Abstract

We present an analytical, computational, and experimental study of frequency mixing and propagation that takes place in the guided-wave nonlinear frequency conversion of ultrashort pulses from the near infrared to the far and the vacuum ultraviolet. In addition to the standard phase-matching conditions for frequency mixing, we observe that cascaded frequency conversion, in which one of the input frequency components is generated simultaneously, is subject to two additional phase-matching conditions. In cascaded quasi-phase matching, one of the input fields oscillates in strength with a period that matches the phase mismatch. In gain-assisted phase matching, the growth of one of the input fields results in growth of the signal, in spite of a phase mismatch for the final mixing process.

© 2002 Optical Society of America

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  12. S. Lejnine, C. G. Durfee, M. M. Murnane, H. C. Kapteyn, V. L. Makarov, and J. P. Langmore, “Crosslinking of proteins to DNA in human nuclei using a 60 femtosecond 266 nm laser,” Nucl. Acids Res. 27, 3676–3684 (1999).
    [CrossRef] [PubMed]
  13. A. Rundquist, C. G. Durfee, 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).
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    [CrossRef]
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    [CrossRef]
  27. R. L. Byer, “Quasi-phasematched nonlinear interactions and devices,” J. Nonlinear Opt. Phys. Mater. 6, 549–592 (1997).
    [CrossRef]
  28. H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonreso-nant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
    [CrossRef]
  29. X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Main-fray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
    [CrossRef] [PubMed]
  30. P. J. Leonard, “Refractive indices, Verdet constants, and po-larizabilities of inert gases,” At. Data Nucl. Data Tables 14, 21–37 (1974).
    [CrossRef]
  31. C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Ultrabroadband phase-matched optical parametric generation in the ultraviolet by use of guided waves,” Opt. Lett. 22, 1565–1568 (1997).
    [CrossRef]
  32. S. Backus, C. Durfee, G. Mourou, H. C. Kapteyn, and M. M. Murnane, “0.2-Terawatt laser system at 1 kHz,” Opt. Lett. 22, 1256–1258 (1997).
    [CrossRef] [PubMed]

2001 (1)

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 0136–01 (2001).
[CrossRef]

2000 (2)

N. A. Anderson, C. G. Durfee, and R. J. Sension, “the Internal conversions of trans- and cis-1, 3, 5-hexatriene in cyclohexane solution studied with sub-50 fs UV pulses,” Chem. Phys. Lett. 323, 365–371 (2000).
[CrossRef]

C. Reinhardt, B. N. Chichkov, and B. Wellegehausen, “Self-induced parametric amplification of high-order harmonics,” Opt. Lett. 25, 1043–1045 (2000).
[CrossRef]

1999 (7)

P. S. Banks, M. D. Feit, and M. D. Perry, “High-intensity third-harmonic generation in beta barium borate through second-order and third-order susceptibilities,” Opt. Lett. 24, 4–7 (1999).
[CrossRef]

C. G. Durfee, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24, 697–699 (1999).
[CrossRef]

S. Lejnine, C. G. Durfee, M. M. Murnane, H. C. Kapteyn, V. L. Makarov, and J. P. Langmore, “Crosslinking of proteins to DNA in human nuclei using a 60 femtosecond 266 nm laser,” Nucl. Acids Res. 27, 3676–3684 (1999).
[CrossRef] [PubMed]

C. G. Durfee, A. 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]

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

E. Constant, D. Garzella, P. Breger, E. Meval, C. Dorrer, C. LeBlanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, “Phase-matched high-order-harmonic generation in a gas-filled hollow fiber,” Phys. Rev. A 59, 4041–4044 (1999).
[CrossRef]

1998 (2)

M. Schnurer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, “Guiding and high-harmonic generation of sub-10-fs pulses in hollow-core fibers at 1015 W/cm2,” Appl. Phys. B 67, 263–266 (1998).
[CrossRef]

A. Rundquist, C. G. Durfee, 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 (3)

1995 (1)

H. Milchberg, C. G. Durfee, and T. McIlrath, “High-order frequency conversion in the plasma waveguide,” Phys. Rev. Lett. 75, 2494–2497 (1995).
[CrossRef] [PubMed]

1993 (1)

H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472–2474 (1993).
[CrossRef]

