Abstract

We present the control of high-harmonic generation (HHG) in hollow fibers using adaptive pulse shaping techniques. The shaping capabilities of our spatial light modulator (SLM) are demonstrated by the excitation of specific fiber modes inside a hollow fiber with a helium-neon laser. Afterwards spatially shaped ultrashort pulses are used to generate phase-matched high-harmonic radiation in a fiber. We show that by controlling the mode structure, we can manipulate the spatial and spectral properties of the generated harmonics.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
  2. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
    [CrossRef] [PubMed]
  3. M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
    [CrossRef] [PubMed]
  4. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug´e, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
    [CrossRef] [PubMed]
  5. C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).
  6. P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, and G. Tondello, "Optimization of high-order harmonic generation by adaptive control of a sub-10-fs pulse wave front," Opt. Lett. 29, 207-209 (2004).
    [CrossRef] [PubMed]
  7. D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, "Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm," Appl. Phys. B 78, 275-280 (2004).
    [CrossRef]
  8. P. Villoresi, "Compensation of optical path lengths in extreme-ultraviolet and soft-x-ray monochromators for ultrafast pulses," Appl. Opt. 38, 6040-6049 (1999).
    [CrossRef]
  9. T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, "Adaptive engineering of coherent soft x-rays," Appl. Phys. B 80, 277-280 (2005).
    [CrossRef]
  10. A. Rundquist, C. G. DurfeeIII, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft X-rays," Science 280, 1412-1415 (1998).
    [CrossRef] [PubMed]
  11. R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft-X-rays," Nature 406, 164-166 (2000).
    [CrossRef] [PubMed]
  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. C. G. DurfeeIII, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
    [CrossRef]
  14. D. Homoelle and A. L. Gaeta, "Nonlinear propagation dynamics of an ultrashort pulse in a hollow waveguide," Opt. Lett. 25, 761-763 (2000).
    [CrossRef]
  15. G. Tempea and T. Brabec, "Theory of self-focusing in a hollow waveguide," Opt. Lett. 23, 762-764 (1998).
    [CrossRef]
  16. HAMAMATSU Photonics K. K., "Parametric aligned nematic liquid crystal spatial light modulator X7665," http://www.hamamatsu.com, info@hamamatsu.de.
  17. Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, and M. H. Wu, "Compact high-efficiency electrically-addressable phase-only spatial light modulator," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee and R. L. Sutherland eds., Proc. SPIE 3951, 158-165 (2000).
    [CrossRef]
  18. T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, "Femtosecond pulse shaping by an evolutionary algorithm with feedback," Appl. Phys. B 65, 779-782 (1997).
    [CrossRef]
  19. R. L. Abrams, "Coupling losses in hollow waveguide laser resonators," IEEE J. Quantum Electron. 8, 838-843 (1972).
    [CrossRef]
  20. 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]
  21. R. M. Jenkins and R. W. J. Devereux, "Effect of field regeneration on the TEM00 transmission characteristics of a circular-section waveguide," Appl. Opt. 315086-5091 (1992).
    [CrossRef] [PubMed]
  22. J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
    [CrossRef]

2005 (2)

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, "Adaptive engineering of coherent soft x-rays," Appl. Phys. B 80, 277-280 (2005).
[CrossRef]

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]

2004 (3)

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, and G. Tondello, "Optimization of high-order harmonic generation by adaptive control of a sub-10-fs pulse wave front," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, "Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm," Appl. Phys. B 78, 275-280 (2004).
[CrossRef]

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[CrossRef]

2001 (2)

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

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug´e, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

2000 (4)

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft-X-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

D. Homoelle and A. L. Gaeta, "Nonlinear propagation dynamics of an ultrashort pulse in a hollow waveguide," Opt. Lett. 25, 761-763 (2000).
[CrossRef]

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, and M. H. Wu, "Compact high-efficiency electrically-addressable phase-only spatial light modulator," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee and R. L. Sutherland eds., Proc. SPIE 3951, 158-165 (2000).
[CrossRef]

1999 (2)

C. G. DurfeeIII, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
[CrossRef]

P. Villoresi, "Compensation of optical path lengths in extreme-ultraviolet and soft-x-ray monochromators for ultrafast pulses," Appl. Opt. 38, 6040-6049 (1999).
[CrossRef]

1998 (2)

G. Tempea and T. Brabec, "Theory of self-focusing in a hollow waveguide," Opt. Lett. 23, 762-764 (1998).
[CrossRef]

A. Rundquist, C. G. DurfeeIII, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft X-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

1997 (1)

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, "Femtosecond pulse shaping by an evolutionary algorithm with feedback," Appl. Phys. B 65, 779-782 (1997).
[CrossRef]

1994 (1)

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

1992 (1)

1991 (1)

A. L’Huillier, K. J. Schafer, and K. C. Kulander, "High-order harmonic generation in Xenon at 1064 nm: The role of phase matching," Phys. Rev. Lett. 66, 2200-2203 (1991).
[CrossRef] [PubMed]

1972 (1)

R. L. Abrams, "Coupling losses in hollow waveguide laser resonators," IEEE J. Quantum Electron. 8, 838-843 (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).

