Abstract

High-order harmonic generation in a hollow fiber filled with a weakly ionizing gas is theoretically analyzed within the framework of the slowly varying envelope approximation. The gas pressure that corresponds to maximum efficiency of frequency conversion, the absorption coefficient, the phase mismatch owing to gas dispersion, and the enhancement of harmonic-generation efficiency owing to waveguide phase matching are estimated for 27th-harmonic generation in hollow fibers filled with helium, neon, argon, krypton, or xenon. As a result of the ionization-induced self-phase modulation of the pump pulse in a hollow fiber filled with a weakly ionizing gas, the phase mismatch changes within the pump pulse, decreasing the overall efficiency of harmonic generation and making the harmonic-generation efficiency less sensitive to the gas pressure in the hollow fiber.

© 2001 Optical Society of America

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1999 (4)

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

C. G. Durfee III, 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. M. Zheltikov, N. I. Koroteev, and A. N. Naumov, “Self- and cross-phase modulation accompanying third-harmonic generation in a hollow waveguide,” JETP 88, 857–867 (1999).
[CrossRef]

C. G. Durfee III, 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]

1998 (3)

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 5368, 1412–1415 (1998).
[CrossRef]

Y. Tamaki, K. Midorikawa, and M. Obara, “Third-harmonic generation by nonlinear phase shift in a hollow fiber,” Appl. Phys. B 67, 59–63 (1998).
[CrossRef]

N. I. Koroteev and A. M. Zheltikov, “Chirp control in third-harmonic generation due to cross-phase modulation,” Appl. Phys. B 67, 53–57 (1998).
[CrossRef]

1997 (2)

1995 (2)

J. Peatross and D. D. Meyerhofer, “Intensity-dependent atomic-phase effects in high-order harmonic generation,” Phys. Rev. A 52, 3976–3987 (1995).
[CrossRef] [PubMed]

J. Peatross, M. V. Fedorov, and K. C. Kulander, “Intensity-dependent phase-matching effects in harmonic generation,” J. Opt. Soc. Am. B 12, 863–870 (1995).
[CrossRef]

1994 (2)

N. I. Koroteev, A. N. Naumov, and A. M. Zheltikov, “Theory of spectra of coherent four-photon scattering with one-photon resonances due to excited and autoionizing atomic states,” Laser Phys. 4, 1160–1172 (1994).

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]

1993 (1)

J. J. Macklin, J. D. Kmetec, and C. L. Gordon III, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766–769 (1993).
[CrossRef] [PubMed]

1992 (1)

Ph. Balcou, A. S. L. Gomes, C. Coruaggia, L. A. Lompre, and A. L’Huillier, “Optimizing high-order harmonic generation in strong fields,” J. Phys. B 25, 4467–4478 (1992).
[CrossRef]

1991 (1)

F. Giammanco, “Collective effects in intense laser fields,” Phys. Rev. A 42, 6939–6951 (1991).
[CrossRef]

1989 (1)

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

1988 (1)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[CrossRef]

1977 (1)

R. B. Miles, G. Laufer, and G. C. Bjorklund, “Coherent anti-Stokes Raman scattering in a hollow dielectric waveguide,” Appl. Phys. Lett. 30, 417–419 (1977).
[CrossRef]

1965 (1)

V. P. Silin, “Nonlinear high-frequency conductivity of a plasma,” Sov. Phys. JETP 20, 1510–1516 (1965).

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and layers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Agostini, P.

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

Backus, S.

C. G. Durfee III, 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]

C. G. Durfee III, 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 III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 5368, 1412–1415 (1998).
[CrossRef]

C. G. Durfee III, 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, 1565–1567 (1997).
[CrossRef]

Balcou, Ph.

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]

Ph. Balcou, A. S. L. Gomes, C. Coruaggia, L. A. Lompre, and A. L’Huillier, “Optimizing high-order harmonic generation in strong fields,” J. Phys. B 25, 4467–4478 (1992).
[CrossRef]

Bjorklund, G. C.

R. B. Miles, G. Laufer, and G. C. Bjorklund, “Coherent anti-Stokes Raman scattering in a hollow dielectric waveguide,” Appl. Phys. Lett. 30, 417–419 (1977).
[CrossRef]

Breger, P.

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

Chang, Z.

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 5368, 1412–1415 (1998).
[CrossRef]

Constant, E.

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

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]

Coruaggia, C.

