Abstract

Circularly polarized extreme ultraviolet (XUV) radiation is highly interesting for investigation of chirality-sensitive light-matter interactions. Recent breakthroughs have enabled the generation of such light sources via high harmonic generation (HHG) from rare gases. There is a growing interest in extending HHG medium from gases to solids, especially to 2D materials, as they hold great promise to develop ultra-compact solid-state photonic devices and provide insights into electronic properties of the materials themselves. However, so far reported, HHG in graphene driven by terahertz to mid-infrared fields generates only low harmonic orders, and no harmonics driven by circularly polarized lasers have been reported. Here, using first-principles simulations within a time-dependent density-functional theory framework, we show that it is possible to generate HHG extending to the XUV spectral region in monolayer extended graphene excited by near-infrared lasers. Moreover, we demonstrate that a single circularly polarized driver is enough to ensure HHG in graphene with circular polarization. The corresponding spectra reflect the six-fold rotational symmetry of the graphene crystal. Extending HHG in graphene to the XUV spectral regime and realizing circular polarization represent an important step toward the development of novel nanoscale attosecond photonic devices and numerous applications, such as spectroscopic investigation and nanoscale imaging of ultrafast chiral and spin dynamics in graphene and other 2D materials.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (10)

T. T. Luu and H. J. Wörner, “Measurement of the berry curvature of solids using high-harmonic spectroscopy,” Nat. Commun. 9, 916 (2018).
[Crossref] [PubMed]

N. Tancogne-Dejean and A. Rubio, “Atomic-like high-harmonic generation from two-dimensional materials,” Sci. Adv. 4, eaao5207 (2018).
[Crossref] [PubMed]

H. K. Avetissian and G. F. Mkrtchian, “Impact of electron-electron coulomb interaction on the high harmonic generation process in graphene,” Phys. Rev. B 97, 115454 (2018).
[Crossref]

C. Liu, Y. Zheng, Z. Zeng, and R. Li, “Driving-laser ellipticity dependence of high-order harmonic generation in graphene,” Phys. Rev. A 97, 063412 (2018).
[Crossref]

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. García de Abajo, and B. Jens, “Ultrafast nonlinear optical response of dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

R. Qin and Z.-Y. Chen, “Strain-controlled high harmonic generation with dirac fermions in silicene,” Nanoscale 10, 22593–22600 (2018).
[Crossref] [PubMed]

P.-C. Huang, C. Hernández-García, J.-T. Huang, P.-Y. Huang, C.-H. Lu, L. Rego, D. D. Hickstein, J. L. Ellis, A. Jaron-Becker, A. Becker, S.-D. Yang, C. G. Durfee, L. Plaja, H. C. Kapteyn, M. M. Murnane, A. H. Kung, and M.-C. Chen, “Polarization control of isolated high-harmonic pulses,” Nat. Photonics 12, 349–354 (2018).
[Crossref]

Z.-Y. Chen, “Spectral control of high harmonics from relativistic plasmas using bicircular fields,” Phys. Rev. E 97, 043202 (2018).
[Crossref] [PubMed]

Z.-Y. Chen, X.-Y. Li, B.-Y. Li, M. Chen, and F. Liu, “Isolated elliptically polarized attosecond soft x-ray with high-brilliance using polarization gating of harmonics from relativistic plasmas at oblique incidence,” Opt. Express 26, 4572–4580 (2018).
[Crossref] [PubMed]

Z.-Y. Chen, “Isolated attosecond pulse in the water window from many-cycle laser-driven plasma mirrors without pulse engineering,” Opt. Lett. 43, 2114–2117 (2018).
[Crossref] [PubMed]

2017 (8)

G. Vampa and T. Brabec, “Merge of high harmonic generation from gases and solids and its implications for attosecond science,” J. Phys. B 50, 083001 (2017).
[Crossref]

N. Yoshikawa, T. Tamaya, and K. Tanaka, “High-harmonic generation in graphene enhanced by elliptically polarized light excitation,” Science 356, 736–738 (2017).
[Crossref] [PubMed]

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thiré, B. E. Schmidt, F. Légaré, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96, 195420 (2017).
[Crossref]

