Abstract

Vector beams, beams with a non-uniform state of polarization, have become an indispensable tool in many areas of science and technology. Harnessing topological light properties paves the way to control and manipulate light–matter interactions at different levels, from the quantum to macroscopic physics. Here we generate tabletop extreme ultraviolet (EUV) vector beams driven by high-order harmonic generation (HHG). Our experimental and theoretical results demonstrate that HHG imprints the polarization state of the fundamental (infrared) beam, ranging from radial to azimuthal, into the higher frequency radiation. Our numerical simulations also demonstrate that the generated high-order harmonic beams can be synthesized into attosecond vector beams in the EUV/soft x-ray regime. Our proposal overcomes the state-of-the-art-limitations for the generation of vector beams far from the visible domain and could be applied in fields such as diffractive imaging, EUV lithography, or ultrafast control of magnetic properties.

© 2017 Optical Society of America

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References

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2016 (7)

C. Guclu, M. Veysi, and F. Capolino, “Photoinduced magnetic nanoprobe excited by an azimuthally polarized vector beam,” ACS Photon. 3, 2049–2058 (2016).
[Crossref]

R. Drevinskas, J. Zhang, M. Beresna, M. Gecevicius, A. G. Kazanskii, Y. P. Svirko, and P. G. Kazansky, “Laser material processing with tightly focused cylindrical vector beams,” Appl. Phys. Lett. 108, 221107 (2016).
[Crossref]

L. Rego, J. San Román, A. Picón, L. Plaja, and C. Hernández-García, “Nonperturbative twist in the generation of extreme-ultraviolet vortex beams,” Phys. Rev. Lett. 117, 163202 (2016).
[Crossref]

R. Géneaux, A. Camper, T. Auguste, O. Gobert, J. Caillat, R. Taïeb, and T. Ruchon, “Synthesis and characterization of attosecond light vortices in the extreme ultraviolet,” Nat. Commun. 7, 12583 (2016).
[Crossref]

C. Chen, Z. Tao, C. Hernández-García, P. Matyba, A. Carr, R. Knut, O. Kfir, D. Zusin, C. Gentry, P. Grychtol, O. Cohen, L. Plaja, A. Becker, A. Jaron-Becker, H. Kapteyn, and M. Murnane, “Tomographic reconstruction of circularly polarized high-harmonic fields: 3D attosecond metrology,” Sci. Adv. 2, e1501333 (2016).
[Crossref]

C. Hernández-García, C. G. Durfee, D. D. Hickstein, T. Popmintchev, A. Meier, M. M. Murnane, H. C. Kapteyn, I. J. Sola, A. Jaron-Becker, and A. Becker, “Schemes for generation of isolated attosecond pulses of pure circular polarization,” Phys. Rev. A 93, 043855 (2016).
[Crossref]

V. Salakhutdinov, M. Sondermann, L. Carbone, E. Giacobino, A. Bramati, and G. Leuchs, “Optical trapping of nanoparticles by full solid-angle focusing,” Optica 3, 1181–1186 (2016).
[Crossref]

2015 (18)

A. Turpin, Y. V. Loiko, A. Peinado, A. Lizana, T. K. Kalkandjiev, J. Campos, and J. Mompart, “Polarization tailored novel vector beams based on conical refraction,” Opt. Express 23, 5704–5715 (2015).
[Crossref]

D. B. Milosevic, “Generation of elliptically polarized attosecond pulse trains,” Opt. Lett. 40, 2381–2384 (2015).
[Crossref]

D. Popmintchev, C. Hernández-García, F. Dollar, C. Mancuso, J. A. Pérez-Hernández, M.-C. Chen, A. Hankla, X. Gao, B. Shim, A. L. Gaeta, M. Tarazkar, D. A. Romanov, R. J. Levis, J. A. Gaffney, M. Foord, S. B. Libby, A. Jaron-Becker, A. Becker, L. Plaja, M. M. Murnane, H. C. Kapteyn, and T. Popmintchev, “Ultraviolet surprise: efficient soft x-ray high-harmonic generation in multiply ionized plasmas,” Science 350, 1225–1231 (2015).
[Crossref]

L. Medišauskas, J. Wragg, H. van der Hart, and M. Y. Ivanov, “Generating isolated elliptically polarized attosecond pulses using bichromatic counterrotating circularly polarized laser fields,” Phys. Rev. Lett., 115, 153001 (2015).
[Crossref]

C. Hernández-García, J. San Román, L. Plaja, and A. Picón, “Quantum-path signatures in attosecond helical beams driven by optical vortices,” New J. Phys. 17, 093029 (2015).

