Abstract

We report the direct observation of periodic intensity modulation of a laser pulse propagating in a hollow-core waveguide. A series of equally spaced plasma sparks along the gas-filled capillary is produced. This effect can be explained by the beating of different fiber modes, which are excited by controlling the size of the focal spot at the capillary entrance. As compared with an artificial modulated waveguide structure, our presented approach represents an easier and more flexible quasi-phase-matching scheme for nonlinear-optical frequency conversion.

© 2007 Optical Society of America

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  1. 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]
  2. A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, 'Quasi-phase-matched generation of coherent extreme-ultraviolet light,' Nature 421, 51-54 (2003).
    [CrossRef] [PubMed]
  3. I. P. Christov, H. C. Kapteyn, and M. M. Murnane, 'Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,' Opt. Express 7, 362-367 (2000).
    [CrossRef] [PubMed]
  4. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, 'Interactions between light waves in a nonlinear dielectric,' Phys. Rev. 127, 1918-1938 (1962).
    [CrossRef]
  5. G. A. Magel, M. M. Fejer, and R. L. Byer, 'Quasi-phase-matched second-harmonic generation of blue light in periodically poled LiNbO3,' Appl. Phys. Lett. 56, 108-110 (1990).
    [CrossRef]
  6. T. Tajima and J. M. Dawson, 'Laser electron-accelerator,' Phys. Rev. Lett. 43, 267-270 (1979).
    [CrossRef]
  7. G. Shvets, N. J. Fisch, A. Pukhov, and J. Meyer-ter-Vehn, 'Generation of periodic accelerating structures in plasma by colliding laser pulses,' Phys. Rev. E 60, 2218-2223 (1999).
    [CrossRef]
  8. T. Pfeifer, R. Kemmer, R. Spitzenpfeil, D. Walter, C. Winterfeldt, G. Gerber, and C. Spielmann, 'Spatial control of high-harmonic generation in hollow fibers,' Opt. Lett. 30, 1497-1499 (2005).
    [CrossRef] [PubMed]
  9. C. G. Durfee and H. M. Milchberg, 'Light pipe for high-intensity laser-pulses,' Phys. Rev. Lett. 71, 2409-2412 (1993).
    [CrossRef] [PubMed]
  10. C. G. Durfee, J. Lynch, and H. M. Milchberg, 'Development of a plasma wave-guide for high-intensity laser-pulses,' Phys. Rev. E 51, 2368-2389 (1995).
    [CrossRef]
  11. E. W. Gaul, S. P. Le Blanc, A. R. Rundquist, R. Zgadzaj, H. Langhoff, and M. C. Downer, 'Production and characterization of a fully ionized He plasma channel,' Appl. Phys. Lett. 77, 4112-4114 (2000).
    [CrossRef]
  12. E. A. J. Marcatili and R. A. Schmeltzer, 'Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,' Bell Syst. Tech. J. 43, 1783-1809 (1964).
  13. R. L. Abrams, 'Coupling losses in hollow waveguide fiber resonators,' IEEE J. Quantum Electron. 8, 838 (1972).
    [CrossRef]
  14. N. Bloembergen, 'Laser-induced electric breakdown in solids,' IEEE J. Quantum Electron. QE-10, 375-386 (1974).
    [CrossRef]
  15. A. L. Campillo, J. W. P. Hsu, K. R. Parameswaran, and M. M. Fejer, 'Direct imaging of multimode interference in a channel waveguide,' Opt. Lett. 28, 399-401 (2003).
    [CrossRef] [PubMed]
  16. F. E. Lytle and B. G. Splawn, 'Performance of submillimeter square hollow waveguides,' Appl. Opt. 41, 6660-6665 (2002).
    [CrossRef] [PubMed]
  17. C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, 'Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,' Phys. Plasmas 8, 3445-3456 (2001).
    [CrossRef]
  18. L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Vol. 3 of Course of Theoretical Physics, 3rd ed. (Pergamon, 1977).
  19. D. Walter, T. Pfeifer, C. Winterfeldt, R. Kemmer, R. Spitzenpfeil, G. Gerber, and C. Spielmann, 'Adaptive spatial control of fiber modes and their excitation for high-harmonic generation,' Opt. Express 14, 3433-3442 (2006).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

2003 (3)

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. Backus, 'Quasi-phase-matched generation of coherent extreme-ultraviolet light,' Nature 421, 51-54 (2003).
[CrossRef] [PubMed]

A. L. Campillo, J. W. P. Hsu, K. R. Parameswaran, and M. M. Fejer, 'Direct imaging of multimode interference in a channel waveguide,' Opt. Lett. 28, 399-401 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, 'Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,' Phys. Plasmas 8, 3445-3456 (2001).
[CrossRef]