Ph. Balcou, A. S. L. Gomes, C. Coruaggia, L. A. Lompre, and A. L’Huillier, “Optimizing high-order harmonic generation in strong fields,” J. Phys. B 25, 4467–4478 (1992).
[CrossRef]

De Silvestri, S.

Dorrer, Ch.

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

Durfee III, C. G.

C. G. Durfee III, 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]

C. G. Durfee III, 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 III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 5368, 1412–1415 (1998).
[CrossRef]

C. G. Durfee III, 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, 1565–1567 (1997).
[CrossRef]

Fedorov, M. V.

Ferencz, K.

Ferray, M.

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

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[CrossRef]

Garzella, D.

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

Giammanco, F.

F. Giammanco, “Collective effects in intense laser fields,” Phys. Rev. A 42, 6939–6951 (1991).
[CrossRef]

Gomes, A. S. L.

Ph. Balcou, A. S. L. Gomes, C. Coruaggia, L. A. Lompre, and A. L’Huillier, “Optimizing high-order harmonic generation in strong fields,” J. Phys. B 25, 4467–4478 (1992).
[CrossRef]

Gordon III, C. L.

J. J. Macklin, J. D. Kmetec, and C. L. Gordon III, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766–769 (1993).
[CrossRef] [PubMed]

Herne, C.

C. G. Durfee III, 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. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 5368, 1412–1415 (1998).
[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]

Kapteyn, H. C.

C. G. Durfee III, 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 III, 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. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 5368, 1412–1415 (1998).
[CrossRef]

C. G. Durfee III, 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, 1565–1567 (1997).
[CrossRef]

Kmetec, J. D.

J. J. Macklin, J. D. Kmetec, and C. L. Gordon III, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766–769 (1993).
[CrossRef] [PubMed]

Koroteev, N. I.

A. M. Zheltikov, N. I. Koroteev, and A. N. Naumov, “Self- and cross-phase modulation accompanying third-harmonic generation in a hollow waveguide,” JETP 88, 857–867 (1999).
[CrossRef]

N. I. Koroteev and A. M. Zheltikov, “Chirp control in third-harmonic generation due to cross-phase modulation,” Appl. Phys. B 67, 53–57 (1998).
[CrossRef]

N. I. Koroteev, A. N. Naumov, and A. M. Zheltikov, “Theory of spectra of coherent four-photon scattering with one-photon resonances due to excited and autoionizing atomic states,” Laser Phys. 4, 1160–1172 (1994).

Krausz, F.

Kulander, K. C.

L’Huillier, A.

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]

Ph. Balcou, A. S. L. Gomes, C. Coruaggia, L. A. Lompre, and A. L’Huillier, “Optimizing high-order harmonic generation in strong fields,” J. Phys. B 25, 4467–4478 (1992).
[CrossRef]

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

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[CrossRef]

Laufer, G.

R. B. Miles, G. Laufer, and G. C. Bjorklund, “Coherent anti-Stokes Raman scattering in a hollow dielectric waveguide,” Appl. Phys. Lett. 30, 417–419 (1977).
[CrossRef]

Le Blanc, C.

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

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]

Li, X. F.

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

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[CrossRef]

Lompre, L. A.

Ph. Balcou, A. S. L. Gomes, C. Coruaggia, L. A. Lompre, and A. L’Huillier, “Optimizing high-order harmonic generation in strong fields,” J. Phys. B 25, 4467–4478 (1992).
[CrossRef]

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

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[CrossRef]

Macklin, J. J.

J. J. Macklin, J. D. Kmetec, and C. L. Gordon III, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766–769 (1993).
[CrossRef] [PubMed]

Mainfray, G.

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

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[CrossRef]

Manus, C.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and layers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Mevel, E.

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

Meyerhofer, D. D.

J. Peatross and D. D. Meyerhofer, “Intensity-dependent atomic-phase effects in high-order harmonic generation,” Phys. Rev. A 52, 3976–3987 (1995).
[CrossRef] [PubMed]

Midorikawa, K.

Y. Tamaki, K. Midorikawa, and M. Obara, “Third-harmonic generation by nonlinear phase shift in a hollow fiber,” Appl. Phys. B 67, 59–63 (1998).
[CrossRef]

Miles, R. B.

R. B. Miles, G. Laufer, and G. C. Bjorklund, “Coherent anti-Stokes Raman scattering in a hollow dielectric waveguide,” Appl. Phys. Lett. 30, 417–419 (1977).
[CrossRef]

Murnane, M. M.