1992 (1)

1989 (1)

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Main-fray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

1988 (1)

P. Qiu and A. Penzkofer, “Picosecond third-harmonic generation in β-BaB2O4,” Appl. Phys. B 45, 225–236 (1988).
[CrossRef]

1985 (1)

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonreso-nant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
[CrossRef]

1982 (1)

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. QE-18, 1062–1072 (1982).
[CrossRef]

1976 (1)

I. V. Tomov and M. C. Richardson, “Fifth-harmonic generation in isotropic media,” IEEE J. Quantum Electron. QE-12, 521–531 (1976).
[CrossRef]

1974 (1)

P. J. Leonard, “Refractive indices, Verdet constants, and po-larizabilities of inert gases,” At. Data Nucl. Data Tables 14, 21–37 (1974).
[CrossRef]

1973 (1)

1969 (1)

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

1967 (1)

L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1810 (1964).
[CrossRef]

Agostini, P.

E. Constant, D. Garzella, P. Breger, E. Meval, C. Dorrer, C. LeBlanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Anderson, N. A.

N. A. Anderson, C. G. Durfee, and R. J. Sension, “the Internal conversions of trans- and cis-1, 3, 5-hexatriene in cyclohexane solution studied with sub-50 fs UV pulses,” Chem. Phys. Lett. 323, 365–371 (2000).
[CrossRef]

Backus, S.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 0136–01 (2001).
[CrossRef]

C. G. Durfee, A. 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]

C. G. Durfee, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24, 697–699 (1999).
[CrossRef]

A. Rundquist, C. G. Durfee, 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]

C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Ultrabroadband phase-matched optical parametric generation in the ultraviolet by use of guided waves,” Opt. Lett. 22, 1565–1568 (1997).
[CrossRef]

S. Backus, C. Durfee, G. Mourou, H. C. Kapteyn, and M. M. Murnane, “0.2-Terawatt laser system at 1 kHz,” Opt. Lett. 22, 1256–1258 (1997).
[CrossRef] [PubMed]

Banfi, G. P.

H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472–2474 (1993).
[CrossRef]

Banks, P. S.

Bartels, R.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 0136–01 (2001).
[CrossRef]

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. QE-18, 1062–1072 (1982).
[CrossRef]

Brabec, T.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

M. Schnurer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, “Guiding and high-harmonic generation of sub-10-fs pulses in hollow-core fibers at 1015 W/cm2,” Appl. Phys. B 67, 263–266 (1998).
[CrossRef]

Breger, P.

E. Constant, D. Garzella, P. Breger, E. Meval, C. Dorrer, C. LeBlanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Byer, R. L.

R. L. Byer, “Quasi-phasematched nonlinear interactions and devices,” J. Nonlinear Opt. Phys. Mater. 6, 549–592 (1997).
[CrossRef]

Chang, Z.

A. Rundquist, C. G. Durfee, 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]

Cheng, Z.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

M. Schnurer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, “Guiding and high-harmonic generation of sub-10-fs pulses in hollow-core fibers at 1015 W/cm2,” Appl. Phys. B 67, 263–266 (1998).
[CrossRef]

Chichkov, B. N.

Constant, E.

E. Constant, D. Garzella, P. Breger, E. Meval, C. Dorrer, C. LeBlanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Degnan, J. J.

DeSalvo, R.

Dorrer, C.

E. Constant, D. Garzella, P. Breger, E. Meval, C. Dorrer, C. LeBlanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Durfee, C.

Durfee, C. G.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 0136–01 (2001).
[CrossRef]

N. A. Anderson, C. G. Durfee, and R. J. Sension, “the Internal conversions of trans- and cis-1, 3, 5-hexatriene in cyclohexane solution studied with sub-50 fs UV pulses,” Chem. Phys. Lett. 323, 365–371 (2000).
[CrossRef]

S. Lejnine, C. G. Durfee, M. M. Murnane, H. C. Kapteyn, V. L. Makarov, and J. P. Langmore, “Crosslinking of proteins to DNA in human nuclei using a 60 femtosecond 266 nm laser,” Nucl. Acids Res. 27, 3676–3684 (1999).
[CrossRef] [PubMed]

C. G. Durfee, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24, 697–699 (1999).
[CrossRef]

C. G. Durfee, A. 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. Durfee, 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]

C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Ultrabroadband phase-matched optical parametric generation in the ultraviolet by use of guided waves,” Opt. Lett. 22, 1565–1568 (1997).
[CrossRef]

H. Milchberg, C. G. Durfee, and T. McIlrath, “High-order frequency conversion in the plasma waveguide,” Phys. Rev. Lett. 75, 2494–2497 (1995).
[CrossRef] [PubMed]

Feit, M. D.

