Abstract

Angular intensity distributions of the Stokes and anti-Stokes waves are analyzed spatially and temporally by the temporally resolved symmetric Gauss–Laguerre decomposition method. Not only the phase-matching angle but also the diffractive propagation in the medium plays an important role in the evolution of the ring-shaped pattern of the anti-Stokes wave. We simulate the sudden breakup in the spatial shape of the first Stokes wave reported by Wada et al. [Opt. Commun. 88, 146 (1992)], using the experimental conditions to investigate the energy flow during multiwave mixing. The ring generation is caused by the second Stokes wave in stimulated Raman scattering rather than by the anti-Stokes wave in parametric four-wave mixing.

© 1997 Optical Society of America

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    [CrossRef]
  2. H. Schomburg, H. F. Dobele, and B. Ruckle, “Generation of tunable narrow-bandwidth VUV radiation by anti-Stokes SRS in H2,” Appl. Phys. B 30, 131 (1983).
    [CrossRef]
  3. N. Morita, L. H. Lin, and T. Yajima, “Generation of picosecond UV pulses by stimulated anti-Stokes Raman scattering,” Appl. Phys. B 31, 63 (1983).
    [CrossRef]
  4. H. F. Dobele and B. Ruckle, “Application of an argon-fluoride laser system to the generation of VUV radiation by stimulated Raman scattering,” Appl. Opt. 23, 1040 (1984).
    [CrossRef] [PubMed]
  5. H. F. Dobele, M. Horl, and M. Rowekamp, “Two-photon excitation of molecular hydrogen and stimulated emission in the vacuum ultraviolet,” Appl. Phys. Lett. 49, 925 (1986).
    [CrossRef]
  6. H. F. Dobele, M. Horl, and M. Rowekamp, “Tuning ranges of KrF and ArF excimer laser amplifiers and of associated vacuum ultraviolet anti-Stokes Raman lines,” Appl. Phys. B 42, 67 (1987).
    [CrossRef]
  7. A. Takahashi, O. Matsumoto, M. Maeda, and Y. Miyazoe, “Tunable VUV generation by anti-Stokes stimulated Raman conversion of XeCl laser radiation,” Jpn. J. Appl. Phys. 26, L954 (1987).
    [CrossRef]
  8. H. Wallmeier and H. Zacharias, “Continuously tunable VUV radiation (129–210 nm) by anti-Stokes Raman scattering in cooled H2,” Appl. Phys. B 45, 263 (1988).
    [CrossRef]
  9. A. Takahashi, M. Maeda, K. Muraoka, and M. Akazaki, “Picosecond VUV anti-Stokes Raman laser pumped by a KrF laser,” Jpn. J. Appl. Phys. 28, L252 (1989).
    [CrossRef]
  10. V. S. D. Gathen, T. Bornemann, V. Kornas, and H. F. Dobele, “VUV generation by high-order CARS,” IEEE J. Quantum Electron. 26, 739 (1990).
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    [CrossRef] [PubMed]
  12. C. Reiser, T. D. Raymond, R. B. Michie, and A. P. Hickman, “Efficient anti-Stokes Raman conversion in collimated beams,” J. Opt. Soc. Am. B 6, 1859 (1989).
    [CrossRef]
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  15. R. Chiao and B. P. Stoicheff, “Angular dependence of master-stimulated Raman radiation in calcite,” Phys. Rev. Lett. 12, 290 (1964).
    [CrossRef]
  16. A. N. Arbatskaya and M. M. Sushchinskii, “Investigation of four-photon processes in stimulated Raman scattering (SRS),” Sov. Phys. JETP 39, 981 (1974).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  29. P. R. Peterson, D. A. Cardimona, and A. Gavrielides, “Anti-Stokes generation in focused geometries,” J. Opt. Soc. Am. B 4, 1970 (1987).
    [CrossRef]
  30. W. K. Bischel and M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transition in H2,” J. Opt. Soc. Am. B 3, 677 (1986).
    [CrossRef]
  31. P. Alsing, P. R. Peterson, D. A. Cardimona, and A. Gavrielides, “Power-dependent dispersion in far-off-resonant Raman scattering,” IEEE J. Quantum Electron. QE-23, 557 (1987).
    [CrossRef]
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    [CrossRef]
  35. X. Cheng and T. Kobayashi, “Raman wave front of higher-order Stokes and four-wave mixing processes,” J. Opt. Soc. Am. B 5, 2363 (1988).
    [CrossRef]
  36. M. Suzuki and H. Tashiro, “Transverse mode selection mechanism in a para-hydrogen Raman laser with multiple reflection pass,” J. Opt. Soc. Am. B 8, 1686 (1991).
    [CrossRef]
  37. M. Strauss, J. Oreg, and A. Bar-Shalom, “Buildup of transverse spatial correlations in stimulated Raman scattering,” Phys. Rev. A 38, 4712 (1988).
    [CrossRef] [PubMed]
  38. W. A. Hamel and J. P. Woerdman, “Nonorthogonality of the longitudinal eigenmodes of a laser,” Phys. Rev. A 40, 2785 (1989).
    [CrossRef] [PubMed]