D. D. Hickstein, F. J. Dollar, P. Grychtol, J. L. Ellis, R. Knut, C. Hernández-García, C. Gentry, D. Zusin, J. M. Shaw, T. Fan, K. M. Dorney, A. Becker, A. Jaroń-Becker, H. C. Kapteyn, M. M. Murnane, and C. G. Durfee, “Non-collinear generation of angularly isolated circularly polarized high harmonics,” Nat. Photonics 9, 743–750 (2015).
[Crossref]

T. Fan, P. Grychtol, R. Knut, C. Hernández-García, D. D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. W. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. M. Dorney, C. Chen, O. G. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milosevic, A. Becker, A. A. Jaron-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism,” Proc. Natl. Acad. Sci. USA 112, 14206–14211 (2015).
[Crossref]

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Rep. 5, 7840 (2015).
[Crossref]

N. Radwell, R. D. Hawley, J. B. Götte, and S. Franke-Arnold, “Achromatic vector vortex beams from a glass cone,” Nat. Commun. 7, 10564 (2015).
[Crossref]

J. J. J. Nivas, S. He, A. Rubano, A. Vecchione, D. Paparo, L. Marrucci, R. Bruzzese, and S. Amoruso, “Direct femtosecond laser surface structuring with optical vortex beams generated by a q-plate,” Sci. Rep. 5, 17929 (2015).
[Crossref]

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
[Crossref]

N. Karedla, S. C. Stein, D. Hähnel, I. Gregor, A. Chizhik, and J. Enderlein, “Simultaneous measurement of the three-dimensional orientation of excitation and emission dipoles,” Phys. Rev. Lett. 115, 173002 (2015).
[Crossref]

S. Roy, K. Ushakova, Q. van den Berg, S. F. Pereira, and H. P. Urbach, “Radially polarized light for detection and nanolocalization of dielectric particles on a planar substrate,” Phys. Rev. Lett. 114, 103903 (2015).
[Crossref]

L. Schächter and W. D. Kimura, “Vacuum channeling radiation by relativistic electrons in a transverse field of a laser-based Bessel beam,” Phys. Rev. Lett. 114, 195501 (2015).
[Crossref]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347, 964–966 (2015).
[Crossref]

E. Karimi and R. W. Boyd, “Classical entanglement?” Science 350, 1172–1173 (2015).
[Crossref]

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A 92, 023833 (2015).
[Crossref]

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref]

2014 (5)

R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Quantum entanglement of complex photon polarization patterns in vector beams,” Phys. Rev. A 89, 060301(R) (2014).
[Crossref]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89, 013840 (2014).
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G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113, 153901 (2014).
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A. Fleischer, O. Kfir, T. Diskin, P. Sidorenko, and O. Cohen, “Spin angular momentum and tunable polarization in high-harmonic generation,” Nat. Photonics 8, 543–549 (2014).
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M. D. Seaberg, B. Zhang, D. F. Gardner, E. R. Shanblatt, M. M. Murnane, H. C. Kapteyn, and D. E. Adams, “Tabletop nanometer extreme ultraviolet imaging in an extended reflection mode using coherent Fresnel ptychography,” Optica 1, 39–44 (2014).
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2013 (5)