Ferray, M.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Main-fray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

Garzella, D.

E. Constant, D. Garzella, P. Breger, E. Meval, C. Dorrer, C. LeBlanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Hagan, D. J.

Hentschel, M.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

M. Schnurer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, “Guiding and high-harmonic generation of sub-10-fs pulses in hollow-core fibers at 1015 W/cm2,” Appl. Phys. B 67, 263–266 (1998).
[CrossRef]

Herne, C.

C. G. Durfee, A. 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. Durfee, 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]

Kálmán, P.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

Kapteyn, H. C.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 0136–01 (2001).
[CrossRef]

C. G. Durfee, A. 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]

C. G. Durfee, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24, 697–699 (1999).
[CrossRef]

S. Lejnine, C. G. Durfee, M. M. Murnane, H. C. Kapteyn, V. L. Makarov, and J. P. Langmore, “Crosslinking of proteins to DNA in human nuclei using a 60 femtosecond 266 nm laser,” Nucl. Acids Res. 27, 3676–3684 (1999).
[CrossRef] [PubMed]

A. Rundquist, C. G. Durfee, 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]

C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Ultrabroadband phase-matched optical parametric generation in the ultraviolet by use of guided waves,” Opt. Lett. 22, 1565–1568 (1997).
[CrossRef]

S. Backus, C. Durfee, G. Mourou, H. C. Kapteyn, and M. M. Murnane, “0.2-Terawatt laser system at 1 kHz,” Opt. Lett. 22, 1256–1258 (1997).
[CrossRef] [PubMed]

Krausz, F.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

M. Schnurer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, “Guiding and high-harmonic generation of sub-10-fs pulses in hollow-core fibers at 1015 W/cm2,” Appl. Phys. B 67, 263–266 (1998).
[CrossRef]

L’Huillier, A.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Main-fray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

Langmore, J. P.

S. Lejnine, C. G. Durfee, M. M. Murnane, H. C. Kapteyn, V. L. Makarov, and J. P. Langmore, “Crosslinking of proteins to DNA in human nuclei using a 60 femtosecond 266 nm laser,” Nucl. Acids Res. 27, 3676–3684 (1999).
[CrossRef] [PubMed]

LeBlanc, C.

E. Constant, D. Garzella, P. Breger, E. Meval, C. Dorrer, C. LeBlanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Lehmeier, H. J.

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonreso-nant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
[CrossRef]

Lejnine, S.

S. Lejnine, C. G. Durfee, M. M. Murnane, H. C. Kapteyn, V. L. Makarov, and J. P. Langmore, “Crosslinking of proteins to DNA in human nuclei using a 60 femtosecond 266 nm laser,” Nucl. Acids Res. 27, 3676–3684 (1999).
[CrossRef] [PubMed]

Leonard, P. J.

P. J. Leonard, “Refractive indices, Verdet constants, and po-larizabilities of inert gases,” At. Data Nucl. Data Tables 14, 21–37 (1974).
[CrossRef]

Leupacher, W.

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonreso-nant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
[CrossRef]

Li, X. F.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Main-fray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

Lompre, L. A.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Main-fray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

Main-fray, G.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Main-fray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

Makarov, V. L.

S. Lejnine, C. G. Durfee, M. M. Murnane, H. C. Kapteyn, V. L. Makarov, and J. P. Langmore, “Crosslinking of proteins to DNA in human nuclei using a 60 femtosecond 266 nm laser,” Nucl. Acids Res. 27, 3676–3684 (1999).
[CrossRef] [PubMed]

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1810 (1964).
[CrossRef]

McIlrath, T.