L. A. Chizhova, F. Libisch, and J. Burgdörfer, “High-harmonic generation in graphene: Interband response and the harmonic cutoff,” Phys. Rev. B 95, 085436 (2017).
[Crossref]

J. D. Cox, A. Marini, and F. J. G. de Abajo, “Plasmon-assisted high-harmonic generation in graphene,” Nat. Commun. 8, 14380 (2017).
[Crossref] [PubMed]

N. Tancogne-Dejean, O. D. Mücke, F. X. Kärtner, and A. Rubio, “Ellipticity dependence of high-harmonic generation in solids originating from coupled intraband and interband dynamics,” Nat. Commun. 8, 745 (2017).
[Crossref] [PubMed]

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13, 262–265 (2017).
[Crossref]

Y. S. You, D. A. Reis, and S. Ghimire, “Anisotropic high-harmonic generation in bulk crystals,” Nat. Phys. 13, 345–349 (2017).
[Crossref]

2016 (5)

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534, 520–523 (2016).
[Crossref] [PubMed]

L. A. Chizhova, F. Libisch, and J. Burgdörfer, “Nonlinear response of graphene to a few-cycle terahertz laser pulse: Role of doping and disorder,” Phys. Rev. B 94, 075412 (2016).
[Crossref]

G. Ma, W. Yu, M. Y. Yu, B. Shen, and L. Veisz, “Intense circularly polarized attosecond pulse generation from relativistic laser plasmas using few-cycle laser pulses,” Opt. Express 24, 10057–10065 (2016).
[Crossref] [PubMed]

Z.-Y. Chen and A. Pukhov, “Bright high-order harmonic generation with controllable polarization from a relativistic plasma mirror,” Nat. Commun. 7, 12515 (2016).
[Crossref] [PubMed]

B. H. Shaw, S. Steinke, J. van Tilborg, and W. P. Leemans, “Reflectance characterization of tape-based plasma mirrors,” Phys. Plasmas 23, 063118 (2016).
[Crossref]

2015 (10)

G. Vampa, C. R. McDonald, G. Orlando, P. B. Corkum, and T. Brabec, “Semiclassical analysis of high harmonic generation in bulk crystals,” Phys. Rev. B 91, 064302 (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]

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 (2015).
[Crossref]

D. D. Hickstein, F. J. Dollar, P. G. 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]

J. Bierbach, M. Yeung, E. Eckner, C. Rödel, S. Kuschel, M. Zepf, and G. G. Paulus, “Long-term operation of surface high-harmonic generation from relativistic oscillating mirrors using a spooling tape,” Opt. Express 23, 12321–12327 (2015).
[Crossref] [PubMed]

X. Andrade, D. A. Strubbe, U. D. Giovannini, A. H. Larsen, M. J. T. Oliveira, J. Alberdi-Rodriguez, A. Varas, I. Theophilou, N. Helbig, M. Verstraete, L. Stella, F. Nogueira, A. Aspuru-Guzik, A. Castro, M. A. L. Marques, and A. Rubio, “Real-space grids and the octopus code as tools for the development of new simulation approaches for electronic systems,” Phys. Chem. Chem. Phys. 17, 31371–31396 (2015).
[Crossref] [PubMed]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522, 462–464 (2015).
[Crossref] [PubMed]

G. Vampa, T. Hammond, N. Thiré, B. Schmidt, F. Légaré, C. McDonald, T. Brabec, D. Klug, and P. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115, 193603 (2015).
[Crossref] [PubMed]

T. T. Luu, M. Garg, S. Y. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521, 498–502 (2015).
[Crossref] [PubMed]

I. Al-Naib, J. E. Sipe, and M. M. Dignam, “Nonperturbative model of harmonic generation in undoped graphene in the terahertz regime,” New J. Phys. 17, 113018 (2015).
[Crossref]

2014 (6)

I. Al-Naib, J. E. Sipe, and M. M. Dignam, “High harmonic generation in undoped graphene: Interplay of inter- and intraband dynamics,” Phys. Rev. B 90, 245423 (2014).
[Crossref]

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical bloch oscillations,” Nat. Photonics 8, 119–123 (2014).
[Crossref]