V. G. Shvedov, C. Hnatovsky, N. Shostka, and W. Krolikowski, “Generation of vector bottle beams with a uniaxial crystal,” J. Opt. Soc. Am. B 30, 1–6 (2013).
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Y. S. Rumala, G. Milione, T. A. Nguyen, S. Pratavieira, Z. Hossain, D. Nolan, S. Slussarenko, E. Karimi, L. Marrucci, and R. R. Alfano, “Tunable supercontinuum light vector vortex beam generator using a q-plate,” Opt. Lett. 38, 5083–5086 (2013).
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C. Hernández-García, I. J. Sola, and L. Plaja, “Signature of the transversal coherence length in high-order harmonic generation,” Phys. Rev. A 88, 043848 (2013).
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C. Hernández-García, A. Picón, J. San Román, and L. Plaja, “Attosecond extreme ultraviolet vortices from high-order harmonic generation,” Phys. Rev. Lett. 111, 083602 (2013).
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V. Marceau, C. Varin, T. Brabec, and M. Piché, “Femtosecond 240-keV electron pulses from direct laser acceleration in a low-density gas,” Phys. Rev. Lett. 111, 224801 (2013).
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2012 (3)

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam–Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
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M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
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2011 (5)

2010 (4)

T. A. Fadeyeva, V. G. Shvedov, Y. V. Izdebskaya, A. V. Volyar, E. Brasselet, D. N. Neshev, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Spatially engineered polarization states and optical vortices in uniaxial crystals,” Opt. Express 18, 10848–10863 (2010).
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C. Hernández-García, J. A. Pérez-Hernández, J. Ramos, E. Conejero Jarque, L. Roso, and L. Plaja, “High-order harmonic propagation in gases within the discrete dipole approximation,” Phys. Rev. A 82, 033432 (2010).
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C. Wagner and N. Harned, “EUV lithography: lithography gets extreme,” Nat. Photonics 4, 24–26 (2010).
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G. Tallents, E. Wagenaars, and G. Pert, “Lithography at EUV wavelengths,” Nat. Photonics 4, 809–811 (2010).
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2009 (3)

A. Sukhov and J. Berakdar, “Local control of ultrafast dynamics of magnetic nanoparticles,” Phys. Rev. Lett. 102, 057204 (2009).
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Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
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F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
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2008 (2)

M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B 41, 132001 (2008).
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Y. I. Salamin, Z. Harman, and C. H. Keitel, “Direct high-power laser acceleration of ions for medical applications,” Phys. Rev. Lett. 100, 155004 (2008).
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2007 (2)

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329–334 (2007).
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M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization inYb:YAG thin-disk lasers,” Opt. Lett. 32, 3272–3274 (2007).
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2006 (5)

2005 (1)

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
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2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
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2001 (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
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2000 (1)

1997 (1)

P. Balcou, P. Salieres, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
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1995 (1)

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51, R3414(R) (1995).
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1994 (1)

P. Dietrich, N. H. Burnett, M. Ivanov, and P. B. Corkum, “High-harmonic generation and correlated two-electron multiphoton ionization with elliptically polarized light,” Phys. Rev. A 50, R3585(R) (1994).

1993 (2)

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E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
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Alfano, R. R.

Ališauskas, S.

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Amoruso, S.

J. J. J. Nivas, S. He, A. Rubano, A. Vecchione, D. Paparo, L. Marrucci, R. Bruzzese, and S. Amoruso, “Direct femtosecond laser surface structuring with optical vortex beams generated by a q-plate,” Sci. Rep. 5, 17929 (2015).
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Anderson, E. H.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
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Andriukaitis, G.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaroń-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Arnold, C.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
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Arpin, P.

T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaroń-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Attwood, D. T.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
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Auguste, T.

