Abstract

High harmonic spectrum of a quasi-monochromatic pump that interacts with isotropic media consists of only odd-order harmonics. Addition of a secondary pump, e.g. a static field or the second harmonic of the primary pump, can results with generation of both odd and even harmonics of the primary pump. We propose a method for quasi-phase matching of only the even-order harmonics of the primary pump. We formulate a theory for this process and demonstrate it numerically. We also show that it leads to attosecond pulse trains with constant carrier envelop phase and high repetition rate.

© 2014 Optical Society of America

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    [CrossRef]
  3. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292(5522), 1689–1692 (2001).
    [CrossRef] [PubMed]
  4. M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
    [CrossRef] [PubMed]
  5. R. I. Tobey, M. E. Siemens, O. Cohen, M. M. Murnane, H. C. Kapteyn, K. A. Nelson, “Ultrafast extreme ultraviolet holography: dynamic monitoring of surface deformation,” Opt. Lett. 32(3), 286–288 (2007).
    [CrossRef] [PubMed]
  6. R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
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  13. M. Kozlov, O. Kfir, A. Fleischer, A. Kaplan, T. Carmon, H. G. Schwefel, G. Bartal, O. Cohen, “Narrow-bandwidth high-order harmonics driven by long-duration hot spots,” New J. Phys. 14(6), 063036 (2012).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  26. M. V. Ammosov, N. B. Delone, V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).
  27. O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007).
    [CrossRef] [PubMed]
  28. D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
    [CrossRef] [PubMed]
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2012 (4)

E. Frumker, C. T. Hebeisen, N. Kajumba, J. B. Bertrand, H. J. Wörner, M. Spanner, D. M. Villeneuve, A. Naumov, P. B. Corkum, “Oriented Rotational Wave-Packet Dynamics Studies via High Harmonic Generation,” Phys. Rev. Lett. 109(11), 113901 (2012).
[CrossRef] [PubMed]

M. Kozlov, O. Kfir, A. Fleischer, A. Kaplan, T. Carmon, H. G. Schwefel, G. Bartal, O. Cohen, “Narrow-bandwidth high-order harmonics driven by long-duration hot spots,” New J. Phys. 14(6), 063036 (2012).
[CrossRef]

L. Z. Liu, K. OKeeffe, S. M. Hooker, “Quasi-phase-matching of high-order-harmonic generation using polarization beating in optical waveguides,” Phys. Rev. A 85(5), 053823 (2012).
[CrossRef]

L. Z. Liu, K. O’Keeffe, S. M. Hooker, “Optical rotation quasi-phase-matching for circularly polarized high harmonic generation,” Opt. Lett. 37(12), 2415–2417 (2012).
[CrossRef] [PubMed]

2011 (1)

S. Guo, S. Q. Duan, N. Yang, W. D. Ch, W. Zhang, “Generation of even harmonics in coupled quantum dots,” Phys. Rev. A 84(1), 015803 (2011).
[CrossRef]

2010 (3)

C. Serrat, J. Biegert, “All-Regions Tunable High Harmonic Enhancement by a Periodic Static Electric field,” Phys. Rev. Lett. 104(7), 073901 (2010).
[CrossRef] [PubMed]

D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81(1), 011803 (2010).
[CrossRef]

P. Sidorenko, M. Kozlov, A. Bahabad, T. Popmintchev, M. Murnane, H. Kapteyn, O. Cohen, “Sawtooth grating-assisted phase-matching,” Opt. Express 18(22), 22686–22692 (2010).
[CrossRef] [PubMed]

2009 (1)

2007 (8)

R. I. Tobey, M. E. Siemens, O. Cohen, M. M. Murnane, H. C. Kapteyn, K. A. Nelson, “Ultrafast extreme ultraviolet holography: dynamic monitoring of surface deformation,” Opt. Lett. 32(3), 286–288 (2007).
[CrossRef] [PubMed]

O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007).
[CrossRef] [PubMed]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007).
[CrossRef]

J. Seres, V. S. Yakovlev, E. Seres, Ch. Streli, P. Wobrauschek, Ch. Spielmann, F. Krausz, “Coherent superposition of laser-driven soft-X-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007).
[CrossRef]

