Abstract

We present a method of producing ultrashort pulses of circularly polarized extreme ultraviolet (EUV) light through high-harmonic generation (HHG). HHG is a powerful tool for generating bright laser-like beams of EUV and soft x-ray light with ultrashort pulse durations, which are important for many spectroscopic and imaging applications in the materials, chemical, and nano sciences. Historically HHG was restricted to linear polarization; however, recent advances are making it possible to precisely control the polarization state of the emitted light simply by adjusting the driving laser beams and geometry. In this work, we gain polarization control by combining two spatially separated and orthogonally linearly polarized HHG sources to produce a far-field beam with a uniform intensity distribution, but with a spatially varying ellipticity that ranges from linearly to fully circularly polarized. This spatially varying ellipticity was characterized using EUV magnetic circular dichroism, which demonstrates that a high degree of circularity is achieved, reaching almost 100% near the magnetic M-edge of cobalt. The spatial modulation of the polarization facilitates measurements of circular dichroism, enabling us to measure spectrally resolved magnetic circular dichroism without the use of an EUV spectrometer, thereby avoiding the associated losses in both flux and spatial resolution, which could enable hyperspectral imaging of chiral systems. Through numerical simulations, we also show the generality of this scheme, which can be applied with either the discrete harmonic orders generated by many-cycle pulses or the high-harmonic supercontinua generated by few-cycle driving laser pulses. Therefore, this technique provides a promising route for the production of bright isolated attosecond pulses with circular polarization that can probe ultrafast spin dynamics in materials.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (5)

L. Seiffert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nat. Phys. 13, 766–770 (2017).
[Crossref]

C. Chen, Z. Tao, A. Carr, P. Matyba, T. Szilvási, S. Emmerich, M. Piecuch, M. Keller, D. Zusin, S. Eich, M. Rollinger, W. You, S. Mathias, U. Thumm, M. Mavrikakis, M. Aeschlimann, P. M. Oppeneer, H. Kapteyn, and M. Murnane, “Distinguishing attosecond electron–electron scattering and screening in transition metals,” Proc. Natl. Acad. Sci. USA 114, E5300–E5307 (2017).
[Crossref]

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

K. M. Dorney, J. L. Ellis, C. Hernández-García, D. D. Hickstein, C. A. Mancuso, N. Brooks, T. Fan, G. Fan, D. Zusin, C. Gentry, P. Grychtol, H. C. Kapteyn, and M. M. Murnane, “Helicity-selective enhancement and polarization control of attosecond high harmonic waveforms driven by bichromatic circularly polarized laser fields,” Phys. Rev. Lett. 119, 063201 (2017).
[Crossref]

J. L. Ellis, K. M. Dorney, C. G. Durfee, C. Hernández-García, F. Dollar, C. A. Mancuso, T. Fan, D. Zusin, C. Gentry, P. Grychtol, H. C. Kapteyn, M. M. Murnane, and D. D. Hickstein, “Phase matching of noncollinear sum and difference frequency high harmonic generation above and below the critical ionization level,” Opt. Express 25, 10126–10144 (2017).
[Crossref]

2016 (8)

G. S. M. Jansen, D. Rudolf, L. Freisem, K. S. E. Eikema, and S. Witte, “Spatially resolved Fourier transform spectroscopy in the extreme ultraviolet,” Optica 3, 1122–1125 (2016).
[Crossref]

A. Oriana, J. Réhault, F. Preda, D. Polli, and G. Cerullo, “Scanning Fourier transform spectrometer in the visible range based on birefringent wedges,” J. Opt. Soc. Am. A 33, 1415–1420 (2016).
[Crossref]

F. Catoire, A. Ferré, O. Hort, A. Dubrouil, L. Quintard, D. Descamps, S. Petit, F. Burgy, E. Mével, Y. Mairesse, and E. Constant, “Complex structure of spatially resolved high-order-harmonic spectra,” Phys. Rev. A 94, 063401 (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]

S. M. Teichmann, F. Silva, S. L. Cousin, M. Hemmer, and J. Biegert, “0.5-keV soft x-ray attosecond continua,” Nat. Commun. 7, 11493 (2016).
[Crossref]