2000 (2)

E. W. Gaul, S. P. Le Blanc, A. R. Rundquist, R. Zgadzaj, H. Langhoff, and M. C. Downer, 'Production and characterization of a fully ionized He plasma channel,' Appl. Phys. Lett. 77, 4112-4114 (2000).
[CrossRef]

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, 'Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,' Opt. Express 7, 362-367 (2000).
[CrossRef] [PubMed]

1999 (1)

G. Shvets, N. J. Fisch, A. Pukhov, and J. Meyer-ter-Vehn, 'Generation of periodic accelerating structures in plasma by colliding laser pulses,' Phys. Rev. E 60, 2218-2223 (1999).
[CrossRef]

1995 (1)

C. G. Durfee, J. Lynch, and H. M. Milchberg, 'Development of a plasma wave-guide for high-intensity laser-pulses,' Phys. Rev. E 51, 2368-2389 (1995).
[CrossRef]

1993 (1)

C. G. Durfee and H. M. Milchberg, 'Light pipe for high-intensity laser-pulses,' Phys. Rev. Lett. 71, 2409-2412 (1993).
[CrossRef] [PubMed]

1990 (1)

G. A. Magel, M. M. Fejer, and R. L. Byer, 'Quasi-phase-matched second-harmonic generation of blue light in periodically poled LiNbO3,' Appl. Phys. Lett. 56, 108-110 (1990).
[CrossRef]

1979 (1)

T. Tajima and J. M. Dawson, 'Laser electron-accelerator,' Phys. Rev. Lett. 43, 267-270 (1979).
[CrossRef]

1974 (1)

N. Bloembergen, 'Laser-induced electric breakdown in solids,' IEEE J. Quantum Electron. QE-10, 375-386 (1974).
[CrossRef]

1972 (1)

R. L. Abrams, 'Coupling losses in hollow waveguide fiber resonators,' IEEE J. Quantum Electron. 8, 838 (1972).
[CrossRef]

1964 (1)

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

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, 'Interactions between light waves in a nonlinear dielectric,' Phys. Rev. 127, 1918-1938 (1962).
[CrossRef]

Abrams, R. L.

R. L. Abrams, 'Coupling losses in hollow waveguide fiber resonators,' IEEE J. Quantum Electron. 8, 838 (1972).
[CrossRef]

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]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, 'Interactions between light waves in a nonlinear dielectric,' Phys. Rev. 127, 1918-1938 (1962).
[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]

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

Bloembergen, N.

N. Bloembergen, 'Laser-induced electric breakdown in solids,' IEEE J. Quantum Electron. QE-10, 375-386 (1974).
[CrossRef]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, 'Interactions between light waves in a nonlinear dielectric,' Phys. Rev. 127, 1918-1938 (1962).
[CrossRef]

Byer, R. L.

G. A. Magel, M. M. Fejer, and R. L. Byer, 'Quasi-phase-matched second-harmonic generation of blue light in periodically poled LiNbO3,' Appl. Phys. Lett. 56, 108-110 (1990).
[CrossRef]

Campillo, A. L.

Christov, I. P.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, '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, 'Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,' Opt. Express 7, 362-367 (2000).
[CrossRef] [PubMed]

Couairon, A.

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, 'Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,' Phys. Plasmas 8, 3445-3456 (2001).
[CrossRef]

Courtois, C.

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, 'Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,' Phys. Plasmas 8, 3445-3456 (2001).
[CrossRef]

Cros, B.

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, 'Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,' Phys. Plasmas 8, 3445-3456 (2001).
[CrossRef]

Dawson, J. M.

T. Tajima and J. M. Dawson, 'Laser electron-accelerator,' Phys. Rev. Lett. 43, 267-270 (1979).
[CrossRef]

Downer, M. C.

E. W. Gaul, S. P. Le Blanc, A. R. Rundquist, R. Zgadzaj, H. Langhoff, and M. C. Downer, 'Production and characterization of a fully ionized He plasma channel,' Appl. Phys. Lett. 77, 4112-4114 (2000).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, 'Interactions between light waves in a nonlinear dielectric,' Phys. Rev. 127, 1918-1938 (1962).
[CrossRef]

Durfee, C. G.

C. G. Durfee, J. Lynch, and H. M. Milchberg, 'Development of a plasma wave-guide for high-intensity laser-pulses,' Phys. Rev. E 51, 2368-2389 (1995).
[CrossRef]

C. G. Durfee and H. M. Milchberg, 'Light pipe for high-intensity laser-pulses,' Phys. Rev. Lett. 71, 2409-2412 (1993).
[CrossRef] [PubMed]

Fejer, M. M.