M. Zepf, B. Dromey, M. Landreman, P. Foster, S. M. Hooker, “Bright Quasi-Phase-Matched Soft-X-Ray Harmonic Radiation from Argon Ions,” Phys. Rev. Lett. 99(14), 143901 (2007).
[CrossRef] [PubMed]

O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. 99(5), 053902 (2007).
[CrossRef] [PubMed]

R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[CrossRef] [PubMed]

H. Kapteyn, O. Cohen, I. Christov, M. Murnane, “Harnessing Attosecond Science in the Quest for Coherent X-rays,” Science 317(5839), 775–778 (2007).
[CrossRef] [PubMed]

2006 (3)

T. Pfeifer, C. Spielmann, G. Gerber, “Femtosecond x-ray science,” Rep. Prog. Phys. 69(2), 443–505 (2006).
[CrossRef]

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, M. B. Gaarde, “Attosecond Pulse Trains Generated Using Two Color Laser Fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
[CrossRef] [PubMed]

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
[CrossRef] [PubMed]

2005 (1)

S. Odžak, D. B. Milošević, “High-order harmonic generation in the presence of a static electric field,” Phys. Rev. A 72(3), 033407 (2005).
[CrossRef]

2003 (1)

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[CrossRef] [PubMed]

2001 (2)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[CrossRef] [PubMed]

1999 (1)

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

1993 (2)

N. Ben-Tal, N. Moiseyev, A. Beswick, “The effect of Hamiltonian symmetry on generation of odd and even harmonics,” J. Phys. B 26(18), 3017–3024 (1993).
[CrossRef]

M. D. Perry, J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48(6), 4051–4054 (1993).
[CrossRef] [PubMed]

1986 (1)

M. V. Ammosov, N. B. Delone, V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

Agostini, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

Augé, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

Backus, S.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[CrossRef] [PubMed]

Bahabad, A.

Balcou, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

Bartal, G.

M. Kozlov, O. Kfir, A. Fleischer, A. Kaplan, T. Carmon, H. G. Schwefel, G. Bartal, O. Cohen, “Narrow-bandwidth high-order harmonics driven by long-duration hot spots,” New J. Phys. 14(6), 063036 (2012).
[CrossRef]

Bartels, R. A.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[CrossRef] [PubMed]

Ben-Tal, N.

N. Ben-Tal, N. Moiseyev, A. Beswick, “The effect of Hamiltonian symmetry on generation of odd and even harmonics,” J. Phys. B 26(18), 3017–3024 (1993).
[CrossRef]

Berrill, M.

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
[CrossRef] [PubMed]

Bertrand, J. B.

E. Frumker, C. T. Hebeisen, N. Kajumba, J. B. Bertrand, H. J. Wörner, M. Spanner, D. M. Villeneuve, A. Naumov, P. B. Corkum, “Oriented Rotational Wave-Packet Dynamics Studies via High Harmonic Generation,” Phys. Rev. Lett. 109(11), 113901 (2012).
[CrossRef] [PubMed]

Beswick, A.

N. Ben-Tal, N. Moiseyev, A. Beswick, “The effect of Hamiltonian symmetry on generation of odd and even harmonics,” J. Phys. B 26(18), 3017–3024 (1993).
[CrossRef]

Biegert, J.

C. Serrat, J. Biegert, “All-Regions Tunable High Harmonic Enhancement by a Periodic Static Electric field,” Phys. Rev. Lett. 104(7), 073901 (2010).
[CrossRef] [PubMed]

D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81(1), 011803 (2010).
[CrossRef]

Brabec, T.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[CrossRef] [PubMed]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

Carmon, T.

M. Kozlov, O. Kfir, A. Fleischer, A. Kaplan, T. Carmon, H. G. Schwefel, G. Bartal, O. Cohen, “Narrow-bandwidth high-order harmonics driven by long-duration hot spots,” New J. Phys. 14(6), 063036 (2012).
[CrossRef]

Cela, J. M.

D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81(1), 011803 (2010).
[CrossRef]

Ch, W. D.

