Abstract

We demonstrate the control of high-harmonic generation in a hollow fiber by shaping the spatial structure of the generating laser pulse. We use a liquid-crystal-based two-dimensional spatial light modulator to control the spatial phase of the driver pulse. An evolutionary algorithm finds the spatial laser phase distribution that is optimal for reaching maximum total harmonic yield and for selectively enhancing the cutoff region of the spectrum. We show that enhacement of harmonic generation is related to coupling into a single fiber mode. Our results directly show that spatial properties of the laser are important parameters in fully controlling the high-harmonic spectrum. It is thus not possible to derive the controllability of the high-harmonic generation from the single-atom response only.

© 2005 Optical Society of America

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T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, Appl. Phys. B 80, 277 (2005).
[CrossRef]

2004

2002

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[CrossRef]

2001

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

I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, Phys. Rev. Lett. 86, 5458 (2001).
[CrossRef] [PubMed]

R. Bartels, S. Backus, I. Christov, H. Kapteyn, and M. Murnane, Chem. Phys. 267, 277 (2001).
[CrossRef]

2000

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. Christov, M. M. Murnane, and H. C. Kapteyn, Nature 406, 164 (2000).
[CrossRef] [PubMed]

1999

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 83, 2187 (1999).
[CrossRef]

1998

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

1997

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997).
[CrossRef]

1992

1964

E. A.J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Albert, O.

Auge, F.

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[CrossRef]

Augé, F.

Backus, S.

R. Bartels, S. Backus, I. Christov, H. Kapteyn, and M. Murnane, Chem. Phys. 267, 277 (2001).
[CrossRef]

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. Christov, M. M. Murnane, and H. C. Kapteyn, Nature 406, 164 (2000).
[CrossRef] [PubMed]

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 83, 2187 (1999).
[CrossRef]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Balcou, P.

D. H. Reitze, S. Kazamias, F. Weihe, G. Mullot, D. Douillet, F. Augé, O. Albert, V. Ramanathan, J. P. Chambaret, D. Hulin, and P. Balcou, Opt. Lett. 29, 86 (2004).
[CrossRef] [PubMed]

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[CrossRef]

Bartels, R.

I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, Phys. Rev. Lett. 86, 5458 (2001).
[CrossRef] [PubMed]

R. Bartels, S. Backus, I. Christov, H. Kapteyn, and M. Murnane, Chem. Phys. 267, 277 (2001).
[CrossRef]

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. Christov, M. M. Murnane, and H. C. Kapteyn, Nature 406, 164 (2000).
[CrossRef] [PubMed]

Baumert, T.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Bonora, S.

Brabec, T.

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

Brixner, T.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Chambaret, J. P.

Chang, Z.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Chang, Z. H.

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997).
[CrossRef]

Christensen, E. L.

Christov, I.

R. Bartels, S. Backus, I. Christov, H. Kapteyn, and M. Murnane, Chem. Phys. 267, 277 (2001).
[CrossRef]

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. Christov, M. M. Murnane, and H. C. Kapteyn, Nature 406, 164 (2000).
[CrossRef] [PubMed]

Christov, I. P.

I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, Phys. Rev. Lett. 86, 5458 (2001).
[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, Nature 414, 509 (2001).
[CrossRef] [PubMed]

DeSilvestri, S.

Devereux, R. W.J.

Douillet, D.

D. H. Reitze, S. Kazamias, F. Weihe, G. Mullot, D. Douillet, F. Augé, O. Albert, V. Ramanathan, J. P. Chambaret, D. Hulin, and P. Balcou, Opt. Lett. 29, 86 (2004).
[CrossRef] [PubMed]

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[CrossRef]

Drescher, M.

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

Durfee, C. G.

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 83, 2187 (1999).
[CrossRef]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Gerber, G.

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, Appl. Phys. B 80, 277 (2005).
[CrossRef]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Grillon, G.

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[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, Nature 414, 509 (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, Nature 414, 509 (2001).
[CrossRef] [PubMed]

Herne, C.

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 83, 2187 (1999).
[CrossRef]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Hulin, D.

D. H. Reitze, S. Kazamias, F. Weihe, G. Mullot, D. Douillet, F. Augé, O. Albert, V. Ramanathan, J. P. Chambaret, D. Hulin, and P. Balcou, Opt. Lett. 29, 86 (2004).
[CrossRef] [PubMed]

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[CrossRef]

Jenkins, R. M.

Kanai, T.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, Appl. Phys. B 78, 275 (2004).
[CrossRef]

Kapteyn, H.

R. Bartels, S. Backus, I. Christov, H. Kapteyn, and M. Murnane, Chem. Phys. 267, 277 (2001).
[CrossRef]

Kapteyn, H. C.

I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, Phys. Rev. Lett. 86, 5458 (2001).
[CrossRef] [PubMed]

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. Christov, M. M. Murnane, and H. C. Kapteyn, Nature 406, 164 (2000).
[CrossRef] [PubMed]

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 83, 2187 (1999).
[CrossRef]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997).
[CrossRef]

Kazamias, S.

D. H. Reitze, S. Kazamias, F. Weihe, G. Mullot, D. Douillet, F. Augé, O. Albert, V. Ramanathan, J. P. Chambaret, D. Hulin, and P. Balcou, Opt. Lett. 29, 86 (2004).
[CrossRef] [PubMed]

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[CrossRef]

Kienberger, R.

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

Krausz, F.

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

Marcatili, E. A.J.