P. Bowlan, E. Martinez-Moreno, K. Reimann, T. Elsaesser, and M. Woerner, “Ultrafast terahertz response of multilayer graphene in the nonperturbative regime,” Phys. Rev. B 89, 041408(R) (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]

E. Pisanty, S. Sukiasyan, and M. Ivanov, “Spin conservation in high-order-harmonic generation using bicircular fields,” Phys. Rev. A 90, 043829 (2014).
[Crossref]

C. von Korff Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging ultrafast demagnetization dynamics after a spatially localized optical excitation,” Phys. Rev. Lett. 112, 217203 (2014).
[Crossref]

2013 (1)

G. A. Garcia, L. Nahon, S. Daly, and I. Powis, “Vibrationally induced inversion of photoelectron forward-backward asymmetry in chiral molecule photoionization by circularly polarized light,” Nat. Commun. 4, 2132 (2013).
[Crossref] [PubMed]

2012 (4)

X. Andrade, J. Alberdi-Rodriguez, D. A. Strubbe, M. J. T. Oliveira, F. Nogueira, A. Castro, J. Muguerza, A. Arruabarrena, S. G. Louie, A. Aspuru-Guzik, A. Rubio, and M. A. L. Marques, “Time-dependent density-functional theory in massively parallel computer architectures: the octopus project,” J. Phys. Condens. Matter 24, 233202 (2012).
[Crossref] [PubMed]

M. A. L. Marques, M. J. T. Oliveira, and T. Burnus, “Libxc: a library of exchange and correlation functionals for density functional theory,” Comput. Phys. Commun. 183, 2272–2281 (2012).
[Crossref]

H. K. Avetissian, A. K. Avetissian, G. F. Mkrtchian, and K. V. Sedrakian, “Multiphoton resonant excitation of fermi-dirac sea in graphene at the interaction with strong laser fields,” J. Nanophoton. 6, 061702 (2012).
[Crossref]

H. K. Avetissian, A. K. Avetissian, G. F. Mkrtchian, and K. V. Sedrakian, “Creation of particle-hole superposition states in graphene at multiphoton resonant excitation by laser radiation,” protectPhys. Rev. B 85, 115443 (2012).
[Crossref]

2011 (2)

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

A. Roberts, D. Cormode, C. Reynolds, T. Newhouse-Illige, B. J. LeRoy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99, 051912 (2011).
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2010 (1)

K. L. Ishikawa, “Nonlinear optical response of graphene in time domain,” Phys. Rev. B 82, 201402(R) (2010).
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2008 (1)

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys. Condens. Matter 20, 384204 (2008).
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2007 (1)

S. A. Mikhailov, “Non-linear electromagnetic response of graphene,” EPL 79, 27002 (2007).
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2006 (1)

A. Castro, H. Appel, M. Oliveira, C. Rozzi, X. Andrade, F. Lorenzen, M. Marques, E. Gross, and A. Rubio, “octopus: a tool for the application of time-dependent density functional theory,” Phys. Status Solidi B 243, 2465–2488 (2006).
[Crossref]

2004 (2)

A. Castro, M. Marques, and A. Rubio, “Propagators for the time-dependent kohn-sham equations,” J. Chem. Phys. 121, 3425–3433 (2004).
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A. Castro, M. Marques, J. A. Alonso, and A. Rubio, “Optical properties of nanostructures from time-dependent density functional theory,” J. Comp. Theor. Nanosci. 1, 231–255 (2004).
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1998 (1)

R. van Leeuwen, “Causality and symmetry in time-dependent density-functional theory,” Phys. Rev. Lett. 80, 1280–1283 (1998).
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1984 (1)

E. Runge and E. K. U. Gross, “Density-functional theory for time-dependent systems,” Phys. Rev. Lett. 52, 997–1000 (1984).
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S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
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Alberdi-Rodriguez, J.