S. Guo, S. Q. Duan, N. Yang, W. D. Ch, W. Zhang, “Generation of even harmonics in coupled quantum dots,” Phys. Rev. A 84(1), 015803 (2011).
[CrossRef]

Christov, I.

H. Kapteyn, O. Cohen, I. Christov, M. Murnane, “Harnessing Attosecond Science in the Quest for Coherent X-rays,” Science 317(5839), 775–778 (2007).
[CrossRef] [PubMed]

Christov, I. P.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[CrossRef] [PubMed]

Cohen, O.

M. Kozlov, O. Kfir, A. Fleischer, A. Kaplan, T. Carmon, H. G. Schwefel, G. Bartal, O. Cohen, “Narrow-bandwidth high-order harmonics driven by long-duration hot spots,” New J. Phys. 14(6), 063036 (2012).
[CrossRef]

P. Sidorenko, M. Kozlov, A. Bahabad, T. Popmintchev, M. Murnane, H. Kapteyn, O. Cohen, “Sawtooth grating-assisted phase-matching,” Opt. Express 18(22), 22686–22692 (2010).
[CrossRef] [PubMed]

O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. 99(5), 053902 (2007).
[CrossRef] [PubMed]

R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[CrossRef] [PubMed]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007).
[CrossRef]

H. Kapteyn, O. Cohen, I. Christov, M. Murnane, “Harnessing Attosecond Science in the Quest for Coherent X-rays,” Science 317(5839), 775–778 (2007).
[CrossRef] [PubMed]

R. I. Tobey, M. E. Siemens, O. Cohen, M. M. Murnane, H. C. Kapteyn, K. A. Nelson, “Ultrafast extreme ultraviolet holography: dynamic monitoring of surface deformation,” Opt. Lett. 32(3), 286–288 (2007).
[CrossRef] [PubMed]

O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007).
[CrossRef] [PubMed]

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
[CrossRef] [PubMed]

Corkum, P.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[CrossRef] [PubMed]

Corkum, P. B.

E. Frumker, C. T. Hebeisen, N. Kajumba, J. B. Bertrand, H. J. Wörner, M. Spanner, D. M. Villeneuve, A. Naumov, P. B. Corkum, “Oriented Rotational Wave-Packet Dynamics Studies via High Harmonic Generation,” Phys. Rev. Lett. 109(11), 113901 (2012).
[CrossRef] [PubMed]

Crane, J. K.

M. D. Perry, J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48(6), 4051–4054 (1993).
[CrossRef] [PubMed]

Delone, N. B.

M. V. Ammosov, N. B. Delone, V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

Di Trapani, P.

D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81(1), 011803 (2010).
[CrossRef]

Drescher, M.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[CrossRef] [PubMed]

Dromey, B.

M. Zepf, B. Dromey, M. Landreman, P. Foster, S. M. Hooker, “Bright Quasi-Phase-Matched Soft-X-Ray Harmonic Radiation from Argon Ions,” Phys. Rev. Lett. 99(14), 143901 (2007).
[CrossRef] [PubMed]

Duan, S. Q.

S. Guo, S. Q. Duan, N. Yang, W. D. Ch, W. Zhang, “Generation of even harmonics in coupled quantum dots,” Phys. Rev. A 84(1), 015803 (2011).
[CrossRef]

Faccio, D.

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M. Zepf, B. Dromey, M. Landreman, P. Foster, S. M. Hooker, “Bright Quasi-Phase-Matched Soft-X-Ray Harmonic Radiation from Argon Ions,” Phys. Rev. Lett. 99(14), 143901 (2007).
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J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, M. B. Gaarde, “Attosecond Pulse Trains Generated Using Two Color Laser Fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
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R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
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D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
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R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
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R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
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Hooker, S. M.