A. L. Campillo, J. W. P. Hsu, K. R. Parameswaran, and M. M. Fejer, 'Direct imaging of multimode interference in a channel waveguide,' Opt. Lett. 28, 399-401 (2003).
[CrossRef] [PubMed]

G. A. Magel, M. M. Fejer, and R. L. Byer, 'Quasi-phase-matched second-harmonic generation of blue light in periodically poled LiNbO3,' Appl. Phys. Lett. 56, 108-110 (1990).
[CrossRef]

Fisch, N. J.

G. Shvets, N. J. Fisch, A. Pukhov, and J. Meyer-ter-Vehn, 'Generation of periodic accelerating structures in plasma by colliding laser pulses,' Phys. Rev. E 60, 2218-2223 (1999).
[CrossRef]

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]

Gaul, E. W.

E. W. Gaul, S. P. Le Blanc, A. R. Rundquist, R. Zgadzaj, H. Langhoff, and M. C. Downer, 'Production and characterization of a fully ionized He plasma channel,' Appl. Phys. Lett. 77, 4112-4114 (2000).
[CrossRef]

Gerber, G.

Gibson, E. 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]

Green, H.

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

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]

Hsu, J. W. P.

Kapteyn, H. C.

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. Backus, '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, 'Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,' Opt. Express 7, 362-367 (2000).
[CrossRef] [PubMed]

Kemmer, R.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Vol. 3 of Course of Theoretical Physics, 3rd ed. (Pergamon, 1977).

Langhoff, H.

E. W. Gaul, S. P. Le Blanc, A. R. Rundquist, R. Zgadzaj, H. Langhoff, and M. C. Downer, 'Production and characterization of a fully ionized He plasma channel,' Appl. Phys. Lett. 77, 4112-4114 (2000).
[CrossRef]

Le Blanc, S. P.

E. W. Gaul, S. P. Le Blanc, A. R. Rundquist, R. Zgadzaj, H. Langhoff, and M. C. Downer, 'Production and characterization of a fully ionized He plasma channel,' Appl. Phys. Lett. 77, 4112-4114 (2000).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Vol. 3 of Course of Theoretical Physics, 3rd ed. (Pergamon, 1977).

Lynch, J.

C. G. Durfee, J. Lynch, and H. M. Milchberg, 'Development of a plasma wave-guide for high-intensity laser-pulses,' Phys. Rev. E 51, 2368-2389 (1995).
[CrossRef]

Lytle, F. E.

Magel, G. A.

G. A. Magel, M. M. Fejer, and R. L. Byer, 'Quasi-phase-matched second-harmonic generation of blue light in periodically poled LiNbO3,' Appl. Phys. Lett. 56, 108-110 (1990).
[CrossRef]

Marcatili, E. A. J.

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

Marquès, J. R.

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, 'Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,' Phys. Plasmas 8, 3445-3456 (2001).
[CrossRef]

Matthieussent, G.

C. Courtois, A. Couairon, B. Cros, J. R. Marquès, and G. Matthieussent, 'Propagation of intense ultrashort laser pulses in a plasma filled capillary tube: simulations and experiments,' Phys. Plasmas 8, 3445-3456 (2001).
[CrossRef]

Meyer-ter-Vehn, J.

G. Shvets, N. J. Fisch, A. Pukhov, and J. Meyer-ter-Vehn, 'Generation of periodic accelerating structures in plasma by colliding laser pulses,' Phys. Rev. E 60, 2218-2223 (1999).
[CrossRef]

Milchberg, H. M.

C. G. Durfee, J. Lynch, and H. M. Milchberg, 'Development of a plasma wave-guide for high-intensity laser-pulses,' Phys. Rev. E 51, 2368-2389 (1995).
[CrossRef]

C. G. Durfee and H. M. Milchberg, 'Light pipe for high-intensity laser-pulses,' Phys. Rev. Lett. 71, 2409-2412 (1993).
[CrossRef] [PubMed]

Murnane, M. M.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, '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, 'Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,' Opt. Express 7, 362-367 (2000).
[CrossRef] [PubMed]

Parameswaran, K. R.

Paul, A.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, '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]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, 'Interactions between light waves in a nonlinear dielectric,' Phys. Rev. 127, 1918-1938 (1962).
[CrossRef]

Pfeifer, T.

Pukhov, A.

G. Shvets, N. J. Fisch, A. Pukhov, and J. Meyer-ter-Vehn, 'Generation of periodic accelerating structures in plasma by colliding laser pulses,' Phys. Rev. E 60, 2218-2223 (1999).
[CrossRef]

Rundquist, A. R.

E. W. Gaul, S. P. Le Blanc, A. R. Rundquist, R. Zgadzaj, H. Langhoff, and M. C. Downer, 'Production and characterization of a fully ionized He plasma channel,' Appl. Phys. Lett. 77, 4112-4114 (2000).
[CrossRef]

Schmeltzer, R. A.