X. Andrade, D. A. Strubbe, U. D. Giovannini, A. H. Larsen, M. J. T. Oliveira, J. Alberdi-Rodriguez, A. Varas, I. Theophilou, N. Helbig, M. Verstraete, L. Stella, F. Nogueira, A. Aspuru-Guzik, A. Castro, M. A. L. Marques, and A. Rubio, “Real-space grids and the octopus code as tools for the development of new simulation approaches for electronic systems,” Phys. Chem. Chem. Phys. 17, 31371–31396 (2015).
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X. Andrade, J. Alberdi-Rodriguez, D. A. Strubbe, M. J. T. Oliveira, F. Nogueira, A. Castro, J. Muguerza, A. Arruabarrena, S. G. Louie, A. Aspuru-Guzik, A. Rubio, and M. A. L. Marques, “Time-dependent density-functional theory in massively parallel computer architectures: the octopus project,” J. Phys. Condens. Matter 24, 233202 (2012).
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Al-Naib, I.

I. Al-Naib, J. E. Sipe, and M. M. Dignam, “Nonperturbative model of harmonic generation in undoped graphene in the terahertz regime,” New J. Phys. 17, 113018 (2015).
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I. Al-Naib, J. E. Sipe, and M. M. Dignam, “High harmonic generation in undoped graphene: Interplay of inter- and intraband dynamics,” Phys. Rev. B 90, 245423 (2014).
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Alonso, J. A.

A. Castro, M. Marques, J. A. Alonso, and A. Rubio, “Optical properties of nanostructures from time-dependent density functional theory,” J. Comp. Theor. Nanosci. 1, 231–255 (2004).
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Andrade, X.

X. Andrade, D. A. Strubbe, U. D. Giovannini, A. H. Larsen, M. J. T. Oliveira, J. Alberdi-Rodriguez, A. Varas, I. Theophilou, N. Helbig, M. Verstraete, L. Stella, F. Nogueira, A. Aspuru-Guzik, A. Castro, M. A. L. Marques, and A. Rubio, “Real-space grids and the octopus code as tools for the development of new simulation approaches for electronic systems,” Phys. Chem. Chem. Phys. 17, 31371–31396 (2015).
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X. Andrade, J. Alberdi-Rodriguez, D. A. Strubbe, M. J. T. Oliveira, F. Nogueira, A. Castro, J. Muguerza, A. Arruabarrena, S. G. Louie, A. Aspuru-Guzik, A. Rubio, and M. A. L. Marques, “Time-dependent density-functional theory in massively parallel computer architectures: the octopus project,” J. Phys. Condens. Matter 24, 233202 (2012).
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A. Castro, H. Appel, M. Oliveira, C. Rozzi, X. Andrade, F. Lorenzen, M. Marques, E. Gross, and A. Rubio, “octopus: a tool for the application of time-dependent density functional theory,” Phys. Status Solidi B 243, 2465–2488 (2006).
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Appel, H.

A. Castro, H. Appel, M. Oliveira, C. Rozzi, X. Andrade, F. Lorenzen, M. Marques, E. Gross, and A. Rubio, “octopus: a tool for the application of time-dependent density functional theory,” Phys. Status Solidi B 243, 2465–2488 (2006).
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Arruabarrena, A.

X. Andrade, J. Alberdi-Rodriguez, D. A. Strubbe, M. J. T. Oliveira, F. Nogueira, A. Castro, J. Muguerza, A. Arruabarrena, S. G. Louie, A. Aspuru-Guzik, A. Rubio, and M. A. L. Marques, “Time-dependent density-functional theory in massively parallel computer architectures: the octopus project,” J. Phys. Condens. Matter 24, 233202 (2012).
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X. Andrade, D. A. Strubbe, U. D. Giovannini, A. H. Larsen, M. J. T. Oliveira, J. Alberdi-Rodriguez, A. Varas, I. Theophilou, N. Helbig, M. Verstraete, L. Stella, F. Nogueira, A. Aspuru-Guzik, A. Castro, M. A. L. Marques, and A. Rubio, “Real-space grids and the octopus code as tools for the development of new simulation approaches for electronic systems,” Phys. Chem. Chem. Phys. 17, 31371–31396 (2015).
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X. Andrade, J. Alberdi-Rodriguez, D. A. Strubbe, M. J. T. Oliveira, F. Nogueira, A. Castro, J. Muguerza, A. Arruabarrena, S. G. Louie, A. Aspuru-Guzik, A. Rubio, and M. A. L. Marques, “Time-dependent density-functional theory in massively parallel computer architectures: the octopus project,” J. Phys. Condens. Matter 24, 233202 (2012).
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Avetissian, A. K.