L. Z. Liu, K. O’Keeffe, S. M. Hooker, “Optical rotation quasi-phase-matching for circularly polarized high harmonic generation,” Opt. Lett. 37(12), 2415–2417 (2012).
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M. Zepf, B. Dromey, M. Landreman, P. Foster, S. M. Hooker, “Bright Quasi-Phase-Matched Soft-X-Ray Harmonic Radiation from Argon Ions,” Phys. Rev. Lett. 99(14), 143901 (2007).
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J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, M. B. Gaarde, “Attosecond Pulse Trains Generated Using Two Color Laser Fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
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E. Frumker, C. T. Hebeisen, N. Kajumba, J. B. Bertrand, H. J. Wörner, M. Spanner, D. M. Villeneuve, A. Naumov, P. B. Corkum, “Oriented Rotational Wave-Packet Dynamics Studies via High Harmonic Generation,” Phys. Rev. Lett. 109(11), 113901 (2012).
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P. Sidorenko, M. Kozlov, A. Bahabad, T. Popmintchev, M. Murnane, H. Kapteyn, O. Cohen, “Sawtooth grating-assisted phase-matching,” Opt. Express 18(22), 22686–22692 (2010).
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H. Kapteyn, O. Cohen, I. Christov, M. Murnane, “Harnessing Attosecond Science in the Quest for Coherent X-rays,” Science 317(5839), 775–778 (2007).
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R. I. Tobey, M. E. Siemens, O. Cohen, M. M. Murnane, H. C. Kapteyn, K. A. Nelson, “Ultrafast extreme ultraviolet holography: dynamic monitoring of surface deformation,” Opt. Lett. 32(3), 286–288 (2007).
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X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007).
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[CrossRef] [PubMed]

O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007).
[CrossRef] [PubMed]

O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. 99(5), 053902 (2007).
[CrossRef] [PubMed]

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
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A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
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M. Kozlov, O. Kfir, A. Fleischer, A. Kaplan, T. Carmon, H. G. Schwefel, G. Bartal, O. Cohen, “Narrow-bandwidth high-order harmonics driven by long-duration hot spots,” New J. Phys. 14(6), 063036 (2012).
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M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
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M. Kozlov, O. Kfir, A. Fleischer, A. Kaplan, T. Carmon, H. G. Schwefel, G. Bartal, O. Cohen, “Narrow-bandwidth high-order harmonics driven by long-duration hot spots,” New J. Phys. 14(6), 063036 (2012).
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P. Sidorenko, M. Kozlov, A. Bahabad, T. Popmintchev, M. Murnane, H. Kapteyn, O. Cohen, “Sawtooth grating-assisted phase-matching,” Opt. Express 18(22), 22686–22692 (2010).
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J. Seres, V. S. Yakovlev, E. Seres, Ch. Streli, P. Wobrauschek, Ch. Spielmann, F. Krausz, “Coherent superposition of laser-driven soft-X-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007).
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M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

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J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, M. B. Gaarde, “Attosecond Pulse Trains Generated Using Two Color Laser Fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
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Lan, P.

Landreman, M.

M. Zepf, B. Dromey, M. Landreman, P. Foster, S. M. Hooker, “Bright Quasi-Phase-Matched Soft-X-Ray Harmonic Radiation from Argon Ions,” Phys. Rev. Lett. 99(14), 143901 (2007).
[CrossRef] [PubMed]

Liu, L. Z.

L. Z. Liu, K. O’Keeffe, S. M. Hooker, “Optical rotation quasi-phase-matching for circularly polarized high harmonic generation,” Opt. Lett. 37(12), 2415–2417 (2012).
[CrossRef] [PubMed]

L. Z. Liu, K. OKeeffe, S. M. Hooker, “Quasi-phase-matching of high-order-harmonic generation using polarization beating in optical waveguides,” Phys. Rev. A 85(5), 053823 (2012).
[CrossRef]

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R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
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Lytle, A. L.

O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. 99(5), 053902 (2007).
[CrossRef] [PubMed]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007).
[CrossRef]

O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007).
[CrossRef] [PubMed]

Mauritsson, J.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, M. B. Gaarde, “Attosecond Pulse Trains Generated Using Two Color Laser Fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
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R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[CrossRef] [PubMed]

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M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
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Mullot, G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292(5522), 1689–1692 (2001).
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P. Sidorenko, M. Kozlov, A. Bahabad, T. Popmintchev, M. Murnane, H. Kapteyn, O. Cohen, “Sawtooth grating-assisted phase-matching,” Opt. Express 18(22), 22686–22692 (2010).
[CrossRef] [PubMed]

H. Kapteyn, O. Cohen, I. Christov, M. Murnane, “Harnessing Attosecond Science in the Quest for Coherent X-rays,” Science 317(5839), 775–778 (2007).
[CrossRef] [PubMed]

Murnane, M. M.