1995

1992

S. Wada, A. Kasai, and H. Tashiro, “Temporal evolution and beam breakup of the Stokes and anti-Stokes waves in stimulated Raman scattering,” Opt. Commun. 88, 146 (1992).
[CrossRef]

S. Wada, A. Kasai, and H. Tashiro, “Efficient generation of higher-order anti-Stokes VUV radiation by steep-rise pumping,” Opt. Lett. 17, 97 (1992).
[CrossRef] [PubMed]

1991

1990

B. Bobbs and C. Warner, “Raman-resonant four-wave mixing and energy transfer,” J. Opt. Soc. Am. B 7, 234 (1990).
[CrossRef]

V. S. D. Gathen, T. Bornemann, V. Kornas, and H. F. Dobele, “VUV generation by high-order CARS,” IEEE J. Quantum Electron. 26, 739 (1990).
[CrossRef]

1989

A. Takahashi, M. Maeda, K. Muraoka, and M. Akazaki, “Picosecond VUV anti-Stokes Raman laser pumped by a KrF laser,” Jpn. J. Appl. Phys. 28, L252 (1989).
[CrossRef]

C. Reiser, T. D. Raymond, R. B. Michie, and A. P. Hickman, “Efficient anti-Stokes Raman conversion in collimated beams,” J. Opt. Soc. Am. B 6, 1859 (1989).
[CrossRef]

W. A. Hamel and J. P. Woerdman, “Nonorthogonality of the longitudinal eigenmodes of a laser,” Phys. Rev. A 40, 2785 (1989).
[CrossRef] [PubMed]

1988

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516 (1988).
[CrossRef] [PubMed]

X. Cheng and T. Kobayashi, “Raman wave front of higher-order Stokes and four-wave mixing processes,” J. Opt. Soc. Am. B 5, 2363 (1988).
[CrossRef]

M. Strauss, J. Oreg, and A. Bar-Shalom, “Buildup of transverse spatial correlations in stimulated Raman scattering,” Phys. Rev. A 38, 4712 (1988).
[CrossRef] [PubMed]

H. Wallmeier and H. Zacharias, “Continuously tunable VUV radiation (129–210 nm) by anti-Stokes Raman scattering in cooled H2,” Appl. Phys. B 45, 263 (1988).
[CrossRef]

1987

H. F. Dobele, M. Horl, and M. Rowekamp, “Tuning ranges of KrF and ArF excimer laser amplifiers and of associated vacuum ultraviolet anti-Stokes Raman lines,” Appl. Phys. B 42, 67 (1987).
[CrossRef]

A. Takahashi, O. Matsumoto, M. Maeda, and Y. Miyazoe, “Tunable VUV generation by anti-Stokes stimulated Raman conversion of XeCl laser radiation,” Jpn. J. Appl. Phys. 26, L954 (1987).
[CrossRef]

P. R. Peterson, D. A. Cardimona, and A. Gavrielides, “Anti-Stokes generation in focused geometries,” J. Opt. Soc. Am. B 4, 1970 (1987).
[CrossRef]

B. Ritchie, “Theory of transient stimulated Raman scattering in H2,” Phys. Rev. A 35, 5108 (1987).
[CrossRef] [PubMed]

P. Alsing, P. R. Peterson, D. A. Cardimona, and A. Gavrielides, “Power-dependent dispersion in far-off-resonant Raman scattering,” IEEE J. Quantum Electron. QE-23, 557 (1987).
[CrossRef]

1986

W. K. Bischel and M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transition in H2,” J. Opt. Soc. Am. B 3, 677 (1986).
[CrossRef]

A. Gavrielides and P. Peterson, “Diffractive Raman scattering in focused geometry,” J. Opt. Soc. Am. B 3, 1394 (1986).
[CrossRef]

J. L. Carlsten, J. Rifkin, and D. C. MacPherson, “Spatial mode structure of stimulated Stokes emission from a Raman generator,” J. Opt. Soc. Am. B 3, 1476 (1986).
[CrossRef]

H. F. Dobele, M. Horl, and M. Rowekamp, “Two-photon excitation of molecular hydrogen and stimulated emission in the vacuum ultraviolet,” Appl. Phys. Lett. 49, 925 (1986).
[CrossRef]

