Abstract

A technique for enhanced generation of selected high harmonics in a gas medium, in a high ionization limit, is proposed in this paper. An aperiodically corrugated hollow-core fiber is employed to modulate the intensity of the fundamental laser pulse along the direction of propagation, resulting in multiple quasi-phase-matched high harmonic emissions at the cutoff region. Simulated annealing (SA) algorithm is applied for optimizing the aperiodic hollow-core fiber. Our simulation shows that the yield of selected harmonics is increased equally by up to 2 orders of magnitude compared with no modulation and this permits flexible control of the quasi-phase-matched emission of selected harmonics by appropriate corrugation.

© 2007 Optical Society of America

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  1. H. C. Kapteyn, M. M. Murnane, and I. P. Christov, "Coherent X-rays from Lasers: Applied Attosecond Science," Phys. Today 3, 39 (2005).
    [CrossRef]
  2. Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, "Generation of Coherent Soft X Rays at 2.7nm Using High Harmonics," Phys. Rev. Lett. 79, 2967-2970 (1997).
    [CrossRef]
  3. E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
    [CrossRef]
  4. C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
    [CrossRef]
  5. D. Attwood, "New opportunities at soft x-ray wavelengths," Phys. Today 45, 24-31 (1992).
    [CrossRef]
  6. E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
    [CrossRef] [PubMed]
  7. A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Buckus, "Quasi-phase-matched generation of coherent extreme-ultraviolet light," Nature 421, 51-54 (2003)
    [CrossRef] [PubMed]
  8. A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
    [CrossRef]
  9. I. P. Christov, H. C. Kapteyn, and M. M. Murnane, "Qusai-phase matching of high-harmonics and attosecond pulses in modulated waveguides," Opt. Express 7, 362-368 (2000).
    [CrossRef] [PubMed]
  10. I. P. Christov, "Control of high harmonic and attosecond pulse generation in aperiodic modulated waveguides," J. Opt. Soc. Am. B 18, 1877-1881 (2001).
    [CrossRef]
  11. X. Y. Zhang, Z. R. Sun, Y. F. Wang, G. L. Chen, Z. G. Wang, R. X. Li, Z. N. Zeng, and Z. Z. Xu, "High-order harmonic and attosecond pulse generation for a few-cycle laser pulse in modulated hollow fibers," J. Phys. B. 40, 2917-2925 (2007).
    [CrossRef]
  12. Y. W. Lee, F. C. Fan, Y. C. Huang, B. Y. Gu, B. Z. Dong, and M. H. Chou, " Nonlinear multiwavelength conversion based on an aperiodic optical superlattice in lithium niobate," Opt. Lett. 27, 2191-2193 (2002).
    [CrossRef]
  13. X. F. Chen, F. Wu, X. L. Zeng, Y. P. Chen, Y. X. Xia and Y. L. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
    [CrossRef]
  14. X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, and Y. L. Chen, " Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings," Opt. Commun. 204, 407-411 (2002).
    [CrossRef]
  15. M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Soviet Phys. JETP. 64, 1191-1194 (1986).

2007

X. Y. Zhang, Z. R. Sun, Y. F. Wang, G. L. Chen, Z. G. Wang, R. X. Li, Z. N. Zeng, and Z. Z. Xu, "High-order harmonic and attosecond pulse generation for a few-cycle laser pulse in modulated hollow fibers," J. Phys. B. 40, 2917-2925 (2007).
[CrossRef]

2006

A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
[CrossRef]

2005

H. C. Kapteyn, M. M. Murnane, and I. P. Christov, "Coherent X-rays from Lasers: Applied Attosecond Science," Phys. Today 3, 39 (2005).
[CrossRef]

2004

E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
[CrossRef]

X. F. Chen, F. Wu, X. L. Zeng, Y. P. Chen, Y. X. Xia and Y. L. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
[CrossRef]

2003

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

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

2002

X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, and Y. L. Chen, " Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings," Opt. Commun. 204, 407-411 (2002).
[CrossRef]

Y. W. Lee, F. C. Fan, Y. C. Huang, B. Y. Gu, B. Z. Dong, and M. H. Chou, " Nonlinear multiwavelength conversion based on an aperiodic optical superlattice in lithium niobate," Opt. Lett. 27, 2191-2193 (2002).
[CrossRef]

2001

2000

1997

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
[CrossRef]

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, "Generation of Coherent Soft X Rays at 2.7nm Using High Harmonics," Phys. Rev. Lett. 79, 2967-2970 (1997).
[CrossRef]

1992

D. Attwood, "New opportunities at soft x-ray wavelengths," Phys. Today 45, 24-31 (1992).
[CrossRef]

1986

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Soviet Phys. JETP. 64, 1191-1194 (1986).