S. Beaulieu, A. Comby, B. Fabre, D. Descamps, A. Ferré, G. Garcia, R. Géneaux, F. Légaré, L. Nahon, S. Petit, T. Ruchon, B. Pons, V. Blanchet, and Y. Mairesse, “Probing ultrafast dynamics of chiral molecules using time-resolved photoelectron circular dichroism,” Faraday Discuss 194, 325–348 (2016).
[Crossref]

Z. Tao, C. Chen, T. Szilvási, M. Keller, M. Mavrikakis, H. Kapteyn, and M. Murnane, “Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids,” Science 353, 62–67 (2016).
[Crossref]

M. Huppert, I. Jordan, D. Baykusheva, A. von Conta, and H. J. Wörner, “Attosecond delays in molecular photoionization,” Phys. Rev. Lett. 117, 093001 (2016).
[Crossref]

2015 (5)

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. Milošević, A. Becker, A. A. Jaroń-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]

D. D. Hickstein, F. J. Dollar, P. Grychtol, J. L. Ellis, R. Knut, C. Hernández-García, D. Zusin, C. Gentry, 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]

G. Lambert, B. Vodungbo, J. Gautier, B. Mahieu, V. Malka, S. Sebban, P. Zeitoun, J. Luning, J. Perron, A. Andreev, S. Stremoukhov, F. Ardana-Lamas, A. Dax, C. P. Hauri, A. Sardinha, and M. Fajardo, “Towards enabling femtosecond helicity-dependent spectroscopy with high-harmonic sources,” Nat. Commun. 6, 6167 (2015).
[Crossref]

A. Ferré, C. Handschin, M. Dumergue, F. Burgy, A. Comby, D. Descamps, B. Fabre, G. A. Garcia, R. Géneaux, L. Merceron, E. Mével, L. Nahon, S. Petit, B. Pons, D. Staedter, S. Weber, T. Ruchon, V. Blanchet, and Y. Mairesse, “A table-top ultrashort light source in the extreme ultraviolet for circular dichroism experiments,” Nat. Photonics 9, 93–98 (2015).
[Crossref]

Y. Meng, C. Zhang, C. Marceau, A. Y. Naumov, P. B. Corkum, and D. M. Villeneuve, “Octave-spanning hyperspectral coherent diffractive imaging in the extreme ultraviolet range,” Opt. Express 23, 28960–28969 (2015).
[Crossref]

2014 (5)

S. Witte, V. T. Tenner, D. W. Noom, and K. S. Eikema, “Lensless diffractive imaging with ultra-broadband table-top sources: from infrared to extreme-ultraviolet wavelengths,” Light Sci. Appl. 3, e163 (2014).
[Crossref]

C. M. Heyl, P. Rudawski, F. Brizuela, S. N. Bengtsson, J. Mauritsson, and A. L’Huillier, “Macroscopic effects in noncollinear high-order harmonic generation,” Phys. Rev. Lett. 112, 143902 (2014).
[Crossref]

M.-C. Chen, C. Mancuso, C. Hernández-García, F. Dollar, B. Galloway, D. Popmintchev, P.-C. Huang, B. Walker, L. Plaja, A. A. Jaroń-Becker, A. Becker, M. M. Murnane, H. C. Kapteyn, and T. Popmintchev, “Generation of bright isolated attosecond soft X-ray pulses driven by multicycle midinfrared lasers,” Proc. Natl. Acad. Sci. USA 111, E2361–E2367 (2014).
[Crossref]

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).
[Crossref]

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2014).
[Crossref]

2013 (1)

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).
[Crossref]

2012 (1)

2011 (2)

F. Süßmann and M. F. Kling, “Attosecond nanoplasmonic streaking of localized fields near metal nanospheres,” Phys. Rev. B 84, 121406 (2011).
[Crossref]

F. Gaie-Levrel, G. A. Garcia, M. Schwell, and L. Nahon, “VUV state-selected photoionization of thermally-desorbed biomolecules by coupling an aerosol source to an imaging photoelectron/photoion coincidence spectrometer: case of the amino acids tryptophan and phenylalanine,” Phys. Chem. Chem. Phys. 13, 7024–7036 (2011).
[Crossref]