R. I. Tobey, M. E. Siemens, O. Cohen, M. M. Murnane, H. C. Kapteyn, K. A. Nelson, “Ultrafast extreme ultraviolet holography: dynamic monitoring of surface deformation,” Opt. Lett. 32(3), 286–288 (2007).
[CrossRef] [PubMed]

R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[CrossRef] [PubMed]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007).
[CrossRef]

O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007).
[CrossRef] [PubMed]

O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. 99(5), 053902 (2007).
[CrossRef] [PubMed]

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
[CrossRef] [PubMed]

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[CrossRef] [PubMed]

Naumov, A.

E. Frumker, C. T. Hebeisen, N. Kajumba, J. B. Bertrand, H. J. Wörner, M. Spanner, D. M. Villeneuve, A. Naumov, P. B. Corkum, “Oriented Rotational Wave-Packet Dynamics Studies via High Harmonic Generation,” Phys. Rev. Lett. 109(11), 113901 (2012).
[CrossRef] [PubMed]

Nelson, K. A.

O’Keeffe, K.

Odžak, S.

S. Odžak, D. B. Milošević, “High-order harmonic generation in the presence of a static electric field,” Phys. Rev. A 72(3), 033407 (2005).
[CrossRef]

OKeeffe, K.

L. Z. Liu, K. OKeeffe, S. M. Hooker, “Quasi-phase-matching of high-order-harmonic generation using polarization beating in optical waveguides,” Phys. Rev. A 85(5), 053823 (2012).
[CrossRef]

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R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[CrossRef] [PubMed]

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[CrossRef] [PubMed]

Paul, P. M.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292(5522), 1689–1692 (2001).
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T. Pfeifer, C. Spielmann, G. Gerber, “Femtosecond x-ray science,” Rep. Prog. Phys. 69(2), 443–505 (2006).
[CrossRef]

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P. Sidorenko, M. Kozlov, A. Bahabad, T. Popmintchev, M. Murnane, H. Kapteyn, O. Cohen, “Sawtooth grating-assisted phase-matching,” Opt. Express 18(22), 22686–22692 (2010).
[CrossRef] [PubMed]

O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. 99(5), 053902 (2007).
[CrossRef] [PubMed]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007).
[CrossRef]

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
[CrossRef] [PubMed]

Raymondson, D. A.

R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[CrossRef] [PubMed]

Reagan, B.

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
[CrossRef] [PubMed]

Reider, G. A.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[CrossRef] [PubMed]

Rocca, J. J.

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
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R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[CrossRef] [PubMed]

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R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[CrossRef] [PubMed]

Schafer, K. J.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, M. B. Gaarde, “Attosecond Pulse Trains Generated Using Two Color Laser Fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
[CrossRef] [PubMed]

Schnürer, M.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

Schwefel, H. G.

M. Kozlov, O. Kfir, A. Fleischer, A. Kaplan, T. Carmon, H. G. Schwefel, G. Bartal, O. Cohen, “Narrow-bandwidth high-order harmonics driven by long-duration hot spots,” New J. Phys. 14(6), 063036 (2012).
[CrossRef]

Scrinzi, A.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

Seres, E.

J. Seres, V. S. Yakovlev, E. Seres, Ch. Streli, P. Wobrauschek, Ch. Spielmann, F. Krausz, “Coherent superposition of laser-driven soft-X-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007).
[CrossRef]

Seres, J.

J. Seres, V. S. Yakovlev, E. Seres, Ch. Streli, P. Wobrauschek, Ch. Spielmann, F. Krausz, “Coherent superposition of laser-driven soft-X-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007).
[CrossRef]

Serrat, C.

C. Serrat, J. Biegert, “All-Regions Tunable High Harmonic Enhancement by a Periodic Static Electric field,” Phys. Rev. Lett. 104(7), 073901 (2010).
[CrossRef] [PubMed]

D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81(1), 011803 (2010).
[CrossRef]

Sidorenko, P.