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Soviet Phys. JETP. 64, 1191-1194 (1986).

Aquila, A.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Attwood, D.

D. Attwood, "New opportunities at soft x-ray wavelengths," Phys. Today 45, 24-31 (1992).
[CrossRef]

Attwood, D. T.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Backus, S.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Bartels, R. A.

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

Buckus, S.

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

Burnett, N.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
[CrossRef]

Chang, Z.

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, "Generation of Coherent Soft X Rays at 2.7nm Using High Harmonics," Phys. Rev. Lett. 79, 2967-2970 (1997).
[CrossRef]

Chen, G. L.

X. Y. Zhang, Z. R. Sun, Y. F. Wang, G. L. Chen, Z. G. Wang, R. X. Li, Z. N. Zeng, and Z. Z. Xu, "High-order harmonic and attosecond pulse generation for a few-cycle laser pulse in modulated hollow fibers," J. Phys. B. 40, 2917-2925 (2007).
[CrossRef]

Chen, X. F.

X. F. Chen, F. Wu, X. L. Zeng, Y. P. Chen, Y. X. Xia and Y. L. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
[CrossRef]

X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, and Y. L. Chen, " Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings," Opt. Commun. 204, 407-411 (2002).
[CrossRef]

Chen, Y. L.

X. F. Chen, F. Wu, X. L. Zeng, Y. P. Chen, Y. X. Xia and Y. L. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
[CrossRef]

X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, and Y. L. Chen, " Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings," Opt. Commun. 204, 407-411 (2002).
[CrossRef]

Chen, Y. P.

X. F. Chen, F. Wu, X. L. Zeng, Y. P. Chen, Y. X. Xia and Y. L. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
[CrossRef]

X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, and Y. L. Chen, " Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings," Opt. Commun. 204, 407-411 (2002).
[CrossRef]

Chou, M. H.

Christov, I. P.

A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
[CrossRef]

H. C. Kapteyn, M. M. Murnane, and I. P. Christov, "Coherent X-rays from Lasers: Applied Attosecond Science," Phys. Today 3, 39 (2005).
[CrossRef]

E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
[CrossRef]

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

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

I. P. Christov, "Control of high harmonic and attosecond pulse generation in aperiodic modulated waveguides," J. Opt. Soc. Am. B 18, 1877-1881 (2001).
[CrossRef]

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, "Qusai-phase matching of high-harmonics and attosecond pulses in modulated waveguides," Opt. Express 7, 362-368 (2000).
[CrossRef] [PubMed]

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Soviet Phys. JETP. 64, 1191-1194 (1986).

Dong, B. Z.

Fan, F. C.

Gaudiosi, D.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Gibson, E. A.

A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
[CrossRef]

E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
[CrossRef]

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Green, H.

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

Gu, B. Y.

Gullikson, E. M.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Huang, Y. C.

Kan, C.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
[CrossRef]

Kapteyn, H. C.

A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
[CrossRef]

H. C. Kapteyn, M. M. Murnane, and I. P. Christov, "Coherent X-rays from Lasers: Applied Attosecond Science," Phys. Today 3, 39 (2005).
[CrossRef]

E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
[CrossRef]

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

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, "Qusai-phase matching of high-harmonics and attosecond pulses in modulated waveguides," Opt. Express 7, 362-368 (2000).
[CrossRef] [PubMed]

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, "Generation of Coherent Soft X Rays at 2.7nm Using High Harmonics," Phys. Rev. Lett. 79, 2967-2970 (1997).
[CrossRef]

Koppitsch, R.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
[CrossRef]

Krainov, V. P.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Soviet Phys. JETP. 64, 1191-1194 (1986).

Krausz, F.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
[CrossRef]

Lee, Y. W.

Lenzner, M.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
[CrossRef]

Li, R. X.

X. Y. Zhang, Z. R. Sun, Y. F. Wang, G. L. Chen, Z. G. Wang, R. X. Li, Z. N. Zeng, and Z. Z. Xu, "High-order harmonic and attosecond pulse generation for a few-cycle laser pulse in modulated hollow fibers," J. Phys. B. 40, 2917-2925 (2007).
[CrossRef]

Lytle, A.