A. P. Hickman, J. A. Paisner, and W. K. Bischel, “Theory of multiwave propagation and frequency conversion in a Raman medium,” Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

J. T. Lin, “Theory of transient stimulated Raman scattering and four-wave-mixing processes in multiple-pump systems: a Hamiltonian approach,” Phys. Rev. A 33, 3210 (1986).
[CrossRef] [PubMed]

1985

G. V. Venkin, G. M. Mikheev, and O. A. Novodvorskii, “Angular distribution of anti-Stokes stimulated Raman scattering components from ground and excited vibrational levels of the hydrogen molecule,” Sov. J. Quantum Electron. 15, 1472 (1985).
[CrossRef]

B. N. Perry, P. Rabinowitz, and D. S. Bomse, “Stimulated Raman scattering with a tightly focused pump beam,” Opt. Lett. 10, 146 (1985).
[CrossRef] [PubMed]

1984

1983

D. J. Brink and D. Proch, “Angular distribution of high-order anti-Stokes stimulated Raman scattering in hydrogen,” J. Opt. Soc. Am. 73, 23 (1983).
[CrossRef]

H. Schomburg, H. F. Dobele, and B. Ruckle, “Generation of tunable narrow-bandwidth VUV radiation by anti-Stokes SRS in H2,” Appl. Phys. B 30, 131 (1983).
[CrossRef]

N. Morita, L. H. Lin, and T. Yajima, “Generation of picosecond UV pulses by stimulated anti-Stokes Raman scattering,” Appl. Phys. B 31, 63 (1983).
[CrossRef]

1982

N. E. Kornienko, A. M. Steba, and V. L. Strizhevskii, “Theory of generation and amplification of Stokes and anti-Stokes waves in gaseous media,” Sov. J. Quantum Electron. 12, 1475 (1982).
[CrossRef]

1981

D. Eimerl, R. S. Hargrove, and J. A. Paisner, “Efficient frequency conversion by stimulated Raman scattering,” Phys. Rev. Lett. 46, 651 (1981).
[CrossRef]

1978

V. Wilke and W. Schmidt, “Tunable UV-radiation by stimulated Raman scattering in hydrogen,” Appl. Phys. 16, 151 (1978).
[CrossRef]

1974

A. N. Arbatskaya and M. M. Sushchinskii, “Investigation of four-photon processes in stimulated Raman scattering (SRS),” Sov. Phys. JETP 39, 981 (1974).

1964

R. Chiao and B. P. Stoicheff, “Angular dependence of master-stimulated Raman radiation in calcite,” Phys. Rev. Lett. 12, 290 (1964).
[CrossRef]

Akazaki, M.

A. Takahashi, M. Maeda, K. Muraoka, and M. Akazaki, “Picosecond VUV anti-Stokes Raman laser pumped by a KrF laser,” Jpn. J. Appl. Phys. 28, L252 (1989).
[CrossRef]

Alsing, P.

P. Alsing, P. R. Peterson, D. A. Cardimona, and A. Gavrielides, “Power-dependent dispersion in far-off-resonant Raman scattering,” IEEE J. Quantum Electron. QE-23, 557 (1987).
[CrossRef]

Arbatskaya, A. N.

A. N. Arbatskaya and M. M. Sushchinskii, “Investigation of four-photon processes in stimulated Raman scattering (SRS),” Sov. Phys. JETP 39, 981 (1974).

Bar-Shalom, A.

M. Strauss, J. Oreg, and A. Bar-Shalom, “Buildup of transverse spatial correlations in stimulated Raman scattering,” Phys. Rev. A 38, 4712 (1988).
[CrossRef] [PubMed]

Bischel, W. K.

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516 (1988).
[CrossRef] [PubMed]

A. P. Hickman, J. A. Paisner, and W. K. Bischel, “Theory of multiwave propagation and frequency conversion in a Raman medium,” Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

W. K. Bischel and M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transition in H2,” J. Opt. Soc. Am. B 3, 677 (1986).
[CrossRef]

Bobbs, B.

Bomse, D. S.

Bornemann, T.

V. S. D. Gathen, T. Bornemann, V. Kornas, and H. F. Dobele, “VUV generation by high-order CARS,” IEEE J. Quantum Electron. 26, 739 (1990).
[CrossRef]

Brink, D. J.

Cardimona, D. A.

P. R. Peterson, D. A. Cardimona, and A. Gavrielides, “Anti-Stokes generation in focused geometries,” J. Opt. Soc. Am. B 4, 1970 (1987).
[CrossRef]

P. Alsing, P. R. Peterson, D. A. Cardimona, and A. Gavrielides, “Power-dependent dispersion in far-off-resonant Raman scattering,” IEEE J. Quantum Electron. QE-23, 557 (1987).
[CrossRef]

Carlsten, J. L.