H. Milchberg, C. G. Durfee, and T. McIlrath, “High-order frequency conversion in the plasma waveguide,” Phys. Rev. Lett. 75, 2494–2497 (1995).
[CrossRef] [PubMed]

Meval, E.

E. Constant, D. Garzella, P. Breger, E. Meval, C. Dorrer, C. LeBlanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Midorikawa, K.

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, “Phase-matched high-order-harmonic generation in a gas-filled hollow fiber,” Phys. Rev. A 59, 4041–4044 (1999).
[CrossRef]

Milchberg, H.

H. Milchberg, C. G. Durfee, and T. McIlrath, “High-order frequency conversion in the plasma waveguide,” Phys. Rev. Lett. 75, 2494–2497 (1995).
[CrossRef] [PubMed]

Misoguti, L.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 0136–01 (2001).
[CrossRef]

Mourou, G.

Murnane, M. M.

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 0136–01 (2001).
[CrossRef]

C. G. Durfee, A. 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]

S. Lejnine, C. G. Durfee, M. M. Murnane, H. C. Kapteyn, V. L. Makarov, and J. P. Langmore, “Crosslinking of proteins to DNA in human nuclei using a 60 femtosecond 266 nm laser,” Nucl. Acids Res. 27, 3676–3684 (1999).
[CrossRef] [PubMed]

C. G. Durfee, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24, 697–699 (1999).
[CrossRef]

A. Rundquist, C. G. Durfee, 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]

C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Ultrabroadband phase-matched optical parametric generation in the ultraviolet by use of guided waves,” Opt. Lett. 22, 1565–1568 (1997).
[CrossRef]

S. Backus, C. Durfee, G. Mourou, H. C. Kapteyn, and M. M. Murnane, “0.2-Terawatt laser system at 1 kHz,” Opt. Lett. 22, 1256–1258 (1997).
[CrossRef] [PubMed]

Nagata, Y.

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, “Phase-matched high-order-harmonic generation in a gas-filled hollow fiber,” Phys. Rev. A 59, 4041–4044 (1999).
[CrossRef]

New, G. H. C.

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Obara, M.

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, “Phase-matched high-order-harmonic generation in a gas-filled hollow fiber,” Phys. Rev. A 59, 4041–4044 (1999).
[CrossRef]

Ostrovskii, L. A.

L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).

Penzkofer, A.

P. Qiu and A. Penzkofer, “Picosecond third-harmonic generation in β-BaB2O4,” Appl. Phys. B 45, 225–236 (1988).
[CrossRef]

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonreso-nant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
[CrossRef]

Perry, M. D.

Qiu, P.

P. Qiu and A. Penzkofer, “Picosecond third-harmonic generation in β-BaB2O4,” Appl. Phys. B 45, 225–236 (1988).
[CrossRef]

Reinhardt, C.

Richardson, M. C.

I. V. Tomov and M. C. Richardson, “Fifth-harmonic generation in isotropic media,” IEEE J. Quantum Electron. QE-12, 521–531 (1976).
[CrossRef]

Rundquist, A.

C. G. Durfee, A. 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. Durfee, 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]

Salin, F.

E. Constant, D. Garzella, P. Breger, E. Meval, C. Dorrer, C. LeBlanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

Sartania, S.

M. Schnurer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, “Guiding and high-harmonic generation of sub-10-fs pulses in hollow-core fibers at 1015 W/cm2,” Appl. Phys. B 67, 263–266 (1998).
[CrossRef]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1810 (1964).
[CrossRef]

Schnurer, M.

M. Schnurer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, “Guiding and high-harmonic generation of sub-10-fs pulses in hollow-core fibers at 1015 W/cm2,” Appl. Phys. B 67, 263–266 (1998).
[CrossRef]

Schnürer, M.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

Sension, R. J.

N. A. Anderson, C. G. Durfee, and R. J. Sension, “the Internal conversions of trans- and cis-1, 3, 5-hexatriene in cyclohexane solution studied with sub-50 fs UV pulses,” Chem. Phys. Lett. 323, 365–371 (2000).
[CrossRef]

Sheik-Bahae, M.

Stegeman, G. I.

Stolen, R. H.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. QE-18, 1062–1072 (1982).
[CrossRef]

Stryland, E. W. V.

Tamaki, Y.