Abrams, R. L.

R. L. Abrams, "Coupling losses in hollow waveguide laser resonators," IEEE J. Quantum Electron. 8, 838-843 (1972).
[CrossRef]

Agostini, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug´e, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Altucci, C.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

Aug´e, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug´e, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Backus, S.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft-X-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

C. G. DurfeeIII, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
[CrossRef]

A. Rundquist, C. G. DurfeeIII, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft X-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Balcou, Ph.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug´e, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

Bartels, R.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft-X-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

Baumert, T.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, "Femtosecond pulse shaping by an evolutionary algorithm with feedback," Appl. Phys. B 65, 779-782 (1997).
[CrossRef]

Biegert, J.

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[CrossRef]

Bonora, S.

Boscolo, A.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

Brabec, T.

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

G. Tempea and T. Brabec, "Theory of self-focusing in a hollow waveguide," Opt. Lett. 23, 762-764 (1998).
[CrossRef]

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug´e, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Brixner, T.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, "Femtosecond pulse shaping by an evolutionary algorithm with feedback," Appl. Phys. B 65, 779-782 (1997).
[CrossRef]

Bruzzese, R.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

Ceccherini, P.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

Chang, Z.

A. Rundquist, C. G. DurfeeIII, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft X-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Christov, I. P.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft-X-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

Corkum, P.

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

Corkum, P. B.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

de Lisio, C.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

De Silvestri, S.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

Devereux, R. W. J.

Drescher, M.

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

Durfee, C. G.

C. G. DurfeeIII, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
[CrossRef]

A. Rundquist, C. G. DurfeeIII, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft X-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Fukuchi, N.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, and M. H. Wu, "Compact high-efficiency electrically-addressable phase-only spatial light modulator," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee and R. L. Sutherland eds., Proc. SPIE 3951, 158-165 (2000).
[CrossRef]

Gaarde, M. B.

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[CrossRef]

Gaeta, A. L.

Gerber, G.

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]

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, "Adaptive engineering of coherent soft x-rays," Appl. Phys. B 80, 277-280 (2005).
[CrossRef]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, "Femtosecond pulse shaping by an evolutionary algorithm with feedback," Appl. Phys. B 65, 779-782 (1997).
[CrossRef]

Hara, T.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, and M. H. Wu, "Compact high-efficiency electrically-addressable phase-only spatial light modulator," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee and R. L. Sutherland eds., Proc. SPIE 3951, 158-165 (2000).
[CrossRef]

Heinzmann, U.

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

Hentschel, M.

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

Herne, C.

C. G. DurfeeIII, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
[CrossRef]

A. Rundquist, C. G. DurfeeIII, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft X-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Homoelle, D.

Igasaki, Y.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, and M. H. Wu, "Compact high-efficiency electrically-addressable phase-only spatial light modulator," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee and R. L. Sutherland eds., Proc. SPIE 3951, 158-165 (2000).
[CrossRef]

Ivanov, M. Yu.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

Jenkins, R. M.

Johnsson, P.

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[CrossRef]

Kanai, T.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, "Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm," Appl. Phys. B 78, 275-280 (2004).
[CrossRef]

Kapteyn, H. C.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft-X-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

C. G. DurfeeIII, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
[CrossRef]

A. Rundquist, C. G. DurfeeIII, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft X-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Keller, U.

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[CrossRef]

Kemmer, R.

Kienberger, R.

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

Kobayashi, Y.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, and M. H. Wu, "Compact high-efficiency electrically-addressable phase-only spatial light modulator," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee and R. L. Sutherland eds., Proc. SPIE 3951, 158-165 (2000).
[CrossRef]

Kornelis, W.

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[CrossRef]

Krausz, F.

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

Kulander, K. C.

A. L’Huillier, K. J. Schafer, and K. C. Kulander, "High-order harmonic generation in Xenon at 1064 nm: The role of phase matching," Phys. Rev. Lett. 66, 2200-2203 (1991).
[CrossRef] [PubMed]

L’Huillier, A.

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[CrossRef]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

A. L’Huillier, K. J. Schafer, and K. C. Kulander, "High-order harmonic generation in Xenon at 1064 nm: The role of phase matching," Phys. Rev. Lett. 66, 2200-2203 (1991).
[CrossRef] [PubMed]

Lewenstein, M.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

Lopez-Martens, R.