Cheng, X.

Chiao, R.

R. Chiao and B. P. Stoicheff, “Angular dependence of master-stimulated Raman radiation in calcite,” Phys. Rev. Lett. 12, 290 (1964).
[CrossRef]

Dobele, H. F.

V. S. D. Gathen, T. Bornemann, V. Kornas, and H. F. Dobele, “VUV generation by high-order CARS,” IEEE J. Quantum Electron. 26, 739 (1990).
[CrossRef]

H. F. Dobele, M. Horl, and M. Rowekamp, “Tuning ranges of KrF and ArF excimer laser amplifiers and of associated vacuum ultraviolet anti-Stokes Raman lines,” Appl. Phys. B 42, 67 (1987).
[CrossRef]

H. F. Dobele, M. Horl, and M. Rowekamp, “Two-photon excitation of molecular hydrogen and stimulated emission in the vacuum ultraviolet,” Appl. Phys. Lett. 49, 925 (1986).
[CrossRef]

H. F. Dobele and B. Ruckle, “Application of an argon-fluoride laser system to the generation of VUV radiation by stimulated Raman scattering,” Appl. Opt. 23, 1040 (1984).
[CrossRef] [PubMed]

H. Schomburg, H. F. Dobele, and B. Ruckle, “Generation of tunable narrow-bandwidth VUV radiation by anti-Stokes SRS in H2,” Appl. Phys. B 30, 131 (1983).
[CrossRef]

Dyer, M. J.

Eimerl, D.

D. Eimerl, R. S. Hargrove, and J. A. Paisner, “Efficient frequency conversion by stimulated Raman scattering,” Phys. Rev. Lett. 46, 651 (1981).
[CrossRef]

Gathen, V. S. D.

V. S. D. Gathen, T. Bornemann, V. Kornas, and H. F. Dobele, “VUV generation by high-order CARS,” IEEE J. Quantum Electron. 26, 739 (1990).
[CrossRef]

Gavrielides, A.

Hamel, W. A.

W. A. Hamel and J. P. Woerdman, “Nonorthogonality of the longitudinal eigenmodes of a laser,” Phys. Rev. A 40, 2785 (1989).
[CrossRef] [PubMed]

Hargrove, R. S.

D. Eimerl, R. S. Hargrove, and J. A. Paisner, “Efficient frequency conversion by stimulated Raman scattering,” Phys. Rev. Lett. 46, 651 (1981).
[CrossRef]

Hickman, A. P.

C. Reiser, T. D. Raymond, R. B. Michie, and A. P. Hickman, “Efficient anti-Stokes Raman conversion in collimated beams,” J. Opt. Soc. Am. B 6, 1859 (1989).
[CrossRef]

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516 (1988).
[CrossRef] [PubMed]

A. P. Hickman, J. A. Paisner, and W. K. Bischel, “Theory of multiwave propagation and frequency conversion in a Raman medium,” Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

Horl, M.

H. F. Dobele, M. Horl, and M. Rowekamp, “Tuning ranges of KrF and ArF excimer laser amplifiers and of associated vacuum ultraviolet anti-Stokes Raman lines,” Appl. Phys. B 42, 67 (1987).
[CrossRef]

H. F. Dobele, M. Horl, and M. Rowekamp, “Two-photon excitation of molecular hydrogen and stimulated emission in the vacuum ultraviolet,” Appl. Phys. Lett. 49, 925 (1986).
[CrossRef]

Kasai, A.

S. Wada, A. Kasai, and H. Tashiro, “Efficient generation of higher-order anti-Stokes VUV radiation by steep-rise pumping,” Opt. Lett. 17, 97 (1992).
[CrossRef] [PubMed]

S. Wada, A. Kasai, and H. Tashiro, “Temporal evolution and beam breakup of the Stokes and anti-Stokes waves in stimulated Raman scattering,” Opt. Commun. 88, 146 (1992).
[CrossRef]

Kobayashi, T.

Kornas, V.

V. S. D. Gathen, T. Bornemann, V. Kornas, and H. F. Dobele, “VUV generation by high-order CARS,” IEEE J. Quantum Electron. 26, 739 (1990).
[CrossRef]

Kornienko, N. E.

N. E. Kornienko, A. M. Steba, and V. L. Strizhevskii, “Theory of generation and amplification of Stokes and anti-Stokes waves in gaseous media,” Sov. J. Quantum Electron. 12, 1475 (1982).
[CrossRef]

Lin, J. T.

J. T. Lin, “Theory of transient stimulated Raman scattering and four-wave-mixing processes in multiple-pump systems: a Hamiltonian approach,” Phys. Rev. A 33, 3210 (1986).
[CrossRef] [PubMed]

Lin, L. H.