2010 (2)

M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in photoemission,” Science 328, 1658–1662 (2010).
[Crossref]

C. Hernández-García, J. A. Pérez-Hernández, J. Ramos, E. C. Jarque, L. Roso, and L. Plaja, “High-order harmonic propagation in gases within the discrete dipole approximation,” Phys. Rev. A 82, 033432 (2010).
[Crossref]

2009 (1)

Y. Nabekawa, T. Shimizu, Y. Furukawa, E. J. Takahashi, and K. Midorikawa, “Interferometry of attosecond pulse trains in the extreme ultraviolet wavelength region,” Phys. Rev. Lett. 102, 213904 (2009).
[Crossref]

2006 (1)

S. Valencia, A. Gaupp, W. Gudat, H.-C. Mertins, P. M. Oppeneer, D. Abramsohn, and C. M. Schneider, “Faraday rotation spectra at shallow core levels: 3p edges of Fe, Co, and Ni,” New J. Phys. 8, 254 (2006).
[Crossref]

2005 (1)

M. Kovačev, S. V. Fomichev, E. Priori, Y. Mairesse, H. Merdji, P. Monchicourt, P. Breger, J. Norin, A. Persson, A. L’Huillier, C.-G. Wahlström, B. Carré, and P. Salières, “Extreme ultraviolet Fourier-transform spectroscopy with high order harmonics,” Phys. Rev. Lett. 95, 223903 (2005).
[Crossref]

2001 (1)

N. Böwering, T. Lischke, B. Schmidtke, N. Müller, T. Khalil, and U. Heinzmann, “Asymmetry in photoelectron emission from chiral molecules induced by circularly polarized light,” Phys. Rev. Lett. 86, 1187–1190 (2001).
[Crossref]

2000 (1)

D. B. Milošević and W. Becker, “Attosecond pulse trains with unusual nonlinear polarization,” Phys. Rev. A 62, 011403 (2000).
[Crossref]

1998 (1)

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

1997 (1)

R. Zerne, C. Altucci, M. Bellini, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, C. Lyngå, and C.-G. Wahlström, “Phase-locked high-order harmonic sources,” Phys. Rev. Lett. 79, 1006–1009 (1997).
[Crossref]

1996 (1)

E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, “Ultrafast spin dynamics in ferromagnetic nickel,” Phys. Rev. Lett. 76, 4250–4253 (1996).
[Crossref]

1995 (2)

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–R3417 (1995).
[Crossref]

M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
[Crossref]

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–R3588 (1994).
[Crossref]

1993 (2)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[Crossref]

K. S. Budil, P. Salières, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437–R3440 (1993).
[Crossref]

1988 (1)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064  nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[Crossref]

1987 (1)

1974 (1)

P. J. Stephens, “Magnetic circular dichroism,” Ann. Rev. Phys. Chem. 25, 201–232 (1974).
[Crossref]

1971 (1)

E. Collett, “Mathematical formulation of the interference laws of Fresnel and Arago,” Am. J. Phys. 39, 1483–1495 (1971).
[Crossref]

1963 (1)

R. Hanau, “Interference of linearly polarized light with perpendicular polarizations,” Am. J. Phys. 31, 303–304 (1963).
[Crossref]

1962 (1)

W. R. Mellen, “Interference of linearly polarized light with perpendicular polarizations,” Am. J. Phys. 30, 772 (1962).
[Crossref]

1802 (1)

T. Young, “The Bakerian lecture: on the theory of light and colours,” Philos. Trans. R. Soc. Lond. 92, 12–48 (1802).
[Crossref]

Abramsohn, D.

S. Valencia, A. Gaupp, W. Gudat, H.-C. Mertins, P. M. Oppeneer, D. Abramsohn, and C. M. Schneider, “Faraday rotation spectra at shallow core levels: 3p edges of Fe, Co, and Ni,” New J. Phys. 8, 254 (2006).
[Crossref]

Adams, D. E.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Aeschlimann, M.