H. K. Avetissian, A. K. Avetissian, G. F. Mkrtchian, and K. V. Sedrakian, “Multiphoton resonant excitation of fermi-dirac sea in graphene at the interaction with strong laser fields,” J. Nanophoton. 6, 061702 (2012).
[Crossref]

H. K. Avetissian, A. K. Avetissian, G. F. Mkrtchian, and K. V. Sedrakian, “Creation of particle-hole superposition states in graphene at multiphoton resonant excitation by laser radiation,” protectPhys. Rev. B 85, 115443 (2012).
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H. K. Avetissian and G. F. Mkrtchian, “Impact of electron-electron coulomb interaction on the high harmonic generation process in graphene,” Phys. Rev. B 97, 115454 (2018).
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H. K. Avetissian, A. K. Avetissian, G. F. Mkrtchian, and K. V. Sedrakian, “Creation of particle-hole superposition states in graphene at multiphoton resonant excitation by laser radiation,” protectPhys. Rev. B 85, 115443 (2012).
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H. K. Avetissian, A. K. Avetissian, G. F. Mkrtchian, and K. V. Sedrakian, “Multiphoton resonant excitation of fermi-dirac sea in graphene at the interaction with strong laser fields,” J. Nanophoton. 6, 061702 (2012).
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M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. García de Abajo, and B. Jens, “Ultrafast nonlinear optical response of dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
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P.-C. Huang, C. Hernández-García, J.-T. Huang, P.-Y. Huang, C.-H. Lu, L. Rego, D. D. Hickstein, J. L. Ellis, A. Jaron-Becker, A. Becker, S.-D. Yang, C. G. Durfee, L. Plaja, H. C. Kapteyn, M. M. Murnane, A. H. Kung, and M.-C. Chen, “Polarization control of isolated high-harmonic pulses,” Nat. Photonics 12, 349–354 (2018).
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D. D. Hickstein, F. J. Dollar, P. G. 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).
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Bierbach, J.

Blanchet, V.

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).
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P. Bowlan, E. Martinez-Moreno, K. Reimann, T. Elsaesser, and M. Woerner, “Ultrafast terahertz response of multilayer graphene in the nonperturbative regime,” Phys. Rev. B 89, 041408(R) (2014).
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Brabec, T.

G. Vampa and T. Brabec, “Merge of high harmonic generation from gases and solids and its implications for attosecond science,” J. Phys. B 50, 083001 (2017).
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G. Vampa, C. R. McDonald, G. Orlando, P. B. Corkum, and T. Brabec, “Semiclassical analysis of high harmonic generation in bulk crystals,” Phys. Rev. B 91, 064302 (2015).
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G. Vampa, T. Hammond, N. Thiré, B. Schmidt, F. Légaré, C. McDonald, T. Brabec, D. Klug, and P. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115, 193603 (2015).
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G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522, 462–464 (2015).
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Browne, D. A.

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534, 520–523 (2016).
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Burgdörfer, J.

L. A. Chizhova, F. Libisch, and J. Burgdörfer, “High-harmonic generation in graphene: Interband response and the harmonic cutoff,” Phys. Rev. B 95, 085436 (2017).
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L. A. Chizhova, F. Libisch, and J. Burgdörfer, “Nonlinear response of graphene to a few-cycle terahertz laser pulse: Role of doping and disorder,” Phys. Rev. B 94, 075412 (2016).
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Burgy, F.

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).
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Burnus, T.

M. A. L. Marques, M. J. T. Oliveira, and T. Burnus, “Libxc: a library of exchange and correlation functionals for density functional theory,” Comput. Phys. Commun. 183, 2272–2281 (2012).
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C. von Korff Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging ultrafast demagnetization dynamics after a spatially localized optical excitation,” Phys. Rev. Lett. 112, 217203 (2014).
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Castro, A.