N. Morita, L. H. Lin, and T. Yajima, “Generation of picosecond UV pulses by stimulated anti-Stokes Raman scattering,” Appl. Phys. B 31, 63 (1983).
[CrossRef]

MacPherson, D. C.

Maeda, M.

A. Takahashi, M. Maeda, K. Muraoka, and M. Akazaki, “Picosecond VUV anti-Stokes Raman laser pumped by a KrF laser,” Jpn. J. Appl. Phys. 28, L252 (1989).
[CrossRef]

A. Takahashi, O. Matsumoto, M. Maeda, and Y. Miyazoe, “Tunable VUV generation by anti-Stokes stimulated Raman conversion of XeCl laser radiation,” Jpn. J. Appl. Phys. 26, L954 (1987).
[CrossRef]

Mangir, M. S.

Matsumoto, O.

A. Takahashi, O. Matsumoto, M. Maeda, and Y. Miyazoe, “Tunable VUV generation by anti-Stokes stimulated Raman conversion of XeCl laser radiation,” Jpn. J. Appl. Phys. 26, L954 (1987).
[CrossRef]

Michie, R. B.

Mikheev, G. M.

G. V. Venkin, G. M. Mikheev, and O. A. Novodvorskii, “Angular distribution of anti-Stokes stimulated Raman scattering components from ground and excited vibrational levels of the hydrogen molecule,” Sov. J. Quantum Electron. 15, 1472 (1985).
[CrossRef]

Miyazoe, Y.

A. Takahashi, O. Matsumoto, M. Maeda, and Y. Miyazoe, “Tunable VUV generation by anti-Stokes stimulated Raman conversion of XeCl laser radiation,” Jpn. J. Appl. Phys. 26, L954 (1987).
[CrossRef]

Morita, N.

N. Morita, L. H. Lin, and T. Yajima, “Generation of picosecond UV pulses by stimulated anti-Stokes Raman scattering,” Appl. Phys. B 31, 63 (1983).
[CrossRef]

Moriwaki, H.

Muraoka, K.

A. Takahashi, M. Maeda, K. Muraoka, and M. Akazaki, “Picosecond VUV anti-Stokes Raman laser pumped by a KrF laser,” Jpn. J. Appl. Phys. 28, L252 (1989).
[CrossRef]

Nakamura, A.

Novodvorskii, O. A.

G. V. Venkin, G. M. Mikheev, and O. A. Novodvorskii, “Angular distribution of anti-Stokes stimulated Raman scattering components from ground and excited vibrational levels of the hydrogen molecule,” Sov. J. Quantum Electron. 15, 1472 (1985).
[CrossRef]

Oreg, J.

M. Strauss, J. Oreg, and A. Bar-Shalom, “Buildup of transverse spatial correlations in stimulated Raman scattering,” Phys. Rev. A 38, 4712 (1988).
[CrossRef] [PubMed]

Ottusch, J. J.

Paisner, J. A.

A. P. Hickman, J. A. Paisner, and W. K. Bischel, “Theory of multiwave propagation and frequency conversion in a Raman medium,” Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

D. Eimerl, R. S. Hargrove, and J. A. Paisner, “Efficient frequency conversion by stimulated Raman scattering,” Phys. Rev. Lett. 46, 651 (1981).
[CrossRef]

Perry, B. N.

Peterson, P.

Peterson, P. R.

P. Alsing, P. R. Peterson, D. A. Cardimona, and A. Gavrielides, “Power-dependent dispersion in far-off-resonant Raman scattering,” IEEE J. Quantum Electron. QE-23, 557 (1987).
[CrossRef]

P. R. Peterson, D. A. Cardimona, and A. Gavrielides, “Anti-Stokes generation in focused geometries,” J. Opt. Soc. Am. B 4, 1970 (1987).
[CrossRef]

Proch, D.

Rabinowitz, P.

Raymond, T. D.

Reiser, C.

Rifkin, J.

Ritchie, B.

B. Ritchie, “Theory of transient stimulated Raman scattering in H2,” Phys. Rev. A 35, 5108 (1987).
[CrossRef] [PubMed]

Rockwell, D. A.

Rowekamp, M.

H. F. Dobele, M. Horl, and M. Rowekamp, “Tuning ranges of KrF and ArF excimer laser amplifiers and of associated vacuum ultraviolet anti-Stokes Raman lines,” Appl. Phys. B 42, 67 (1987).
[CrossRef]

H. F. Dobele, M. Horl, and M. Rowekamp, “Two-photon excitation of molecular hydrogen and stimulated emission in the vacuum ultraviolet,” Appl. Phys. Lett. 49, 925 (1986).
[CrossRef]

Ruckle, B.

