HHG), leading to the emission of attosecond twisted beams in the extreme-ultraviolet
(XUV) regime. We explore the details of the mapping of the driving vortex to its harmonic spectrum. In particular, we
show that the geometry of the harmonic vortices is convoluted, arising from the superposition of the contribution from the
short and long quantum paths responsible of HHG. Finally, we show how to take advantage of transverse phase-matching
to select twisted attosecond beams with different spatiotemporal properties.
Keywords: attosecond science; extreme-ultraviolet vortices; high harmonic generation; orbital angular momentum; twisted beams; vortex
beams
1. Introduction
Twisted beams, also called optical vortices, exhibit a helical
phase structure that imprints orbital angular momentum
(OAM) to the beam, in addition to the spin angular mo-
mentum associated with the polarization
[1–3]
. These singular
beams, commonly generated in the optical spectral region,
have potential technological applications in optical com-
munication, micromanipulation, phase-contrast microscopy,
among others
[4–7]
. The production of twisted beams in the
extreme-ultraviolet (XUV) and x-ray regimes is of great
interest as it allows for the extension of the applications of
optical vortices down to the nanometric scale. In this short-
wavelength regime one can drastically reduce the diffrac-
tion limit, as well as exploit the selectively site-specific
excitation, with an important impact in microscopy and
spectroscopy
[8–14]
. Several proposals have been explored
in order to generate x-ray vortices in synchrotrons and
FEL facilities
[15–18]
. However, the generation of twisted
beams carrying OAM in the x-ray regime is limited by the
availability of efficient optical and diffractive elements.
In the last years, high-order harmonic generation (HHG)
has been used to generate XUV vortices by imprint-
ing the phase singularities in the infrared (IR) driving
Correspondence to: C. Hern
´
andez-Garc
´
ıa, Plaza de la Merced s/n, E-
37008, Salamanca, Spain. Email: carloshergar@usal.es
beam
[13, 19, 20]
. HHG is a unique non-perturbative process,
that combines microscopic and macroscopic physics to
produce coherent XUV to soft x-ray radiation in the form
of attosecond pulses
[21–25]
. When an intense IR beam is
focused into a gas target, the laser–matter interaction in each
atom or molecule results in the emission of higher-order
harmonics of the driving field. Microscopically, HHG can be
understood with simple semiclassical arguments
[26, 27]
: an
electron is first tunnel-ionized from an atom, then accelerated
in the continuum, and, due to the oscillatory behavior of
the driving field, its recollision with the parent ion leads
to the emission of higher-frequency radiation. Interestingly,
there are two possible electronic quantum paths leading to
the same kinetic energy at the recollision process – and
thus to the same harmonic – known as short and long
trajectories
[28, 29]
. Macroscopically, the coherent addition of
the radiation emitted from all the atoms in the target – also
known as phase-matching
[30–32]
– plays a relevant role for
the efficient production of XUV/soft x-ray harmonics
[30, 33]
.
One can define longitudinal – or transverse – phase-matching
as the interference of the harmonic emission emitted from
different atoms in the target placed along the longitudinal
or transverse direction
[34]
. Transverse phase-matching is
especially relevant in HHG driven by vortex beams due to
their involved transverse field structure
[35]
.
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