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, “Phase-matched high-order-harmonic generation in a gas-filled hollow fiber,” Phys. Rev. A 59, 4041–4044 (1999).
[CrossRef]

Tan, H.

H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472–2474 (1993).
[CrossRef]

Tempea, G.

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

M. Schnurer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, “Guiding and high-harmonic generation of sub-10-fs pulses in hollow-core fibers at 1015 W/cm2,” Appl. Phys. B 67, 263–266 (1998).
[CrossRef]

Tomaselli, A.

H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472–2474 (1993).
[CrossRef]

Tomov, I. V.

I. V. Tomov and M. C. Richardson, “Fifth-harmonic generation in isotropic media,” IEEE J. Quantum Electron. QE-12, 521–531 (1976).
[CrossRef]

Vanherzeele, H.

Ward, J. F.

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Wellegehausen, B.

Appl. Opt. (1)

Appl. Phys. B (2)

P. Qiu and A. Penzkofer, “Picosecond third-harmonic generation in β-BaB2O4,” Appl. Phys. B 45, 225–236 (1988).
[CrossRef]

M. Schnurer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, “Guiding and high-harmonic generation of sub-10-fs pulses in hollow-core fibers at 1015 W/cm2,” Appl. Phys. B 67, 263–266 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472–2474 (1993).
[CrossRef]

At. Data Nucl. Data Tables (1)

P. J. Leonard, “Refractive indices, Verdet constants, and po-larizabilities of inert gases,” At. Data Nucl. Data Tables 14, 21–37 (1974).
[CrossRef]

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1810 (1964).
[CrossRef]

Chem. Phys. Lett. (1)

N. A. Anderson, C. G. Durfee, and R. J. Sension, “the Internal conversions of trans- and cis-1, 3, 5-hexatriene in cyclohexane solution studied with sub-50 fs UV pulses,” Chem. Phys. Lett. 323, 365–371 (2000).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. QE-18, 1062–1072 (1982).
[CrossRef]

I. V. Tomov and M. C. Richardson, “Fifth-harmonic generation in isotropic media,” IEEE J. Quantum Electron. QE-12, 521–531 (1976).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

R. L. Byer, “Quasi-phasematched nonlinear interactions and devices,” J. Nonlinear Opt. Phys. Mater. 6, 549–592 (1997).
[CrossRef]

JETP Lett. (1)

L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).

Nucl. Acids Res. (1)

S. Lejnine, C. G. Durfee, M. M. Murnane, H. C. Kapteyn, V. L. Makarov, and J. P. Langmore, “Crosslinking of proteins to DNA in human nuclei using a 60 femtosecond 266 nm laser,” Nucl. Acids Res. 27, 3676–3684 (1999).
[CrossRef] [PubMed]

Opt. Commun. (1)

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonreso-nant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. (1)

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Phys. Rev. A (2)

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, “Phase-matched high-order-harmonic generation in a gas-filled hollow fiber,” Phys. Rev. A 59, 4041–4044 (1999).
[CrossRef]

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Main-fray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

E. Constant, D. Garzella, P. Breger, E. Meval, C. Dorrer, C. LeBlanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[CrossRef]

H. Milchberg, C. G. Durfee, and T. McIlrath, “High-order frequency conversion in the plasma waveguide,” Phys. Rev. Lett. 75, 2494–2497 (1995).
[CrossRef] [PubMed]

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation of broadband VUV light using third-order cascaded processes,” Phys. Rev. Lett. 87, 0136–01 (2001).
[CrossRef]

C. G. Durfee, A. 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]

M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft x-ray pulses,” Phys. Rev. Lett. 83, 722–725 (1999).
[CrossRef]

Science (1)

A. Rundquist, C. G. Durfee, 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]

Other (4)

L. Misoguti, S. Backus, C. G. Durfee, R. Bartels, M. M. Murnane, and H. C. Kapteyn, “Generation and measurement of ultrafast tunable VUV light,” in Ultrafast Phenomena XII, T. Elsaesser, ed., Vol. 66 of Springer Series in Chemical Physics V (Springer-Verlag, Berlin, 2000), pp. 301–303.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Guided-wave optical parametric amplification in gases: a novel phase-matching technique for ultrafast pulses,” in Applications of High Field and Short Wavelength Sources, L. DiMauro, M. M. Murnane, and A. L’Huillier, eds. (Plenum, New York, 1998), pp. 71–78.