C. Chen, Z. Tao, A. Carr, P. Matyba, T. Szilvási, S. Emmerich, M. Piecuch, M. Keller, D. Zusin, S. Eich, M. Rollinger, W. You, S. Mathias, U. Thumm, M. Mavrikakis, M. Aeschlimann, P. M. Oppeneer, H. Kapteyn, and M. Murnane, “Distinguishing attosecond electron–electron scattering and screening in transition metals,” Proc. Natl. Acad. Sci. USA 114, E5300–E5307 (2017).
[Crossref]

Altucci, C.

R. Zerne, C. Altucci, M. Bellini, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, C. Lyngå, and C.-G. Wahlström, “Phase-locked high-order harmonic sources,” Phys. Rev. Lett. 79, 1006–1009 (1997).
[Crossref]

Andreev, A.

G. Lambert, B. Vodungbo, J. Gautier, B. Mahieu, V. Malka, S. Sebban, P. Zeitoun, J. Luning, J. Perron, A. Andreev, S. Stremoukhov, F. Ardana-Lamas, A. Dax, C. P. Hauri, A. Sardinha, and M. Fajardo, “Towards enabling femtosecond helicity-dependent spectroscopy with high-harmonic sources,” Nat. Commun. 6, 6167 (2015).
[Crossref]

Ardana-Lamas, F.

G. Lambert, B. Vodungbo, J. Gautier, B. Mahieu, V. Malka, S. Sebban, P. Zeitoun, J. Luning, J. Perron, A. Andreev, S. Stremoukhov, F. Ardana-Lamas, A. Dax, C. P. Hauri, A. Sardinha, and M. Fajardo, “Towards enabling femtosecond helicity-dependent spectroscopy with high-harmonic sources,” Nat. Commun. 6, 6167 (2015).
[Crossref]

Azzeer, A. M.

M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in photoemission,” Science 328, 1658–1662 (2010).
[Crossref]

Backus, S.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

Baykusheva, D.

M. Huppert, I. Jordan, D. Baykusheva, A. von Conta, and H. J. Wörner, “Attosecond delays in molecular photoionization,” Phys. Rev. Lett. 117, 093001 (2016).
[Crossref]

Beaulieu, S.

S. Beaulieu, A. Comby, B. Fabre, D. Descamps, A. Ferré, G. Garcia, R. Géneaux, F. Légaré, L. Nahon, S. Petit, T. Ruchon, B. Pons, V. Blanchet, and Y. Mairesse, “Probing ultrafast dynamics of chiral molecules using time-resolved photoelectron circular dichroism,” Faraday Discuss 194, 325–348 (2016).
[Crossref]

Beaurepaire, E.

E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, “Ultrafast spin dynamics in ferromagnetic nickel,” Phys. Rev. Lett. 76, 4250–4253 (1996).
[Crossref]

Becker, A.

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]

D. D. Hickstein, F. J. Dollar, P. Grychtol, J. L. Ellis, R. Knut, C. Hernández-García, D. Zusin, C. Gentry, 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. Milošević, A. Becker, A. A. Jaroń-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]

M.-C. Chen, C. Mancuso, C. Hernández-García, F. Dollar, B. Galloway, D. Popmintchev, P.-C. Huang, B. Walker, L. Plaja, A. A. Jaroń-Becker, A. Becker, M. M. Murnane, H. C. Kapteyn, and T. Popmintchev, “Generation of bright isolated attosecond soft X-ray pulses driven by multicycle midinfrared lasers,” Proc. Natl. Acad. Sci. USA 111, E2361–E2367 (2014).
[Crossref]

P.-C. Huang, C.-H. Lu, C. Hernandez-Garcia, R.-T. Huang, P.-S. Wu, D. D. Hickstein, D. Thrasher, J. L. Ellis, A. H. Kung, S.-D. Yang, A. Jaron-Becker, A. Becker, H. C. Kapteyn, M. M. Murnane, C. G. Durfee, and M.-C. Chen, “Isolated, circularly polarized, attosecond pulse generation,” in Conference on Lasers and Electro-Optics (2016), paper JTh4A.7.

Becker, W.

D. B. Milošević and W. Becker, “Attosecond pulse trains with unusual nonlinear polarization,” Phys. Rev. A 62, 011403 (2000).
[Crossref]

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–R3417 (1995).
[Crossref]

Bellini, M.