A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
[CrossRef]

E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
[CrossRef]

Murnane, M. M.

A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
[CrossRef]

H. C. Kapteyn, M. M. Murnane, and I. P. Christov, "Coherent X-rays from Lasers: Applied Attosecond Science," Phys. Today 3, 39 (2005).
[CrossRef]

E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
[CrossRef]

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

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

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, "Qusai-phase matching of high-harmonics and attosecond pulses in modulated waveguides," Opt. Express 7, 362-368 (2000).
[CrossRef] [PubMed]

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, "Generation of Coherent Soft X Rays at 2.7nm Using High Harmonics," Phys. Rev. Lett. 79, 2967-2970 (1997).
[CrossRef]

Paul, A.

A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
[CrossRef]

E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
[CrossRef]

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

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

Popmintchev, T.

A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
[CrossRef]

E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
[CrossRef]

Rundquist, A.

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, "Generation of Coherent Soft X Rays at 2.7nm Using High Harmonics," Phys. Rev. Lett. 79, 2967-2970 (1997).
[CrossRef]

Sartania, S.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
[CrossRef]

Schnurer, M.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
[CrossRef]

Spielman, C.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
[CrossRef]

Sun, Z. R.

X. Y. Zhang, Z. R. Sun, Y. F. Wang, G. L. Chen, Z. G. Wang, R. X. Li, Z. N. Zeng, and Z. Z. Xu, "High-order harmonic and attosecond pulse generation for a few-cycle laser pulse in modulated hollow fibers," J. Phys. B. 40, 2917-2925 (2007).
[CrossRef]

Tobey, R.

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

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Wagner, N.

E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
[CrossRef]

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Wang, H.

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, "Generation of Coherent Soft X Rays at 2.7nm Using High Harmonics," Phys. Rev. Lett. 79, 2967-2970 (1997).
[CrossRef]

Wang, Y. F.

X. Y. Zhang, Z. R. Sun, Y. F. Wang, G. L. Chen, Z. G. Wang, R. X. Li, Z. N. Zeng, and Z. Z. Xu, "High-order harmonic and attosecond pulse generation for a few-cycle laser pulse in modulated hollow fibers," J. Phys. B. 40, 2917-2925 (2007).
[CrossRef]

Wang, Z. G.

X. Y. Zhang, Z. R. Sun, Y. F. Wang, G. L. Chen, Z. G. Wang, R. X. Li, Z. N. Zeng, and Z. Z. Xu, "High-order harmonic and attosecond pulse generation for a few-cycle laser pulse in modulated hollow fibers," J. Phys. B. 40, 2917-2925 (2007).
[CrossRef]

Weiman, S.

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

Wobrauschek, P.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
[CrossRef]

Wu, F.

X. F. Chen, F. Wu, X. L. Zeng, Y. P. Chen, Y. X. Xia and Y. L. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
[CrossRef]

X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, and Y. L. Chen, " Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings," Opt. Commun. 204, 407-411 (2002).
[CrossRef]

Xia, Y. X.

X. F. Chen, F. Wu, X. L. Zeng, Y. P. Chen, Y. X. Xia and Y. L. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
[CrossRef]

X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, and Y. L. Chen, " Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings," Opt. Commun. 204, 407-411 (2002).
[CrossRef]

Xu, Z. Z.

X. Y. Zhang, Z. R. Sun, Y. F. Wang, G. L. Chen, Z. G. Wang, R. X. Li, Z. N. Zeng, and Z. Z. Xu, "High-order harmonic and attosecond pulse generation for a few-cycle laser pulse in modulated hollow fibers," J. Phys. B. 40, 2917-2925 (2007).
[CrossRef]

Zeng, X. L.

X. F. Chen, F. Wu, X. L. Zeng, Y. P. Chen, Y. X. Xia and Y. L. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
[CrossRef]

X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, and Y. L. Chen, " Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings," Opt. Commun. 204, 407-411 (2002).
[CrossRef]

Zeng, Z. N.

X. Y. Zhang, Z. R. Sun, Y. F. Wang, G. L. Chen, Z. G. Wang, R. X. Li, Z. N. Zeng, and Z. Z. Xu, "High-order harmonic and attosecond pulse generation for a few-cycle laser pulse in modulated hollow fibers," J. Phys. B. 40, 2917-2925 (2007).
[CrossRef]

Zhang, X. S.