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Figures (10)

Fig. 1
Fig. 1

Phase mismatch Δk (in inverse centimeters) versus argon pressure (Torr) in a capillary of 125-µm inner diameter. Dashed curve, Δk4; solid curve, Δk3+Δk4; dotted curve Δk3.

Fig. 2
Fig. 2

Calculated small-signal yield of ω4 (thicker curve) and ω3 (thinner curve) versus propagation length. Units are arbitrary, but the scale is uniform for all plots: (a) Δk3+Δk4=0, (b) Δk3=0, (c) Δk4=0.

Fig. 3
Fig. 3

Schematic of the experimental layout for cascaded frequency generation. Typically, less than 1 mJ from the amplifier is used for the experiment. BBO, β-barium borate.

Fig. 4
Fig. 4

Measured yield of frequency-converted light at ω3 (266 nm) for a capillary inner diameter of 125 µm as a function of argon-gas pressure, for three capillary lengths.

Fig. 5
Fig. 5

Measured yield of frequency-converted light at ω4 (200 nm) for the same conditions as for Fig. 3.

Fig. 6
Fig. 6

Measured yield of frequency-converted light at ω5 (160 nm) for the same conditions as for Fig. 3.

Fig. 7
Fig. 7

Calculated yield of frequency-converted light at ω3 for conditions similar to those for Figs. 35. (a) Intensity plot of yield versus length and pressure. Darkest shading in the image corresponds to greatest intensity. (b) Lineouts for yield versus pressure for lengths shown in Fig. 3. Three lengths are shown: 10 cm (dotted curve), 40 cm (dashed curve), and 80 cm (solid curve).

Fig. 8
Fig. 8

Calculated yield of frequency-converted light at ω4 for conditions similar to those for Figs. 35. (a) Intensity plot of yield versus length and pressure. Darkest shading in the image corresponds to greatest intensity. (b) Lineouts for yield versus pressure for lengths shown in Fig. 3. Three lengths are shown: 10 cm (dotted curve), 40 cm (dashed curve), and 80 cm (solid curve).

Fig. 9
Fig. 9

Calculated yield of frequency-converted light at ω5 for conditions similar to those for Figs. 35. (a) Intensity plot of yield versus length and pressure. Darkest shading in the image corresponds to greatest intensity. (b) Lineouts for yield versus pressure for lengths shown in Fig. 3. Three lengths are shown: 10 cm (dotted curve), 30 cm (dashed curve), 80 cm (solid curve).

Fig. 10
Fig. 10

(a) Measured yield of light at ω4 for a two-segment capillary (20 cm+20 cm) as the pressure of argon in the second segment was varied. The first segment was set at a pressure of 95 Torr to optimize the yield at ω3. (b) Calculated yield for conditions shown in (a).

Tables (1)

Tables Icon

Table 1 Frequency-Mixing Terms Included in the Propagation Code

Equations (11)

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

αnm=unm2π2 λ2a3 νEH2,
k=2πn(λ)λ 1-12 unmλ2πa22πλ+2πNaδ(λ)λ-Nereλ-unm2λ4πa2.
Δk=2πNaδ3λ3+Mδ1λ1-Nδ2λ2-u4πa2(λ3+Mλ1-Nλ2)=Δkmat-Δkmode.
E3(z)=ik3χ(3)E22E1*[exp(iΔk3z)-1]Δk3.
E4(z)=k3k4[χ(3)]2E23(E1*)2
×exp[i(Δk3+Δk4)z]-1Δk3(Δk3+Δk4)
-exp(iΔk4z)-1Δk3Δk4.
I4(z)|k3k4[χ(3)]2E23(E1*)2|2 2(Δkj)4×[1+12(Δkj z)2-Δkjz sin(Δkjz)-cos(Δkj z)],
I5(E1*)6E28k34k52[χ(3)]6×[8+Δk54z4+4(Δk52z2-2)×cos(Δk5z)-8Δk5z sin(Δk5z)]/Δk56.
Iexp(2gz)g2+Δk2,
I5(E1*)6E28k34k52[χ(3)]6z4/(Δk52+α52).

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