R. Zerne, C. Altucci, M. Bellini, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, C. Lyngå, and C.-G. Wahlström, “Phase-locked high-order harmonic sources,” Phys. Rev. Lett. 79, 1006–1009 (1997).
[Crossref]

Bengtsson, S. N.

C. M. Heyl, P. Rudawski, F. Brizuela, S. N. Bengtsson, J. Mauritsson, and A. L’Huillier, “Macroscopic effects in noncollinear high-order harmonic generation,” Phys. Rev. Lett. 112, 143902 (2014).
[Crossref]

Bevis, C.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Biegert, J.

S. M. Teichmann, F. Silva, S. L. Cousin, M. Hemmer, and J. Biegert, “0.5-keV soft x-ray attosecond continua,” Nat. Commun. 7, 11493 (2016).
[Crossref]

Bigot, J.-Y.

E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, “Ultrafast spin dynamics in ferromagnetic nickel,” Phys. Rev. Lett. 76, 4250–4253 (1996).
[Crossref]

Blanchet, V.

S. Beaulieu, A. Comby, B. Fabre, D. Descamps, A. Ferré, G. Garcia, R. Géneaux, F. Légaré, L. Nahon, S. Petit, T. Ruchon, B. Pons, V. Blanchet, and Y. Mairesse, “Probing ultrafast dynamics of chiral molecules using time-resolved photoelectron circular dichroism,” Faraday Discuss 194, 325–348 (2016).
[Crossref]

A. Ferré, C. Handschin, M. Dumergue, F. Burgy, A. Comby, D. Descamps, B. Fabre, G. A. Garcia, R. Géneaux, L. Merceron, E. Mével, L. Nahon, S. Petit, B. Pons, D. Staedter, S. Weber, T. Ruchon, V. Blanchet, and Y. Mairesse, “A table-top ultrashort light source in the extreme ultraviolet for circular dichroism experiments,” Nat. Photonics 9, 93–98 (2015).
[Crossref]

Böwering, N.

N. Böwering, T. Lischke, B. Schmidtke, N. Müller, T. Khalil, and U. Heinzmann, “Asymmetry in photoelectron emission from chiral molecules induced by circularly polarized light,” Phys. Rev. Lett. 86, 1187–1190 (2001).
[Crossref]

Boyer, K.

Breger, P.

M. Kovačev, S. V. Fomichev, E. Priori, Y. Mairesse, H. Merdji, P. Monchicourt, P. Breger, J. Norin, A. Persson, A. L’Huillier, C.-G. Wahlström, B. Carré, and P. Salières, “Extreme ultraviolet Fourier-transform spectroscopy with high order harmonics,” Phys. Rev. Lett. 95, 223903 (2005).
[Crossref]

Brida, D.

Brizuela, F.

C. M. Heyl, P. Rudawski, F. Brizuela, S. N. Bengtsson, J. Mauritsson, and A. L’Huillier, “Macroscopic effects in noncollinear high-order harmonic generation,” Phys. Rev. Lett. 112, 143902 (2014).
[Crossref]

Brooks, N.

K. M. Dorney, J. L. Ellis, C. Hernández-García, D. D. Hickstein, C. A. Mancuso, N. Brooks, T. Fan, G. Fan, D. Zusin, C. Gentry, P. Grychtol, H. C. Kapteyn, and M. M. Murnane, “Helicity-selective enhancement and polarization control of attosecond high harmonic waveforms driven by bichromatic circularly polarized laser fields,” Phys. Rev. Lett. 119, 063201 (2017).
[Crossref]

Budil, K. S.

K. S. Budil, P. Salières, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437–R3440 (1993).
[Crossref]

Burgdörfer, J.

M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in photoemission,” Science 328, 1658–1662 (2010).
[Crossref]

Burgy, F.