H. F. Dobele and B. Ruckle, “Application of an argon-fluoride laser system to the generation of VUV radiation by stimulated Raman scattering,” Appl. Opt. 23, 1040 (1984).
[CrossRef] [PubMed]

H. Schomburg, H. F. Dobele, and B. Ruckle, “Generation of tunable narrow-bandwidth VUV radiation by anti-Stokes SRS in H2,” Appl. Phys. B 30, 131 (1983).
[CrossRef]

Schmidt, W.

V. Wilke and W. Schmidt, “Tunable UV-radiation by stimulated Raman scattering in hydrogen,” Appl. Phys. 16, 151 (1978).
[CrossRef]

Schomburg, H.

H. Schomburg, H. F. Dobele, and B. Ruckle, “Generation of tunable narrow-bandwidth VUV radiation by anti-Stokes SRS in H2,” Appl. Phys. B 30, 131 (1983).
[CrossRef]

Steba, A. M.

N. E. Kornienko, A. M. Steba, and V. L. Strizhevskii, “Theory of generation and amplification of Stokes and anti-Stokes waves in gaseous media,” Sov. J. Quantum Electron. 12, 1475 (1982).
[CrossRef]

Stoicheff, B. P.

R. Chiao and B. P. Stoicheff, “Angular dependence of master-stimulated Raman radiation in calcite,” Phys. Rev. Lett. 12, 290 (1964).
[CrossRef]

Strauss, M.

M. Strauss, J. Oreg, and A. Bar-Shalom, “Buildup of transverse spatial correlations in stimulated Raman scattering,” Phys. Rev. A 38, 4712 (1988).
[CrossRef] [PubMed]

Strizhevskii, V. L.

N. E. Kornienko, A. M. Steba, and V. L. Strizhevskii, “Theory of generation and amplification of Stokes and anti-Stokes waves in gaseous media,” Sov. J. Quantum Electron. 12, 1475 (1982).
[CrossRef]

Sushchinskii, M. M.

A. N. Arbatskaya and M. M. Sushchinskii, “Investigation of four-photon processes in stimulated Raman scattering (SRS),” Sov. Phys. JETP 39, 981 (1974).

Suzuki, M.

Takahashi, A.

A. Takahashi, M. Maeda, K. Muraoka, and M. Akazaki, “Picosecond VUV anti-Stokes Raman laser pumped by a KrF laser,” Jpn. J. Appl. Phys. 28, L252 (1989).
[CrossRef]

A. Takahashi, O. Matsumoto, M. Maeda, and Y. Miyazoe, “Tunable VUV generation by anti-Stokes stimulated Raman conversion of XeCl laser radiation,” Jpn. J. Appl. Phys. 26, L954 (1987).
[CrossRef]

Tashiro, H.

Venkin, G. V.

G. V. Venkin, G. M. Mikheev, and O. A. Novodvorskii, “Angular distribution of anti-Stokes stimulated Raman scattering components from ground and excited vibrational levels of the hydrogen molecule,” Sov. J. Quantum Electron. 15, 1472 (1985).
[CrossRef]

Wada, S.

Wallmeier, H.

H. Wallmeier and H. Zacharias, “Continuously tunable VUV radiation (129–210 nm) by anti-Stokes Raman scattering in cooled H2,” Appl. Phys. B 45, 263 (1988).
[CrossRef]

Warner, C.

Wilke, V.

V. Wilke and W. Schmidt, “Tunable UV-radiation by stimulated Raman scattering in hydrogen,” Appl. Phys. 16, 151 (1978).
[CrossRef]

Woerdman, J. P.

W. A. Hamel and J. P. Woerdman, “Nonorthogonality of the longitudinal eigenmodes of a laser,” Phys. Rev. A 40, 2785 (1989).
[CrossRef] [PubMed]

Yajima, T.

N. Morita, L. H. Lin, and T. Yajima, “Generation of picosecond UV pulses by stimulated anti-Stokes Raman scattering,” Appl. Phys. B 31, 63 (1983).
[CrossRef]

Zacharias, H.

H. Wallmeier and H. Zacharias, “Continuously tunable VUV radiation (129–210 nm) by anti-Stokes Raman scattering in cooled H2,” Appl. Phys. B 45, 263 (1988).
[CrossRef]

Appl. Opt.

Appl. Phys.