Siemens, M. E.

Song, C.

R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[CrossRef] [PubMed]

Spanner, M.

E. Frumker, C. T. Hebeisen, N. Kajumba, J. B. Bertrand, H. J. Wörner, M. Spanner, D. M. Villeneuve, A. Naumov, P. B. Corkum, “Oriented Rotational Wave-Packet Dynamics Studies via High Harmonic Generation,” Phys. Rev. Lett. 109(11), 113901 (2012).
[CrossRef] [PubMed]

Spielmann, C.

T. Pfeifer, C. Spielmann, G. Gerber, “Femtosecond x-ray science,” Rep. Prog. Phys. 69(2), 443–505 (2006).
[CrossRef]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[CrossRef] [PubMed]

Spielmann, Ch.

J. Seres, V. S. Yakovlev, E. Seres, Ch. Streli, P. Wobrauschek, Ch. Spielmann, F. Krausz, “Coherent superposition of laser-driven soft-X-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007).
[CrossRef]

Streli, Ch.

J. Seres, V. S. Yakovlev, E. Seres, Ch. Streli, P. Wobrauschek, Ch. Spielmann, F. Krausz, “Coherent superposition of laser-driven soft-X-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007).
[CrossRef]

Tempea, G.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

Tobey, R.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[CrossRef] [PubMed]

Tobey, R. I.

R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[CrossRef] [PubMed]

R. I. Tobey, M. E. Siemens, O. Cohen, M. M. Murnane, H. C. Kapteyn, K. A. Nelson, “Ultrafast extreme ultraviolet holography: dynamic monitoring of surface deformation,” Opt. Lett. 32(3), 286–288 (2007).
[CrossRef] [PubMed]

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

Villeneuve, D. M.

E. Frumker, C. T. Hebeisen, N. Kajumba, J. B. Bertrand, H. J. Wörner, M. Spanner, D. M. Villeneuve, A. Naumov, P. B. Corkum, “Oriented Rotational Wave-Packet Dynamics Studies via High Harmonic Generation,” Phys. Rev. Lett. 109(11), 113901 (2012).
[CrossRef] [PubMed]

Walker, B. C.

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
[CrossRef] [PubMed]

Wang, X.

Weiman, S.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[CrossRef] [PubMed]

Wobrauschek, P.

J. Seres, V. S. Yakovlev, E. Seres, Ch. Streli, P. Wobrauschek, Ch. Spielmann, F. Krausz, “Coherent superposition of laser-driven soft-X-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007).
[CrossRef]

Wörner, H. J.

E. Frumker, C. T. Hebeisen, N. Kajumba, J. B. Bertrand, H. J. Wörner, M. Spanner, D. M. Villeneuve, A. Naumov, P. B. Corkum, “Oriented Rotational Wave-Packet Dynamics Studies via High Harmonic Generation,” Phys. Rev. Lett. 109(11), 113901 (2012).
[CrossRef] [PubMed]

Yakovlev, V. S.

J. Seres, V. S. Yakovlev, E. Seres, Ch. Streli, P. Wobrauschek, Ch. Spielmann, F. Krausz, “Coherent superposition of laser-driven soft-X-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007).
[CrossRef]

Yang, N.

S. Guo, S. Q. Duan, N. Yang, W. D. Ch, W. Zhang, “Generation of even harmonics in coupled quantum dots,” Phys. Rev. A 84(1), 015803 (2011).
[CrossRef]

Zepf, M.

M. Zepf, B. Dromey, M. Landreman, P. Foster, S. M. Hooker, “Bright Quasi-Phase-Matched Soft-X-Ray Harmonic Radiation from Argon Ions,” Phys. Rev. Lett. 99(14), 143901 (2007).
[CrossRef] [PubMed]

Zhang, Q.

Zhang, W.

S. Guo, S. Q. Duan, N. Yang, W. D. Ch, W. Zhang, “Generation of even harmonics in coupled quantum dots,” Phys. Rev. A 84(1), 015803 (2011).
[CrossRef]

Zhang, X.