E. A.J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[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, Nature 414, 509 (2001).
[CrossRef] [PubMed]

Misoguti, L.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. Christov, M. M. Murnane, and H. C. Kapteyn, Nature 406, 164 (2000).
[CrossRef] [PubMed]

Miyamoto, N.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, Appl. Phys. B 78, 275 (2004).
[CrossRef]

Mourou, G.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, Appl. Phys. B 78, 275 (2004).
[CrossRef]

Mullot, G.

Murnane, M.

R. Bartels, S. Backus, I. Christov, H. Kapteyn, and M. Murnane, Chem. Phys. 267, 277 (2001).
[CrossRef]

Murnane, M. M.

I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, Phys. Rev. Lett. 86, 5458 (2001).
[CrossRef] [PubMed]

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. Christov, M. M. Murnane, and H. C. Kapteyn, Nature 406, 164 (2000).
[CrossRef] [PubMed]

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 83, 2187 (1999).
[CrossRef]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997).
[CrossRef]

Nees, J.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, Appl. Phys. B 78, 275 (2004).
[CrossRef]

Nisoli, M.

Painter, J. C.

Pascolini, M.

Peatross, J.

Pfeifer, T.

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, Appl. Phys. B 80, 277 (2005).
[CrossRef]

Planchon, T.

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[CrossRef]

Poletto, L.

Powers, N. D.

Ramanathan, V.

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, Nature 414, 509 (2001).
[CrossRef] [PubMed]

Reitze, D. H.

Rhynard, S. E.

Rundquist, A.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997).
[CrossRef]

Rundquist, A. R.

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 83, 2187 (1999).
[CrossRef]

Sansone, G.

Schmeltzer, R. A.

E. A.J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Sebban, S.

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[CrossRef]

Sekikawa, T.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, Appl. Phys. B 78, 275 (2004).
[CrossRef]

Seyfried, V.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Spielmann, C.

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, Appl. Phys. B 80, 277 (2005).
[CrossRef]

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

Stagira, S.

Strehle, M.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Sutherland, J. R.

Tondello, G.

Valentin, C.

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[CrossRef]

Vdovin, G.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. Christov, M. M. Murnane, and H. C. Kapteyn, Nature 406, 164 (2000).
[CrossRef] [PubMed]

Villoresi, P.

Vozzi, C.

Walter, D.

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, Appl. Phys. B 80, 277 (2005).
[CrossRef]

Wang, H. W.

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997).
[CrossRef]

Watanabe, S.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, Appl. Phys. B 78, 275 (2004).
[CrossRef]

Weihe, F.

D. H. Reitze, S. Kazamias, F. Weihe, G. Mullot, D. Douillet, F. Augé, O. Albert, V. Ramanathan, J. P. Chambaret, D. Hulin, and P. Balcou, Opt. Lett. 29, 86 (2004).
[CrossRef] [PubMed]

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[CrossRef]

Winterfeldt, C.

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, Appl. Phys. B 80, 277 (2005).
[CrossRef]

Yoshitomi, D.

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, Appl. Phys. B 78, 275 (2004).
[CrossRef]

Zeek, E.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. Christov, M. M. Murnane, and H. C. Kapteyn, Nature 406, 164 (2000).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. B

D. Yoshitomi, J. Nees, N. Miyamoto, T. Sekikawa, T. Kanai, G. Mourou, and S. Watanabe, Appl. Phys. B 78, 275 (2004).
[CrossRef]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, Appl. Phys. B 80, 277 (2005).
[CrossRef]

Bell Syst. Tech. J.

E. A.J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Chem. Phys.

R. Bartels, S. Backus, I. Christov, H. Kapteyn, and M. Murnane, Chem. Phys. 267, 277 (2001).
[CrossRef]

Eur. Phys. J. D

S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Auge, D. Hulin, and P. Balcou, Eur. Phys. J. D 21, 353 (2002).
[CrossRef]

Nature

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

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. Christov, M. M. Murnane, and H. C. Kapteyn, Nature 406, 164 (2000).
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Opt. Express

Opt. Lett.

Phys. Rev. Lett.

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 83, 2187 (1999).
[CrossRef]

I. P. Christov, R. Bartels, H. C. Kapteyn, and M. M. Murnane, Phys. Rev. Lett. 86, 5458 (2001).
[CrossRef] [PubMed]

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997).
[CrossRef]

Science

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Pressure dependence of HHG in hollow fibers for excitation of two fiber modes: (a) experiment and (b) simulation. Emission at lower pressures is caused by the EH 11 mode, at higher pressures by the EH 12 mode. The simulation provides additional confidence by reproducing the shift of the intensity maximum for each mode to higher pressures with decreasing wavelength.

Fig. 2
Fig. 2

Spatial laser pulse shape optimization of selective harmonic emission in a single harmonic (23rd harmonic order; see text for details). The signal in H23 is enhanced by more than 2 orders of magnitude, whereas the overall signal increases approximately tenfold. The inset shows the normalized fitness versus generation number of the evolutionary optimization. One generation was acquired in 100 s.

Fig. 3
Fig. 3

Spatially resolved HHG spectra corresponding to the optimization shown in Fig. 2: (a), (c) before and (b), (d) after optimization at (a), (b) high and (c), (d) low pressure. A bimodal spectral structure is visible (a) before optimization owing to the presence of at least two different fiber modes (causing different amounts of ionization-induced blueshift). The optimal spatially shaped laser pulse produces a single-mode harmonic spectrum at approximately ten times more overall intensity in (b); the CCD integration time for (b) was reduced by a factor of 10 compared with (a). At low pressure (20 mbars), the difference in initial fiber mode distribution becomes even more evident.

Equations (1)

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Δ k = N a [ n ( ω ) n ( q ω ) ] ω c + ω p 2 ( 1 q 2 ) 2 q c ω + u n l 2 c ( 1 q 2 ) 2 q a 2 ω ,

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