F. Catoire, A. Ferré, O. Hort, A. Dubrouil, L. Quintard, D. Descamps, S. Petit, F. Burgy, E. Mével, Y. Mairesse, and E. Constant, “Complex structure of spatially resolved high-order-harmonic spectra,” Phys. Rev. A 94, 063401 (2016).
[Crossref]

A. Ferré, C. Handschin, M. Dumergue, F. Burgy, A. Comby, D. Descamps, B. Fabre, G. A. Garcia, R. Géneaux, L. Merceron, E. Mével, L. Nahon, S. Petit, B. Pons, D. Staedter, S. Weber, T. Ruchon, V. Blanchet, and Y. Mairesse, “A table-top ultrashort light source in the extreme ultraviolet for circular dichroism experiments,” Nat. Photonics 9, 93–98 (2015).
[Crossref]

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–R3588 (1994).
[Crossref]

Calegari, F.

L. Seiffert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nat. Phys. 13, 766–770 (2017).
[Crossref]

Carr, A.

C. Chen, Z. Tao, A. Carr, P. Matyba, T. Szilvási, S. Emmerich, M. Piecuch, M. Keller, D. Zusin, S. Eich, M. Rollinger, W. You, S. Mathias, U. Thumm, M. Mavrikakis, M. Aeschlimann, P. M. Oppeneer, H. Kapteyn, and M. Murnane, “Distinguishing attosecond electron–electron scattering and screening in transition metals,” Proc. Natl. Acad. Sci. USA 114, E5300–E5307 (2017).
[Crossref]

Carré, B.

M. Kovačev, S. V. Fomichev, E. Priori, Y. Mairesse, H. Merdji, P. Monchicourt, P. Breger, J. Norin, A. Persson, A. L’Huillier, C.-G. Wahlström, B. Carré, and P. Salières, “Extreme ultraviolet Fourier-transform spectroscopy with high order harmonics,” Phys. Rev. Lett. 95, 223903 (2005).
[Crossref]

Carva, K.

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. Milošević, A. Becker, A. A. Jaroń-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]

Castrovilli, M. C.

L. Seiffert, Q. Liu, S. Zherebtsov, A. Trabattoni, P. Rupp, M. C. Castrovilli, M. Galli, F. Süßmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F. Frassetto, I. Halfpap, V. Mondes, C. Graf, E. Rühl, F. Krausz, M. Nisoli, T. Fennel, F. Calegari, and M. F. Kling, “Attosecond chronoscopy of electron scattering in dielectric nanoparticles,” Nat. Phys. 13, 766–770 (2017).
[Crossref]

Catoire, F.

F. Catoire, A. Ferré, O. Hort, A. Dubrouil, L. Quintard, D. Descamps, S. Petit, F. Burgy, E. Mével, Y. Mairesse, and E. Constant, “Complex structure of spatially resolved high-order-harmonic spectra,” Phys. Rev. A 94, 063401 (2016).
[Crossref]

Cavalieri, A. L.

M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in photoemission,” Science 328, 1658–1662 (2010).
[Crossref]

Cerullo, G.

Chang, Z.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

Chen, C.

C. Chen, Z. Tao, A. Carr, P. Matyba, T. Szilvási, S. Emmerich, M. Piecuch, M. Keller, D. Zusin, S. Eich, M. Rollinger, W. You, S. Mathias, U. Thumm, M. Mavrikakis, M. Aeschlimann, P. M. Oppeneer, H. Kapteyn, and M. Murnane, “Distinguishing attosecond electron–electron scattering and screening in transition metals,” Proc. Natl. Acad. Sci. USA 114, E5300–E5307 (2017).
[Crossref]

Z. Tao, C. Chen, T. Szilvási, M. Keller, M. Mavrikakis, H. Kapteyn, and M. Murnane, “Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids,” Science 353, 62–67 (2016).
[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. Milošević, A. Becker, A. A. Jaroń-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]

Chen, M.-C.