O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. 99(5), 053902 (2007).
[CrossRef] [PubMed]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007).
[CrossRef]

O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007).
[CrossRef] [PubMed]

Zhou, X.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007).
[CrossRef]

J. Phys. B (1)

N. Ben-Tal, N. Moiseyev, A. Beswick, “The effect of Hamiltonian symmetry on generation of odd and even harmonics,” J. Phys. B 26(18), 3017–3024 (1993).
[CrossRef]

Nat. Phys. (2)

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007).
[CrossRef]

J. Seres, V. S. Yakovlev, E. Seres, Ch. Streli, P. Wobrauschek, Ch. Spielmann, F. Krausz, “Coherent superposition of laser-driven soft-X-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007).
[CrossRef]

Nature (2)

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[CrossRef] [PubMed]

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[CrossRef] [PubMed]

New J. Phys. (1)

M. Kozlov, O. Kfir, A. Fleischer, A. Kaplan, T. Carmon, H. G. Schwefel, G. Bartal, O. Cohen, “Narrow-bandwidth high-order harmonics driven by long-duration hot spots,” New J. Phys. 14(6), 063036 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (5)

D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81(1), 011803 (2010).
[CrossRef]

L. Z. Liu, K. OKeeffe, S. M. Hooker, “Quasi-phase-matching of high-order-harmonic generation using polarization beating in optical waveguides,” Phys. Rev. A 85(5), 053823 (2012).
[CrossRef]

S. Guo, S. Q. Duan, N. Yang, W. D. Ch, W. Zhang, “Generation of even harmonics in coupled quantum dots,” Phys. Rev. A 84(1), 015803 (2011).
[CrossRef]

S. Odžak, D. B. Milošević, “High-order harmonic generation in the presence of a static electric field,” Phys. Rev. A 72(3), 033407 (2005).
[CrossRef]

M. D. Perry, J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48(6), 4051–4054 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett. (8)

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, M. B. Gaarde, “Attosecond Pulse Trains Generated Using Two Color Laser Fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
[CrossRef] [PubMed]

E. Frumker, C. T. Hebeisen, N. Kajumba, J. B. Bertrand, H. J. Wörner, M. Spanner, D. M. Villeneuve, A. Naumov, P. B. Corkum, “Oriented Rotational Wave-Packet Dynamics Studies via High Harmonic Generation,” Phys. Rev. Lett. 109(11), 113901 (2012).
[CrossRef] [PubMed]

R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hädrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, F. Salmassi, “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams,” Phys. Rev. Lett. 99(9), 098103 (2007).
[CrossRef] [PubMed]

M. Zepf, B. Dromey, M. Landreman, P. Foster, S. M. Hooker, “Bright Quasi-Phase-Matched Soft-X-Ray Harmonic Radiation from Argon Ions,” Phys. Rev. Lett. 99(14), 143901 (2007).
[CrossRef] [PubMed]

O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. 99(5), 053902 (2007).
[CrossRef] [PubMed]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

C. Serrat, J. Biegert, “All-Regions Tunable High Harmonic Enhancement by a Periodic Static Electric field,” Phys. Rev. Lett. 104(7), 073901 (2010).
[CrossRef] [PubMed]

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. C. Walker, M. M. Murnane, H. C. Kapteyn, J. J. Rocca, “High-Order Harmonic Generation from Ions in a Capillary Discharge,” Phys. Rev. Lett. 96(20), 203001 (2006).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

T. Pfeifer, C. Spielmann, G. Gerber, “Femtosecond x-ray science,” Rep. Prog. Phys. 69(2), 443–505 (2006).
[CrossRef]

Science (2)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292(5522), 1689–1692 (2001).
[CrossRef] [PubMed]

H. Kapteyn, O. Cohen, I. Christov, M. Murnane, “Harnessing Attosecond Science in the Quest for Coherent X-rays,” Science 317(5839), 775–778 (2007).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

M. V. Ammosov, N. B. Delone, V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

Other (1)

O. Kfir, P. Sidorenko, A. Paul, T. Popmintchev, H. Kapteyn, M. Murnane, and O. Cohen, “Extended Phase-Matching of High Harmonics Driven by Focusing Light in Planar Waveguide”, Frontiers in Optic (Optical Society of America, Rochester, NY, 2012), paper LTh1H.4.