V. Wilke and W. Schmidt, “Tunable UV-radiation by stimulated Raman scattering in hydrogen,” Appl. Phys. 16, 151 (1978).
[CrossRef]

Appl. Phys. B

H. Schomburg, H. F. Dobele, and B. Ruckle, “Generation of tunable narrow-bandwidth VUV radiation by anti-Stokes SRS in H2,” Appl. Phys. B 30, 131 (1983).
[CrossRef]

N. Morita, L. H. Lin, and T. Yajima, “Generation of picosecond UV pulses by stimulated anti-Stokes Raman scattering,” Appl. Phys. B 31, 63 (1983).
[CrossRef]

H. F. Dobele, M. Horl, and M. Rowekamp, “Tuning ranges of KrF and ArF excimer laser amplifiers and of associated vacuum ultraviolet anti-Stokes Raman lines,” Appl. Phys. B 42, 67 (1987).
[CrossRef]

H. Wallmeier and H. Zacharias, “Continuously tunable VUV radiation (129–210 nm) by anti-Stokes Raman scattering in cooled H2,” Appl. Phys. B 45, 263 (1988).
[CrossRef]

Appl. Phys. Lett.

H. F. Dobele, M. Horl, and M. Rowekamp, “Two-photon excitation of molecular hydrogen and stimulated emission in the vacuum ultraviolet,” Appl. Phys. Lett. 49, 925 (1986).
[CrossRef]

IEEE J. Quantum Electron.

V. S. D. Gathen, T. Bornemann, V. Kornas, and H. F. Dobele, “VUV generation by high-order CARS,” IEEE J. Quantum Electron. 26, 739 (1990).
[CrossRef]

P. Alsing, P. R. Peterson, D. A. Cardimona, and A. Gavrielides, “Power-dependent dispersion in far-off-resonant Raman scattering,” IEEE J. Quantum Electron. QE-23, 557 (1987).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

A. Takahashi, M. Maeda, K. Muraoka, and M. Akazaki, “Picosecond VUV anti-Stokes Raman laser pumped by a KrF laser,” Jpn. J. Appl. Phys. 28, L252 (1989).
[CrossRef]

A. Takahashi, O. Matsumoto, M. Maeda, and Y. Miyazoe, “Tunable VUV generation by anti-Stokes stimulated Raman conversion of XeCl laser radiation,” Jpn. J. Appl. Phys. 26, L954 (1987).
[CrossRef]

Opt. Commun.

S. Wada, A. Kasai, and H. Tashiro, “Temporal evolution and beam breakup of the Stokes and anti-Stokes waves in stimulated Raman scattering,” Opt. Commun. 88, 146 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. Strauss, J. Oreg, and A. Bar-Shalom, “Buildup of transverse spatial correlations in stimulated Raman scattering,” Phys. Rev. A 38, 4712 (1988).
[CrossRef] [PubMed]

W. A. Hamel and J. P. Woerdman, “Nonorthogonality of the longitudinal eigenmodes of a laser,” Phys. Rev. A 40, 2785 (1989).
[CrossRef] [PubMed]

A. P. Hickman, J. A. Paisner, and W. K. Bischel, “Theory of multiwave propagation and frequency conversion in a Raman medium,” Phys. Rev. A 33, 1788 (1986).
[CrossRef] [PubMed]

J. T. Lin, “Theory of transient stimulated Raman scattering and four-wave-mixing processes in multiple-pump systems: a Hamiltonian approach,” Phys. Rev. A 33, 3210 (1986).
[CrossRef] [PubMed]

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516 (1988).
[CrossRef] [PubMed]

B. Ritchie, “Theory of transient stimulated Raman scattering in H2,” Phys. Rev. A 35, 5108 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett.

R. Chiao and B. P. Stoicheff, “Angular dependence of master-stimulated Raman radiation in calcite,” Phys. Rev. Lett. 12, 290 (1964).
[CrossRef]

D. Eimerl, R. S. Hargrove, and J. A. Paisner, “Efficient frequency conversion by stimulated Raman scattering,” Phys. Rev. Lett. 46, 651 (1981).
[CrossRef]

Sov. J. Quantum Electron.

N. E. Kornienko, A. M. Steba, and V. L. Strizhevskii, “Theory of generation and amplification of Stokes and anti-Stokes waves in gaseous media,” Sov. J. Quantum Electron. 12, 1475 (1982).
[CrossRef]

G. V. Venkin, G. M. Mikheev, and O. A. Novodvorskii, “Angular distribution of anti-Stokes stimulated Raman scattering components from ground and excited vibrational levels of the hydrogen molecule,” Sov. J. Quantum Electron. 15, 1472 (1985).
[CrossRef]

Sov. Phys. JETP

A. N. Arbatskaya and M. M. Sushchinskii, “Investigation of four-photon processes in stimulated Raman scattering (SRS),” Sov. Phys. JETP 39, 981 (1974).