M.-C. Chen, C. Mancuso, C. Hernández-García, F. Dollar, B. Galloway, D. Popmintchev, P.-C. Huang, B. Walker, L. Plaja, A. A. Jaroń-Becker, A. Becker, M. M. Murnane, H. C. Kapteyn, and T. Popmintchev, “Generation of bright isolated attosecond soft X-ray pulses driven by multicycle midinfrared lasers,” Proc. Natl. Acad. Sci. USA 111, E2361–E2367 (2014).
[Crossref]

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Supplementary Material (1)

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» Supplement 1       Supporting information document with additional details

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Figures (4)

Fig. 1.
Fig. 1. Experimental setup. A common-path interferometer creates two orthogonally polarized and angularly separated beams, which are focused to two spatially separated focal spots for driving the high-harmonic generation (HHG) process in a neon gas jet. The interferometer consists of a birefringent plate and a pair of birefringent wedges (α-BBO), which split an incoming pulse into two orthogonally polarized and angularly separated pulses. The degree of angular separation is controlled by the rotation of the second wedge about the vertical axis. A lens then focuses the two orthogonally polarized beams into a gas jet and maps the angular separation into a spatial separation at the focus (exaggerated for clarity). The spatially separated focal spots each independently drive the HHG process, yielding two orthogonally polarized HHG beams, which diverge to overlap in the far field and thereby produce a far-field distribution with a spatially varying ellipticity (SVE-HHG). This ellipticity distribution is measured using the extreme ultraviolet magnetic circular dichroism (EUV MCD) response of a cobalt thin film. The fundamental is blocked with an aluminum filter (not shown) to isolate the EUV light before the magnetic sample. For clarity, idealized data are shown in the examples here.
Fig. 2.
Fig. 2. Spatially varying ellipticity in SVE-HHG is characterized via EUV magnetic circular dichroism (EUV MCD). (a) The spectrally resolved intensity of harmonics transmitted through a uniformly magnetized 20-nm-thick cobalt thin film shows a spatially uniform intensity profile. (b) Subtraction of the harmonic intensity transmitted through the cobalt thin film with two opposite magnetizations shows a sinusoidal spatial variation vertically along each harmonic profile. This is due to the differential absorption in MCD, which reveals the spatially varying ellipticity across the high-harmonic beam profile. (c) The amplitude of our measured EUV MCD asymmetry (red circles) is compared with values in the literature (Valencia et al. [44]) for the magnetic asymmetry expected from a 20-nm-thick cobalt film [44] (blue line with errors represented by the shaded region) to determine the maximum ellipticity present in the far-field polarization distribution. The close agreement with previous measurements indicates a high degree of circularity. The errors on the SVE-HHG data points represent the statistical errors in the fitting procedure and therefore do not capture any systematic effects. We estimate that the systematic errors present are smaller than the statistical ones shown here.
Fig. 3.
Fig. 3. Energy-resolved EUV MCD without the use of a spectrometer. (a) Intensity profile of the high-harmonic beam transmitted through a thin cobalt film (20 nm). (b) Subtraction of the transmission through the two opposite magnetizations shows the coherent superposition of the spatially varying ellipticity of several harmonic orders contributing to the MCD signal. (c) A Fourier transform (FT) of the spatially varying EUV MCD asymmetry recovers the transmitted harmonic spectrum multiplied by the energy-dependent dichroic response of the material (solid blue curve). Therefore, scaling by the transmitted spectral weights of the individual harmonic orders isolates the material’s dichroic response (dotted red curve). (d) The relative EUV MCD asymmetry obtained using a spatial FT to separate the spectral content (blue) is in excellent agreement with the values obtained by spectrally dispersing the harmonic orders with a spectrometer (black), indicating that this scheme recovers the spectrally resolved MCD response of magnetic materials without the need for a grating. The blue shaded region indicates the standard deviation in the FT-recovered MCD asymmetry.
Fig. 4.
Fig. 4. Numerical simulations of SVE-HHG visualized by taking the projection of the far-field polarization distribution along pure right-circular polarization. (a) For multicycle pulses, the HHG emission is spectrally resolved into well-separated harmonic orders, which each exhibit a polarization modulation with a spatial frequency that depends on the harmonic order; (b) for near-single-cycle pulses, an HHG supercontinuum is produced. However, every energy level still exhibits sinusoidally varying elliptictiy with a well-defined spatial frequency that increases with increasing photon energy. (c) This HHG supercontinuum corresponds to an isolated attosecond pulse in the time domain, which is either circularly, elliptically, or linearly polarized depending on divergence angle (±0.02  mrad for circular; see Supplement 1).

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