R. Géneaux, A. Camper, T. Auguste, O. Gobert, J. Caillat, R. Taïeb, and T. Ruchon, “Synthesis and characterization of attosecond light vortices in the extreme ultraviolet,” Nat. Commun. 7, 12583 (2016).
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V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Rep. 5, 7840 (2015).
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T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaroń-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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P. Balcou, P. Salieres, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
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T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaroń-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347, 964–966 (2015).
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M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89, 013840 (2014).
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Bauer, T.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347, 964–966 (2015).
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M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89, 013840 (2014).
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C. Chen, Z. Tao, C. Hernández-García, P. Matyba, A. Carr, R. Knut, O. Kfir, D. Zusin, C. Gentry, P. Grychtol, O. Cohen, L. Plaja, A. Becker, A. Jaron-Becker, H. Kapteyn, and M. Murnane, “Tomographic reconstruction of circularly polarized high-harmonic fields: 3D attosecond metrology,” Sci. Adv. 2, e1501333 (2016).
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C. Hernández-García, C. G. Durfee, D. D. Hickstein, T. Popmintchev, A. Meier, M. M. Murnane, H. C. Kapteyn, I. J. Sola, A. Jaron-Becker, and A. Becker, “Schemes for generation of isolated attosecond pulses of pure circular polarization,” Phys. Rev. A 93, 043855 (2016).
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D. Popmintchev, C. Hernández-García, F. Dollar, C. Mancuso, J. A. Pérez-Hernández, M.-C. Chen, A. Hankla, X. Gao, B. Shim, A. L. Gaeta, M. Tarazkar, D. A. Romanov, R. J. Levis, J. A. Gaffney, M. Foord, S. B. Libby, A. Jaron-Becker, A. Becker, L. Plaja, M. M. Murnane, H. C. Kapteyn, and T. Popmintchev, “Ultraviolet surprise: efficient soft x-ray high-harmonic generation in multiply ionized plasmas,” Science 350, 1225–1231 (2015).
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D. D. Hickstein, F. J. Dollar, P. Grychtol, J. L. Ellis, R. Knut, C. Hernández-García, C. Gentry, D. Zusin, J. M. Shaw, T. Fan, K. M. Dorney, A. Becker, A. Jaroń-Becker, H. C. Kapteyn, M. M. Murnane, and C. G. Durfee, “Non-collinear generation of angularly isolated circularly polarized high harmonics,” Nat. Photonics 9, 743–750 (2015).
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T. Fan, P. Grychtol, R. Knut, C. Hernández-García, D. D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. W. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. M. Dorney, C. Chen, O. G. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milosevic, A. Becker, A. A. Jaron-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism,” Proc. Natl. Acad. Sci. USA 112, 14206–14211 (2015).
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T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaroń-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Becker, W.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51, R3414(R) (1995).
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Benedetti, E.

I. J. Sola, E. Mével, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
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Berakdar, J.

A. Sukhov and J. Berakdar, “Local control of ultrafast dynamics of magnetic nanoparticles,” Phys. Rev. Lett. 102, 057204 (2009).
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R. Drevinskas, J. Zhang, M. Beresna, M. Gecevicius, A. G. Kazanskii, Y. P. Svirko, and P. G. Kazansky, “Laser material processing with tightly focused cylindrical vector beams,” Appl. Phys. Lett. 108, 221107 (2016).
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L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
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Boyd, R. W.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347, 964–966 (2015).
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E. Karimi and R. W. Boyd, “Classical entanglement?” Science 350, 1172–1173 (2015).
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G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113, 153901 (2014).
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Brabec, T.

V. Marceau, C. Varin, T. Brabec, and M. Piché, “Femtosecond 240-keV electron pulses from direct laser acceleration in a low-density gas,” Phys. Rev. Lett. 111, 224801 (2013).
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Bramati, A.

Brasselet, E.

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T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaroń-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
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K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87 (2000).
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J. J. J. Nivas, S. He, A. Rubano, A. Vecchione, D. Paparo, L. Marrucci, R. Bruzzese, and S. Amoruso, “Direct femtosecond laser surface structuring with optical vortex beams generated by a q-plate,” Sci. Rep. 5, 17929 (2015).
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Burnett, N. H.

P. Dietrich, N. H. Burnett, M. Ivanov, and P. B. Corkum, “High-harmonic generation and correlated two-electron multiphoton ionization with elliptically polarized light,” Phys. Rev. A 50, R3585(R) (1994).

Caillat, J.