Other

A. S. Davydov, Quantum Mechanics (Pergamon, New York, 1965), Sect. 81.

L. F. Shampine and A. C. Hindmarsh, Scientific Subroutine Library II Manual, 99SP-0050–5 (Fujitsu Ltd., Tokyo, 1980).

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Figures (7)

Fig. 1
Fig. 1

Growth curves of the S1 and the AS waves are shown as a function of the phase mismatch Δk. The horizontal axes are the propagation lengths, and the vertical axes are output power in arbitrary units. The S1 and the AS waves are considered in the calculations. (a) Δk=0.5 cm-1, (b) Δk=3 cm-1, and (c) Δk=10 cm-1. The solid curves are the depleted pump (P) wave, the dashed curves are the S1 wave, and the dotted curves are the AS wave.

Fig. 2
Fig. 2

Radial intensity distributions of the individual waves at the cell exit in Fig. 1. (a) Δk=0.5 cm-1, (b) Δk=3 cm-1, and (c) Δk=10 cm-1. The solid, dashed, and dotted curves correspond to the P, S1, and AS waves, respectively.

Fig. 3
Fig. 3

Growth curves of the individual waves in multiwave mixing. The S2 wave is also considered in the calculation. The solid, dashed, dotted-dashed, and dotted curves correspond to the P, S1, S2, and AS waves, respectively.

Fig. 4
Fig. 4

Temporal intensity changes of the individual waves at the cell exit in Fig. 3. The horizontal axis is the time scale 2 (ns/division), and the vertical axis is intensity in arbitrary units. The thick-solid, thin-solid, dashed, dotted-dashed, and dotted curves correspond to the initial P, depleted P, S1, S2, and AS waves, respectively.

Fig. 5
Fig. 5

Spatial and temporal intensity distributions of the individual waves in Fig. 3. The radial distance, time, and output intensity are shown on the x, y, and z axes, respectively. The z axes in the individual waves are not to the same scale.

Fig. 6
Fig. 6

Comparison between the temporal intensity changes of the simulations and the experimental results27 in the individual waves. The vertical intensity axes in the individual waves are not to the same scale.

Fig. 7
Fig. 7

Comparison between the temporal and the spatial intensity distributions of the simulations and the experimental results27 in the individual waves. The vertical intensity axes in the individual waves are not to the same scale. The radial distance, time, and output intensity are shown on the x, y, and z axes, respectively.

Equations (26)

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E(r, z, t)=jαAαj(z, t)Uαj[r, z, wj(z)]×exp[i(ωjt+n(ωj)kjz)]=jEj(r, z, t)exp[i(ωjt+n(ωj)kjz)],
A(z, t)αjz=mβγδωjgm,j+1A(z, t)βj+1×-tA(z, t)γ*mA(z, t)δm-1×exp(-t-tT2)dt×exp(iΔm,j+1z)Cα,β,γ,δjmQα,β,γ,δj,m-mβγδωjgm,jA(z, t)βj-1×-tA(z, t)γm-1A(z, t)δm×exp(-t-tT2)dt×exp(-iΔm,jz)Cα,β,γ,δj-1,mQβ,α,δ,γj-1,m,
Cα,β,γ,δj,m=(ωjωj+1ωmωm-1)1/2πz0c(1+z2/z02)(ωj+ωm)×exp[-2i(α-β+γ-δ)tan-1(z/z0)],
Qα,β,γ,δj,m=0 exp(-x)Lαωjxωj+ωmLβωj+1xωj+ωm×Lγωmxωj+ωmLδωm-1xωj+ωmdx,
Δm,j=Δm-Δj,Δikin(ωi)-ki-1n(ωi-1),
gi,j=πNα12(ωi)α12(ωj)2cΓ,
n(ωj)-1=2πNα11(ωj),
α11(ω1)=8.84×10-25 cm3,
α11(ω0)=8.63×10-25 cm3,
α11(ω-1)=8.50×10-25 cm3,
α11(ω-2)=8.34×10-25 cm3,
α12(ω1)=1.23×10-25 cm3,
α12(ω0)=1.17×10-25 cm3,
α12(ω-1)=1.07×10-25 cm3,
α12(ω-2)=0.98×10-25 cm3.
Aα1zQαβγδ00
×exp[-2i(α+γ-2β)tan-1(z/z0)]
×exp(-iΔ0,1z).
exp-iz2αz0-(k-1n-1-k0n0)+2γz0-(k1n1-k0n0).
PDASZ=-RAS-F1-F2,
PDPZ=RAS-RS1+F2-F3,
PDS1Z=RS1-RS2+F1-F2,
PDS2Z=RS2+F2+F3.
F1(AS-P-P-S1),
F2(AS-P-S1-S2),
F3(P-S1-S1-S2).

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