A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
[CrossRef]

E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
[CrossRef]

Zhang, X. Y.

X. Y. Zhang, Z. R. Sun, Y. F. Wang, G. L. Chen, Z. G. Wang, R. X. Li, Z. N. Zeng, and Z. Z. Xu, "High-order harmonic and attosecond pulse generation for a few-cycle laser pulse in modulated hollow fibers," J. Phys. B. 40, 2917-2925 (2007).
[CrossRef]

Zhou, X. B.

A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
[CrossRef]

IEEE J. Quantum Electron.

A. Paul, E. A. Gibson, X. S. Zhang, A. Lytle, T. Popmintchev, X. B. Zhou, M. M. Murnane, I. P. Christov, and H. C. Kapteyn, "Phase-matching techniques for coherent soft x-ray generation," IEEE J. Quantum Electron. 42, 14-26 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum. Electron.

E. A. Gibson, X. S. Zhang, T. Popmintchev, A. Paul, N. Wagner, A. Lytle, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Extreme Nonlinear Optics: Attosecond Photonics at Short Wavelengths," IEEE J. Sel. Top. Quantum. Electron. 10, 1339-1350 (2004).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B.

X. Y. Zhang, Z. R. Sun, Y. F. Wang, G. L. Chen, Z. G. Wang, R. X. Li, Z. N. Zeng, and Z. Z. Xu, "High-order harmonic and attosecond pulse generation for a few-cycle laser pulse in modulated hollow fibers," J. Phys. B. 40, 2917-2925 (2007).
[CrossRef]

Nature

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

Opt. Commun.

X. L. Zeng, X. F. Chen, F. Wu, Y. P. Chen, Y. X. Xia, and Y. L. Chen, " Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings," Opt. Commun. 204, 407-411 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

X. F. Chen, F. Wu, X. L. Zeng, Y. P. Chen, Y. X. Xia and Y. L. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818 (2004).
[CrossRef]

Phys. Rev. Lett.

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, "Generation of Coherent Soft X Rays at 2.7nm Using High Harmonics," Phys. Rev. Lett. 79, 2967-2970 (1997).
[CrossRef]

Phys. Today

H. C. Kapteyn, M. M. Murnane, and I. P. Christov, "Coherent X-rays from Lasers: Applied Attosecond Science," Phys. Today 3, 39 (2005).
[CrossRef]

D. Attwood, "New opportunities at soft x-ray wavelengths," Phys. Today 45, 24-31 (1992).
[CrossRef]

Science

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, "Coherent soft x-ray generation in the water window with quasi-phase matching," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, "Generation of Coherent X-ray Pulses in the Water Window using 5fs Laser Pulses," Science 278, 661-664 (1997).
[CrossRef]

Soviet Phys. JETP.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Soviet Phys. JETP. 64, 1191-1194 (1986).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the constructed aperiodically corrugated fiber by SA method in part.

Fig. 2.
Fig. 2.

Enhancement factor over no modulation as a function of harmonic order, using aperiodically modulated fibers with different unit block length ▵L. All the modulation depth is 0.1.

Fig. 3.
Fig. 3.

Enhancement factor over no modulation as a function of harmonic order, using aperiodically modulated fibers with modulation depth of 0.1 and 0.2. The unit block length ▵L is 10µm.

Fig. 4.
Fig. 4.

Harmonic emissions from the aperiodically modulated fibers through orders of 25th to 301th, with a modulation depth of 0.1 and unit block length of 10µm.

Equations (5)

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

Δ k = k q ω q k ω = q u 11 2 λ 4 π a 2 + P η N atm r e ( q λ λ q ) 2 π ( 1 η ) P q λ ( δ ( λ ) δ ( λ q ) ) ,
Δ k ( λ ) = q u 11 2 λ 4 π a 2 + q n e e 2 λ 4 π m e ε 0 c 2 ,
E q ω ( L ) 0 L E ω q ( z ) d ( z ) exp ( i Δ k z ) d z ,
E q ω ( L ) E ω q d eff L 1 L 0 L g ( z ) exp ( i Δ k ( λ ) z ) d z = E ω q d eff L × G ( Δ k )
G [ Δ k ( λ ) ] = 1 L 0 L g ( z ) exp ( i Δ k ( λ ) z ) d z = 1 N · Δ L p = 0 N 1 g ( z p ) z p z p + Δ L exp ( i Δ k ( λ ) ξ ) d ξ ,

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