X. Andrade, D. A. Strubbe, U. D. Giovannini, A. H. Larsen, M. J. T. Oliveira, J. Alberdi-Rodriguez, A. Varas, I. Theophilou, N. Helbig, M. Verstraete, L. Stella, F. Nogueira, A. Aspuru-Guzik, A. Castro, M. A. L. Marques, and A. Rubio, “Real-space grids and the octopus code as tools for the development of new simulation approaches for electronic systems,” Phys. Chem. Chem. Phys. 17, 31371–31396 (2015).
[Crossref] [PubMed]

X. Andrade, J. Alberdi-Rodriguez, D. A. Strubbe, M. J. T. Oliveira, F. Nogueira, A. Castro, J. Muguerza, A. Arruabarrena, S. G. Louie, A. Aspuru-Guzik, A. Rubio, and M. A. L. Marques, “Time-dependent density-functional theory in massively parallel computer architectures: the octopus project,” J. Phys. Condens. Matter 24, 233202 (2012).
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A. Castro, H. Appel, M. Oliveira, C. Rozzi, X. Andrade, F. Lorenzen, M. Marques, E. Gross, and A. Rubio, “octopus: a tool for the application of time-dependent density functional theory,” Phys. Status Solidi B 243, 2465–2488 (2006).
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A. Castro, M. Marques, and A. Rubio, “Propagators for the time-dependent kohn-sham equations,” J. Chem. Phys. 121, 3425–3433 (2004).
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A. Castro, M. Marques, J. A. Alonso, and A. Rubio, “Optical properties of nanostructures from time-dependent density functional theory,” J. Comp. Theor. Nanosci. 1, 231–255 (2004).
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Chen, M.

Chen, M.-C.

P.-C. Huang, C. Hernández-García, J.-T. Huang, P.-Y. Huang, C.-H. Lu, L. Rego, D. D. Hickstein, J. L. Ellis, A. Jaron-Becker, A. Becker, S.-D. Yang, C. G. Durfee, L. Plaja, H. C. Kapteyn, M. M. Murnane, A. H. Kung, and M.-C. Chen, “Polarization control of isolated high-harmonic pulses,” Nat. Photonics 12, 349–354 (2018).
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Chen, Z.-Y.

R. Qin and Z.-Y. Chen, “Strain-controlled high harmonic generation with dirac fermions in silicene,” Nanoscale 10, 22593–22600 (2018).
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Z.-Y. Chen, “Isolated attosecond pulse in the water window from many-cycle laser-driven plasma mirrors without pulse engineering,” Opt. Lett. 43, 2114–2117 (2018).
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Z.-Y. Chen, “Spectral control of high harmonics from relativistic plasmas using bicircular fields,” Phys. Rev. E 97, 043202 (2018).
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Z.-Y. Chen, X.-Y. Li, B.-Y. Li, M. Chen, and F. Liu, “Isolated elliptically polarized attosecond soft x-ray with high-brilliance using polarization gating of harmonics from relativistic plasmas at oblique incidence,” Opt. Express 26, 4572–4580 (2018).
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Z.-Y. Chen and A. Pukhov, “Bright high-order harmonic generation with controllable polarization from a relativistic plasma mirror,” Nat. Commun. 7, 12515 (2016).
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L. A. Chizhova, F. Libisch, and J. Burgdörfer, “High-harmonic generation in graphene: Interband response and the harmonic cutoff,” Phys. Rev. B 95, 085436 (2017).
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L. A. Chizhova, F. Libisch, and J. Burgdörfer, “Nonlinear response of graphene to a few-cycle terahertz laser pulse: Role of doping and disorder,” Phys. Rev. B 94, 075412 (2016).
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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 (2015).
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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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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).
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Corkum, P.

G. Vampa, T. Hammond, N. Thiré, B. Schmidt, F. Légaré, C. McDonald, T. Brabec, D. Klug, and P. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett. 115, 193603 (2015).
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M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thiré, B. E. Schmidt, F. Légaré, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96, 195420 (2017).
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G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522, 462–464 (2015).
[Crossref] [PubMed]

G. Vampa, C. R. McDonald, G. Orlando, P. B. Corkum, and T. Brabec, “Semiclassical analysis of high harmonic generation in bulk crystals,” Phys. Rev. B 91, 064302 (2015).
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Cormode, D.