C. G. Durfee III, 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 III, 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. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 5368, 1412–1415 (1998).
[CrossRef]

C. G. Durfee III, 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, 1565–1567 (1997).
[CrossRef]

Naumov, A. N.

A. M. Zheltikov, N. I. Koroteev, and A. N. Naumov, “Self- and cross-phase modulation accompanying third-harmonic generation in a hollow waveguide,” JETP 88, 857–867 (1999).
[CrossRef]

N. I. Koroteev, A. N. Naumov, and A. M. Zheltikov, “Theory of spectra of coherent four-photon scattering with one-photon resonances due to excited and autoionizing atomic states,” Laser Phys. 4, 1160–1172 (1994).

Nisoli, M.

Obara, M.

Y. Tamaki, K. Midorikawa, and M. Obara, “Third-harmonic generation by nonlinear phase shift in a hollow fiber,” Appl. Phys. B 67, 59–63 (1998).
[CrossRef]

Peatross, J.

J. Peatross, M. V. Fedorov, and K. C. Kulander, “Intensity-dependent phase-matching effects in harmonic generation,” J. Opt. Soc. Am. B 12, 863–870 (1995).
[CrossRef]

J. Peatross and D. D. Meyerhofer, “Intensity-dependent atomic-phase effects in high-order harmonic generation,” Phys. Rev. A 52, 3976–3987 (1995).
[CrossRef] [PubMed]

Rundquist, A.

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 5368, 1412–1415 (1998).
[CrossRef]

Rundquist, A. R.

C. G. Durfee III, 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]

Salin, F.

E. Constant, D. Garzella, P. Breger, E. Mevel, Ch. Dorrer, C. Le Blanc, 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.

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and layers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Silin, V. P.

V. P. Silin, “Nonlinear high-frequency conductivity of a plasma,” Sov. Phys. JETP 20, 1510–1516 (1965).

Spielmann, Ch.

Svelto, O.

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Tamaki, Y.

Y. Tamaki, K. Midorikawa, and M. Obara, “Third-harmonic generation by nonlinear phase shift in a hollow fiber,” Appl. Phys. B 67, 59–63 (1998).
[CrossRef]

Zheltikov, A. M.

A. M. Zheltikov, N. I. Koroteev, and A. N. Naumov, “Self- and cross-phase modulation accompanying third-harmonic generation in a hollow waveguide,” JETP 88, 857–867 (1999).
[CrossRef]

N. I. Koroteev and A. M. Zheltikov, “Chirp control in third-harmonic generation due to cross-phase modulation,” Appl. Phys. B 67, 53–57 (1998).
[CrossRef]

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Appl. Phys. B (2)

Y. Tamaki, K. Midorikawa, and M. Obara, “Third-harmonic generation by nonlinear phase shift in a hollow fiber,” Appl. Phys. B 67, 59–63 (1998).
[CrossRef]

N. I. Koroteev and A. M. Zheltikov, “Chirp control in third-harmonic generation due to cross-phase modulation,” Appl. Phys. B 67, 53–57 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

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[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 layers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. B (2)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31–L35 (1988).
[CrossRef]

Ph. Balcou, A. S. L. Gomes, C. Coruaggia, L. A. Lompre, and A. L’Huillier, “Optimizing high-order harmonic generation in strong fields,” J. Phys. B 25, 4467–4478 (1992).
[CrossRef]

JETP (1)

A. M. Zheltikov, N. I. Koroteev, and A. N. Naumov, “Self- and cross-phase modulation accompanying third-harmonic generation in a hollow waveguide,” JETP 88, 857–867 (1999).
[CrossRef]

Laser Phys. (1)

N. I. Koroteev, A. N. Naumov, and A. M. Zheltikov, “Theory of spectra of coherent four-photon scattering with one-photon resonances due to excited and autoionizing atomic states,” Laser Phys. 4, 1160–1172 (1994).

Opt. Lett. (3)

Phys. Rev. A (4)

J. Peatross and D. D. Meyerhofer, “Intensity-dependent atomic-phase effects in high-order harmonic generation,” Phys. Rev. A 52, 3976–3987 (1995).
[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]

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[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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

C. G. Durfee III, 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]

Science (1)

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 5368, 1412–1415 (1998).
[CrossRef]

Sov. Phys. JETP (1)

V. P. Silin, “Nonlinear high-frequency conductivity of a plasma,” Sov. Phys. JETP 20, 1510–1516 (1965).

Other (7)

C. G. Durfee III, A. Rundquist, Z. Chang, C. Herne, F. Weihe, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matching of high-order harmonic generation in capillary waveguides,” in International Quantum Electronic Conference (IQEC’98), Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper QPD5.