R. Géneaux, A. Camper, T. Auguste, O. Gobert, J. Caillat, R. Taïeb, and T. Ruchon, “Synthesis and characterization of attosecond light vortices in the extreme ultraviolet,” Nat. Commun. 7, 12583 (2016).
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T. Fan, P. Grychtol, R. Knut, C. Hernández-García, D. D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. W. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. M. Dorney, C. Chen, O. G. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milosevic, A. Becker, A. A. Jaron-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism,” Proc. Natl. Acad. Sci. USA 112, 14206–14211 (2015).
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W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15  nm,” Nature 435, 1210–1213 (2005).
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C. Chen, Z. Tao, C. Hernández-García, P. Matyba, A. Carr, R. Knut, O. Kfir, D. Zusin, C. Gentry, P. Grychtol, O. Cohen, L. Plaja, A. Becker, A. Jaron-Becker, H. Kapteyn, and M. Murnane, “Tomographic reconstruction of circularly polarized high-harmonic fields: 3D attosecond metrology,” Sci. Adv. 2, e1501333 (2016).
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T. Popmintchev, M. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaroń-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Chen, M.-C.

D. Popmintchev, C. Hernández-García, F. Dollar, C. Mancuso, J. A. Pérez-Hernández, M.-C. Chen, A. Hankla, X. Gao, B. Shim, A. L. Gaeta, M. Tarazkar, D. A. Romanov, R. J. Levis, J. A. Gaffney, M. Foord, S. B. Libby, A. Jaron-Becker, A. Becker, L. Plaja, M. M. Murnane, H. C. Kapteyn, and T. Popmintchev, “Ultraviolet surprise: efficient soft x-ray high-harmonic generation in multiply ionized plasmas,” Science 350, 1225–1231 (2015).
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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1.

Scheme for the generation of (a) EUV radial and (b) azimuthal vector beams. A vertically, or horizontally, linearly polarized IR beam is converted into a radial, or azimuthal, IR beam by an s-waveplate, respectively. The resulting vector beam is focused into a gas jet, where each atom interacts with the local IR field, emitting linearly polarized harmonics in the EUV/x-ray regime. Upon propagation, the far-field high-order harmonics are emitted in the form of (a) radial or (b) azimuthal vector beams. (c) Spatial intensity distribution of the IR vector beam generated in the lab with the s-waveplate, after passing through a vertical linear polarizer (the analyzer). With the help of a half-waveplate (axis angle α ) placed before the s-waveplate, the input IR linear polarization is varied from vertical ( α = 0 ° ) to horizontal ( α = 45 ° ).

Fig. 2.
Fig. 2.

Angular intensity plots showing the spatial far-field profile of the 17th harmonic (46.5 nm, 26.7 eV, first and third rows) and the 23rd harmonic (34.3 nm, 36.1 eV, second and fourth), driven by a radial, (a) and (b), and azimuthal, (c) and (d), IR vector beam. For each case, we show (from left to right) the vertical and horizontal polarization projections, and the sum of both components. It can be observed that each harmonic is emitted as a radial or azimuthal vector beam, according to the driving beam.

Fig. 3.
Fig. 3.

(a) Experimental setup. A Gaussian linearly polarized IR beam is converted into a vector beam after passing through a half-waveplate and the s-waveplate. High-order harmonics are generated after focusing the beam into an Ar gas jet. The spectrometer input slit is placed at three different spatial positions of the harmonic beam, as indicated on the inset (note that the inset background is taken from Fig. 2). An aluminum filter is used to remove the IR beam, and the harmonics are separated by means of a diffraction grating. The HHG spectra recorded at (b) slit position 1 and (c) slit position 2 is shown as a function of the half-waveplate angle axis ( α ). The π / 2 periodicity allows us to identify the cases where the vector beam is radially or azimuthally polarized. In plot (d) we show the 19th harmonic signal as a function of α for the three slit positions selected. The yield at each position is normalized separately.

Fig. 4.
Fig. 4.

Attosecond vector beams. (a) Far-field divergence of the 17th (blue), 19th (orange), 21st (green), and 23rd (red) harmonics with x-polarization detected at y = 0    mrad . (b) Isosurface representation of the attosecond radial vector beam resulting after performing the Fourier transform of the high-order harmonics presented in Fig. 3(b). The color scale represents the polarization azimuth, as indicated by the arrows. (c) Attosecond pulse train (top) and time-frequency analysis (bottom) detected at y = 0 , x = 0.5    mrad . The positive slope of the time-frequency structures indicates that the attosecond pulses are emitted with positive chirp.

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