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

Shvets, G.

G. Shvets, N. J. Fisch, A. Pukhov, and J. Meyer-ter-Vehn, 'Generation of periodic accelerating structures in plasma by colliding laser pulses,' Phys. Rev. E 60, 2218-2223 (1999).
[CrossRef]

Spielmann, C.

Spitzenpfeil, R.

Splawn, B. G.

Tajima, T.

T. Tajima and J. M. Dawson, 'Laser electron-accelerator,' Phys. Rev. Lett. 43, 267-270 (1979).
[CrossRef]

Tobey, R.

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. Backus, 'Quasi-phase-matched generation of coherent extreme-ultraviolet light,' Nature 421, 51-54 (2003).
[CrossRef] [PubMed]

Wagner, N.

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]

Walter, D.

Weiman, S.

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

Winterfeldt, C.

Zgadzaj, R.

E. W. Gaul, S. P. Le Blanc, A. R. Rundquist, R. Zgadzaj, H. Langhoff, and M. C. Downer, 'Production and characterization of a fully ionized He plasma channel,' Appl. Phys. Lett. 77, 4112-4114 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

E. W. Gaul, S. P. Le Blanc, A. R. Rundquist, R. Zgadzaj, H. Langhoff, and M. C. Downer, 'Production and characterization of a fully ionized He plasma channel,' Appl. Phys. Lett. 77, 4112-4114 (2000).
[CrossRef]

G. A. Magel, M. M. Fejer, and R. L. Byer, 'Quasi-phase-matched second-harmonic generation of blue light in periodically poled LiNbO3,' Appl. Phys. Lett. 56, 108-110 (1990).
[CrossRef]

Bell Syst. Tech. J. (1)

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

IEEE J. Quantum Electron. (2)

R. L. Abrams, 'Coupling losses in hollow waveguide fiber resonators,' IEEE J. Quantum Electron. 8, 838 (1972).
[CrossRef]

N. Bloembergen, 'Laser-induced electric breakdown in solids,' IEEE J. Quantum Electron. QE-10, 375-386 (1974).
[CrossRef]

Nature (1)

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Figures (4)

Fig. 1
Fig. 1

Radial intensity distributions. (a) Pure hollow-fiber modes EH 11 (solid curve) and EH 12 (dashed curve), normalized to integral power. (b) Superposition of both modes shown in (a) with mixing ratio 1:25 of EH 12 to EH 11 for additive (solid curve) and subtractive interference (dashed curve).

Fig. 2
Fig. 2

Coupling a Gaussian beam with width w into hollow-fiber modes (fiber inner radius a). For EH 11 (solid curve) a maximum of 98% efficiency is obtained for w a = 0.64 (dotted curve). At smaller input beam diameters, higher-order modes are excited, in particular EH 12 (dashed curve).

Fig. 3
Fig. 3

Photographic image (above) and axial lineout (below) of the periodic plasma sparks created by fiber-mode beating. The laser enters the capillary from the right-hand side. The distance between two on-axis plasma maxima is in agreement with the calculated value [see Eq. (3)] of 2.6 mm (indicated in figure) for the contribution of the two lowest-order relevant fiber modes EH 11 and EH 12 . A periodic intensity modulation along the propagation path of the laser light can thus be achieved without a structured waveguide, which is important for quasi-phase-matching applications in nonlinear optics. The positions of the intensity maxima are marked by dotted lines.

Fig. 4
Fig. 4

Computer simulation results for light propagation in a gas-filled capillary (pressure 1   bar ). Shown is the free-electron density produced from the passage of the 10 fs laser pulse with an intensity of 10 15 W cm 2 . As in the experiment, a periodic intensity modulation along the capillary axis leads to a periodic series of regions with high free-electron (plasma) density. A less-pronounced off-axis intensity modulation occurs in antiphase to the on-axis modulation. This is due to a transient ringlike intensity distribution when the on-axis electric fields of the fiber modes interfere destructively.

Equations (9)

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E r n m = J n 1 ( u n m r a ) cos ( n θ ) exp ( i ( γ z ω t ) ) ,
E θ n m = J n 1 ( u n m r a ) sin ( n θ ) exp ( i ( γ z ω t ) ) ,
E z n m = 0 ,
J n 1 ( u n m ) = 0 ,
γ = k ( 1 1 2 ( u n m λ 2 π a ) 2 ( 1 i ( ν 2 + 1 ) 2 π a ν 2 1 ) ) ,
Δ z = 2 π Δ k z ,
w = 0.64 a ,
Δ k pm = n k n ,
Δ k pm = m Δ k eff ,

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