A. Roberts, D. Cormode, C. Reynolds, T. Newhouse-Illige, B. J. LeRoy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99, 051912 (2011).
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M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. García de Abajo, and B. Jens, “Ultrafast nonlinear optical response of dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
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G. A. Garcia, L. Nahon, S. Daly, and I. Powis, “Vibrationally induced inversion of photoelectron forward-backward asymmetry in chiral molecule photoionization by circularly polarized light,” Nat. Commun. 4, 2132 (2013).
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J. D. Cox, A. Marini, and F. J. G. de Abajo, “Plasmon-assisted high-harmonic generation in graphene,” Nat. Commun. 8, 14380 (2017).
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M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thiré, B. E. Schmidt, F. Légaré, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96, 195420 (2017).
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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).
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DiChiara, A. D.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

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I. Al-Naib, J. E. Sipe, and M. M. Dignam, “Nonperturbative model of harmonic generation in undoped graphene in the terahertz regime,” New J. Phys. 17, 113018 (2015).
[Crossref]

I. Al-Naib, J. E. Sipe, and M. M. Dignam, “High harmonic generation in undoped graphene: Interplay of inter- and intraband dynamics,” Phys. Rev. B 90, 245423 (2014).
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S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
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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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D. D. Hickstein, F. J. Dollar, P. G. 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).
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D. D. Hickstein, F. J. Dollar, P. G. 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).
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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).
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A. Roberts, D. Cormode, C. Reynolds, T. Newhouse-Illige, B. J. LeRoy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99, 051912 (2011).
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Figures (5)

Fig. 1
Fig. 1 (a) Typical waveform of the applied vector potential (red) and induced electronic current (blue). The 800 nm near-infrared laser has a FWHM pulse duration of 15 fs and intensity of IL = 3 TW/cm2. (b) Intensity of the 9th harmonic (blue dots) scales as I L 2 (orange line) instead of I L 9 (dashed green line), showing nonperturbative characteristic of the higher-order harmonic generation process studied here.
Fig. 2
Fig. 2 High harmonic spectra up to the 15th order with a driving intensity of 3 TW/cm2, demonstrating the possibility of HHG in graphene extending to the XUV spectral region. The linearly polarized fundamental field is directed along either the armchair (AC) or zigzag (ZZ) directions of the crystal. The inset shows the crystal structure of monolayer graphene and the definition of the AC and ZZ directions.
Fig. 3
Fig. 3 Evolution of the HHG spectra as a function of time, i.e., spectrogram of the HHG process, for laser polarization orientating along the (a) ZZ and (b) AC direction respectively, revealing the high harmonic emission in phase at each field peak, suggesting intraband contribution is the dominate mechanism for the HHG in this study. The white curves are the waveform of the laser pulses. The pump laser intensity is 3 TW/cm2. Colorbar represents spectral intensity (arb. units) in logarithmic scale.
Fig. 4
Fig. 4 Ellipticity dependence of the peak harmonic intensity for different harmonic orders. The major axis of the elliptical polarization of the driving field is fixed relative to the (a-d) ZZ and (e-h) AC directions. The driving field intensity is 3 TW/cm2. For each harmonic order, intensity of the field components parallel (I) or perpendicular (I) to the major axis of the laser polarization is normalized by the maximum intensity between the two (max{I, I}). The total intensity (Itotal = I + I) is normalized by the maximum Itotal. For the 5th and 7th harmonics, harmonic intensity is non-zero with circularly polarized driving pulse, in contrast to the 3rd and 9th harmonics.
Fig. 5
Fig. 5 (a) High harmonic spectra in graphene driven by a single circularly polarized laser field with intensity of 3 TW/cm2. The selection rule of the harmonic orders (n = 6m ± 1 (m = 1, 2, 3, · · ·)) reflects the six-fold rotational symmetry of the graphene crystal. 3D plots of the electric field vector (purple) of the (b) 11th and (c) 13th harmonic demonstrate the generated high harmonics are circularly polarized with opposite helicity. Also shown in panels (b) and (c) are the waveform of the two orthogonal electric field components Ex (green) and Ey (blue), as well as the projection of ExEy (gray).

Equations (2)

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A ( t ) = I L c ω f ( t ) [ 1 1 + 2 cos ( ω t + ϕ ) e ^ x + 1 + 2 sin ( ω t + ϕ ) e ^ y ] ,
HHG ( ω ) = | 𝒯 ( t j ( r , t ) d 3 r ) | 2 ,

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