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Figures (5)

Fig. 1
Fig. 1

Influence of secondary static field on the phases and intensities of even and odd harmonics. Phases (a-c) and intensities (d-f) of the 86th, 70th and 85th harmonics as a function of the static field. The phases of even and odd harmonics are odd and even functions of the static field, respectively.

Fig. 2
Fig. 2

Influence of the relative phase between the fundamental and its second harmonic drivers, Δφ, on the phases and intensities of even and odd harmonics. Phases (a-c) and intensities (d-f) of the 84th, 60th and 85th harmonics as a function of the relative phase for different intensities of the second harmonic field: 0.6 × 10 11 W / c m 2 (blue), 2.4 × 10 11 W / c m 2 (red) and 9.6 × 10 11 W / c m 2 (black).A π shift in the relative phase results with a π-shift in phases of even harmonics (sign flip of their fields) and no shift in phases of odd harmonics.

Fig. 3
Fig. 3

Numerical demonstration of QPM of only even harmonics using a periodic static field. (a) Harmonic spectra driven by a fundamental driver and a static field with sign (direction of polarization) that is flipped periodically during propagation with periodicity that corresponds to the coherence length of the 88th cutoff harmonic (red) and with static field with a constant sign (black). The inset shows the spectra near the 88th harmonic, showing that only even order harmonics are enhanced. (b) Buildup of the 88th harmonic (red), the 87th harmonic with periodic static field (dashed blue) and the 88th harmonic with constant static field (dotted black). The buildup of the 88th harmonic with periodic static field exhibits a typical QPM structure. (c) and (d) show the same data as (a) and (b), respectively, with the only difference that the periodicity of the static field corresponds to the coherence length of the 70th plateau harmonic.

Fig. 4
Fig. 4

Generation of APT with stable CEP without reducing the repetition rate. (a) Normalized APT, EQPM(t), corresponds to the red spectrum in Fig. 3(a) in the spectral region 83 ± 5 harmonics. (b) Averaged sum of EQPM and its T0/2 time-shifted field. The fact that the average sum is very similar to EQPM shows that consecutive pulses are very similar, i.e. they all have the same CEP. (c) Normalized APT, ESA(t), corresponds to the spectral region 83 ± 5 harmonics of a spectrum generated by only the fundamental driver and without propagation. (d) Averaged sum of ESA and its T0/2 time-shifted field. The fact that the central pulses of the average are almost zero corresponds to the known fact that consecutive pulses in ordinarily generated APT have opposite phases.

Fig. 5
Fig. 5

Numerical demonstration of QPM of only even harmonics using a bi-chromatic drivers that consists of a fundamental pump field and its second harmonic. (a) Harmonic spectra when the two drivers experience dispersion Δn = 8.7 × 10−3 (red) and Δn = 0. The inset shows the spectrum near the 86th harmonic, showing that it consists of only even order harmonic. (b) Coherent buildups of the 86th (red) and the 85th (dashed blue) with Δn = 8.7 × 10−3 and the 86th harmonic with Δn = 0 (dotted black). The 86th harmonic Δn = 8.7 × 10−3 rises much more rapidly than the other buildup curves. (c) Harmonic spectra when the two drivers experience dispersion Δn = 7 × 10−3 (red) and Δn = 0 (black). The inset shows the spectrum near the 70th harmonic, showing that it consists of only even order harmonic. (d) Coherent buildups of the 70th (red) and the 71th (dashed blue) with Δn = 7 × 10−3 and the 70th harmonic with Δn = 0 (dotted black). The 70th harmonic Δn = 7 × 10−3 rises much more rapidly than the other buildup curves.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E HHG a ( t )= E HHG b ( t+ T 0 /2 )
E q a e iπq = E q b
E 0 z = 1 2 c τ ω p 2 E 0 d τ 2 π I P ( E 0 + E D C ) c n e [ E 0 + E D C ] τ
E H H G z = 2 π c P H H G τ
E B C z = 1 2 c τ ω p 2 E B C d τ 2 π I P E c n e E B C τ 1 c τ Δ n ˜ ( t ' ) E B C ( τ t ' ) d t '

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