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A. N. Zaidel and E. Ya. Shreider, Vacuum Ultraviolet Spectroscopy (Nauka, Moscow, USSR, 1967; in Russian).

M. A. Blokhin and I. G. Shveitser, Handbook on X-Ray Spectra (Nauka, Moscow, 1982; in Russian).

W. A. Roth and K. Scheel, eds., Landolt Börnstein Physikalisch-Chemische Tabellen (Springer-Verlag, Berlin, 1931, 1935), Vols. II and III.

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, Orlando, Fla., 1984).

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Figures (4)

Fig. 1
Fig. 1

Intensity of the qth harmonic as a function of the normalized propagation length in a hollow fiber calculated by use of Eq. (15) in the case of exact phase matching (curve 1) and with Δkqn=2κq (curve 2).

Fig. 2
Fig. 2

Intensity of the 27th harmonic of 780-nm fundamental radiation generated in a hollow fiber with an inner diameter of 150 µm filled with 1, xenon; 2, krypton; 3, argon; 4, neon; or 5, helium as a function of gas pressure. The transverse distribution of the pump intensity corresponds to the EH11 waveguide mode.

Fig. 3
Fig. 3

Energy of 1, 2, the 27th and 3, 4, the 21st harmonics of 790-nm fundamental radiation generated in an argon-filled hollow fiber with an inner diameter of 150 µm and length L=2 cm as a function of the gas pressure 1, 3 in the absence of ionization and 2, 4 when 0.8% of atoms are ionized during the pump pulse. The transverse distribution of the pump intensity corresponds to the EH11 waveguide mode. The pump pulse is assumed to have a rectangular shape.

Fig. 4
Fig. 4

Phase mismatch for dashed lines, the 21st and solid lines, the 27th harmonics of 790-nm fundamental radiation generated in an argon-filled hollow fiber with an inner diameter of 150 µm as a function of gas pressure on 3, 4 the leading edge of the pulse (θ/τ=0), where ionization does not play an important role, and 1, 2, the trailing edge of the pulse (θ/τ=1), where 0.8% of atoms are ionized. The transverse distribution of the pump intensity corresponds to the EH11 waveguide mode. The pump pulse has a rectangular shape (dashed line, inset), giving rise to a linear growth in the effective electron concentration as a function of time θ (solid line, inset); n is the concentration of argon atoms.

Tables (1)

Tables Icon

Table 1 Optimal Gas Pressure p0a

Equations (21)

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E1=An(θ, z)fn(ρ)exp[-i(ωt-Knz)]+c.c.,
Eq=Bq(θ, z, ρ)exp[-i(qωt-Kqz)]+c.c.,
ωa/c1,
Kncωn1(ω)-11,
fn(ρ)=J0(unρ/a),
Knωn1(ω)c 1-uncaωn1(ω)212+Im[μ(ω)]aωc,
μ(ω)=[ε2(ω)+n12(ω)]2n12(ω)[ε2(ω)-n12(ω)]1/2
An(θ, z)z=2iπω2Knc2χn(1)(θ)An(θ, z).
χn(1)(θ)=-e2mω2neffn(θ),
neffn(θ)=fn(ρ)ne(θ, ρ)dρ|fn(ρ)|2dρ,
ne(θ, ρ)=n-θw[I(θ, ρ)]dθ,
An(θ, z)=A0(θ)exp[iδKn(θ)z],
δKn(θ)=-2πe2Knc2mneffn(θ)
dBqdz+[κq-iδKq(θ)]Bq
=2iπω2q2Kqc2PqNL(θ, ρ)×exp{-i[Kq-qKn-qδKn(θ)]z},
δKq(θ)=-2πe2Kqc2mneff2(θ)
Iq(θ, ρ)=2πKqqω|PqNL(θ, ρ)|2×1-exp[-iΔkqn(θ)z-κqz]-iΔkqn(θ)-κq2,
Δkqn(θ)=Kq+δKq(θ)-qKn-qδKn(θ)Δk0+Δkwn+δkqn(θ)
κqz1,
Iq(θ, ρ)=2πKqqω|PqNL(θ, ρ)|2{[ΔKqn(θ)]2+(κq)2}-1.
η=1+(Δk0/κq)2.

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