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[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).

Mauritsson, J.

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[CrossRef]

Milosevic, N.

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

Misoguti, L.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft-X-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

Miyamoto, N.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, "Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm," Appl. Phys. B 78, 275-280 (2004).
[CrossRef]

Mourou, G.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, "Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm," Appl. Phys. B 78, 275-280 (2004).
[CrossRef]

Muller, H. G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug´e, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Mullot, G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug´e, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Murnane, M. M.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft-X-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

C. G. DurfeeIII, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
[CrossRef]

A. Rundquist, C. G. DurfeeIII, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft X-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Nees, J.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, "Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm," Appl. Phys. B 78, 275-280 (2004).
[CrossRef]

Nisoli, M.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

Pascolini, M.

Paul, P. M.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug´e, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Pfeifer, T.

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, "Adaptive engineering of coherent soft x-rays," Appl. Phys. B 80, 277-280 (2005).
[CrossRef]

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]

Poletto, L.

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, and G. Tondello, "Optimization of high-order harmonic generation by adaptive control of a sub-10-fs pulse wave front," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

Reider, G. A.

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

Rundquist, A.

A. Rundquist, C. G. DurfeeIII, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft X-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

Rundquist, A. R.

C. G. DurfeeIII, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
[CrossRef]

Schafer, K. J.

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[CrossRef]

A. L’Huillier, K. J. Schafer, and K. C. Kulander, "High-order harmonic generation in Xenon at 1064 nm: The role of phase matching," Phys. Rev. Lett. 66, 2200-2203 (1991).
[CrossRef] [PubMed]

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).

Sekikawa, T.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, "Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm," Appl. Phys. B 78, 275-280 (2004).
[CrossRef]

Seyfried, V.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, "Femtosecond pulse shaping by an evolutionary algorithm with feedback," Appl. Phys. B 65, 779-782 (1997).
[CrossRef]

Spielmann, C.

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]

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, "Adaptive engineering of coherent soft x-rays," Appl. Phys. B 80, 277-280 (2005).
[CrossRef]

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

Spitzenpfeil, R.

Stagira, S.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

Strehle, M.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, "Femtosecond pulse shaping by an evolutionary algorithm with feedback," Appl. Phys. B 65, 779-782 (1997).
[CrossRef]

Svelto, O.

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

Tempea, G.

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug´e, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Tondello, G.

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, and G. Tondello, "Optimization of high-order harmonic generation by adaptive control of a sub-10-fs pulse wave front," Opt. Lett. 29, 207-209 (2004).
[CrossRef] [PubMed]

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

Toyoda, H.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, and M. H. Wu, "Compact high-efficiency electrically-addressable phase-only spatial light modulator," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee and R. L. Sutherland eds., Proc. SPIE 3951, 158-165 (2000).
[CrossRef]

Varju, K.

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[CrossRef]

Vdovin, G.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft-X-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

Villoresi, P.

Walter, D.

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]

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, "Adaptive engineering of coherent soft x-rays," Appl. Phys. B 80, 277-280 (2005).
[CrossRef]

Watanabe, S.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, "Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm," Appl. Phys. B 78, 275-280 (2004).
[CrossRef]

Winterfeldt, C.

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]

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, "Adaptive engineering of coherent soft x-rays," Appl. Phys. B 80, 277-280 (2005).
[CrossRef]

Wu, M. H.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, and M. H. Wu, "Compact high-efficiency electrically-addressable phase-only spatial light modulator," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee and R. L. Sutherland eds., Proc. SPIE 3951, 158-165 (2000).
[CrossRef]

Yoshida, N.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, and M. H. Wu, "Compact high-efficiency electrically-addressable phase-only spatial light modulator," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee and R. L. Sutherland eds., Proc. SPIE 3951, 158-165 (2000).
[CrossRef]

Yoshitomi, D.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, "Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm," Appl. Phys. B 78, 275-280 (2004).
[CrossRef]

Zeek, E.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft-X-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. B (3)

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, "Adaptive engineering of coherent soft x-rays," Appl. Phys. B 80, 277-280 (2005).
[CrossRef]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, "Femtosecond pulse shaping by an evolutionary algorithm with feedback," Appl. Phys. B 65, 779-782 (1997).
[CrossRef]

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, "Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm," Appl. Phys. B 78, 275-280 (2004).
[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. (1)

R. L. Abrams, "Coupling losses in hollow waveguide laser resonators," IEEE J. Quantum Electron. 8, 838-843 (1972).
[CrossRef]

Nature (2)

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft-X-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

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

Opt. Lett. (4)

Phys. Rev. A (2)

J. Mauritsson, P. Johnsson, R. Lopez-Martens, K. Varju, W. Kornelis, J. Biegert, U. Keller, M. B. Gaarde, K. J. Schafer, and A. L’Huillier, "Measurement and control of the frequency chirp rate of high-order harmonic pulses," Phys. Rev. A 70, 021801 (2004).
[CrossRef]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

A. L’Huillier, K. J. Schafer, and K. C. Kulander, "High-order harmonic generation in Xenon at 1064 nm: The role of phase matching," Phys. Rev. Lett. 66, 2200-2203 (1991).
[CrossRef] [PubMed]

C. G. DurfeeIII, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
[CrossRef]

PRA (1)

C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, A. Boscolo, P. Ceccherini, L. Poletto, G. Tondello, and P. Villoresi, "Tunable soft-X-ray radiation by high-order harmonic generation," PRA 61, 021801 (2000).

Proc. SPIE (1)

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, and M. H. Wu, "Compact high-efficiency electrically-addressable phase-only spatial light modulator," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee and R. L. Sutherland eds., Proc. SPIE 3951, 158-165 (2000).
[CrossRef]

Science (2)

A. Rundquist, C. G. DurfeeIII, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft X-rays," Science 280, 1412-1415 (1998).
[CrossRef] [PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug´e, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001).
[CrossRef] [PubMed]

Other (1)

HAMAMATSU Photonics K. K., "Parametric aligned nematic liquid crystal spatial light modulator X7665," http://www.hamamatsu.com, info@hamamatsu.de.

Supplementary Material (6)

» Media 1: MPG (1738 KB)     
» Media 2: MPG (881 KB)     
» Media 3: MPG (881 KB)     
» Media 4: MPG (2308 KB)     
» Media 5: MPG (1627 KB)     
» Media 6: MPG (2447 KB)     

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Figures (10)

Fig. 1.
Fig. 1.

Setup used to test the shaping capabilities of the PAL-SLM. A spatially shaped laser beam is optimized to excite a distribution of fiber modes. The optimization goal was a predefined intensity distribution on a CCD camera.

Fig. 2.
Fig. 2.

Three optimized fiber outputs (movies in bottom row) next to their corresponding target masks (top row). From left to right: fundamental mode (a), (d) (1.69 MB); double mode (b), (e) (0.86 MB); triple mode (c), (f) (0.86 MB).

Fig. 3.
Fig. 3.

The optimization of the fiber output to a ring mode (target mask as inset in (a)). (b) shows the fiber output prior to the optimization and (c) a snapshot during the optimization process. The optimized result is (d) ((2.25 MB) movie of the optimization). The graph in (a) shows the rise of the maximum fitness as a function of generation number.

Fig. 4.
Fig. 4.

Calculated intensity distribution (a) and corresponding phase profile (b) at the fiber entrance found as the fittest phase profile of the PAL-SLM of the ring-mode optimization (Fig. 3). The size of the entrance hole is indicated by a circle.

Fig. 5.
Fig. 5.

Calculated intensity distribution (a) and corresponding phase profile (b) at the fiber entrance of the fittest phase profile of the PAL-SLM of the triple-mode optimization (Fig. 2(f)).

Fig. 6.
Fig. 6.

Two more complex target masks (a,c) and the corresponding optimized results (b,d) (movies of the optimization: (1.58 MB) (b); (2,38 MB) (d)). This final test proves that a suitable superposition of a large number of different fiber modes can be excited. These optimizations took about 300 generations of 40 individual pulse shapes per generation to complete.

Fig. 7.
Fig. 7.

Setup used to generate high-harmonic radiation by spatially modulated ultrashort laser pulses.

Fig. 8.
Fig. 8.

Optimization of the high harmonic yield with spatially shaped laser pulses. The overall signal could be increased by about a factor of 5 (upper graph; shifted by an offset for better separation) compared to the reference signal that was obtained for a flat phase profile on the PAL-SLM (lower graph).

Fig. 9.
Fig. 9.

Spectra of high harmonics before (a), (c) and after (b), (d) an optimization of the signal of the 23rd harmonic (see region A in (b)) recorded at a pressure of 170 mbar. (c) and (d) show the spatially resolved data and (a) and (b) the integrated signal along the spatial coordinate. Notice the bimodal structure only visible in (c). The optimized spectrum in (d) was recorded with a factor of 10 less integration time compared to (c).

Fig. 10.
Fig. 10.

The spatially resolved harmonic spectrum obtained for the same spatial pulse profiles used in Fig. 9 was recorded again for a much lower pressure of 20 mbar (before (a), (c) and after (b), (d) the optimization). Here it is evident that different harmonics have different spatial profiles presumably originating from different fiber modes excited by the 800 nm driving pulse.

Equations (2)

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k 2 π λ + 2 π N a δ ( λ ) λ N e r e λ u nm 2 λ 4 π a 2
Δ k = q k laser k x ray = 0 .

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