Abstract

We describe a means for efficient, energy-scalable generation of first-order anti-Stokes light by four-wave mixing, using collimated pump and first-order Stokes seed beams. We performed a one-dimensional, plane-wave analysis of the process, assuming steady-state conditions and monochromatic beams. A prescription for designing the optimum anti-Stokes converter with this technique is derived from this analysis, and we show that energy conversion efficiencies from pump light to anti-Stokes light of ~30% might be possible. We also report an unoptimized, proof-of-concept experiment that produced 40 mJ of anti-Stokes-shifted light at 432 nm from 1.2 J of 527-nm pump light in a 60-cm-long hydrogen cell.

© 1991 Optical Society of America

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  1. V. Wilke and W. Schmidt, “Tunable coherent radiation source covering a spectral range from 185 to 880 nm,” Appl. Phys. 18, 177 (1979).
    [CrossRef]
  2. D. J. Brink and D. Proch, “Efficient tunable ultraviolet source based on stimulated Raman scattering of an excimer-pumped dye laser,” Opt. Lett. 7, 494 (1982).
    [CrossRef] [PubMed]
  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. Döbele, M. Röwenkamp, and B. Rückle, “Amplification of 193 nm radiation in argon fluoride and generation of tunable UV radiation by high-order anti-Stokes Raman scattering,” IEEE J. Quantum Electron. QE-20, 1284 (1984).
    [CrossRef]
  5. P. R. Peterson, D. A. Cardimona, and A. Gavrieledes, “Anti-Stokes generation in focused geometries,” J. Opt. Soc. Am. B 4, 1970 (1987).
    [CrossRef]
  6. J. J. Yeh and D. Chen, “Anti-Stokes Raman scattering in H2pumped by an alexandrite laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WM42.
  7. B. Ritchie, “Theory of transient stimulated Raman scattering in H2,” Phys. Rev. A 35, 5108 (1987).
    [CrossRef] [PubMed]
  8. 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]
  9. C. Reuser, 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]
  10. Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. A 137, 1787 (1965).
  11. J. R. Ackerhalt, “Novel analytic solutions to general four-wave-mixing problems in a Raman medium,” Phys. Rev. Lett. 46, 922 (1981).
    [CrossRef]
  12. M. D. Duncan, R. Mahon, J. Reintjes, and L. L. Tankersley, “Parametric Raman gain suppression in D2and H2,” Opt. Lett. 11, 803 (1986).
    [CrossRef] [PubMed]
  13. In our laboratory, we have achieved gIp0L= 14 in a hydrogen Raman amplifier without self-oscillation, using a 35-nsec, frequency-doubled Nd:YAG pump laser. See M. S. Mangir, J. O. White, J. J. Ottusch, H. W. Bruesselbach, and D. A. Rockwell, “Tunable high energy Raman laser source,” Final Report DAAH01-84-C-A052 (Hughes Research Laboratories, Malibu, Calif., 1988).
  14. Expanding the pump and Stokes seed beams in the plane defined by their k vectors has two benefits: (a) it facilitates better beam overlap throughout the interaction region (less beam walk-off) and (b) it reduces the diffraction divergence of each beam in the direction to which the phase-matching condition is most sensitive. To clarify the second point, we consider a diffracted component of the Stokes beam whose wave vector is ks+ Δks. The deviation angle from perfect phase matching θ for this component is a first-order function of Δk if Δks is in the plane of the interaction and is a second-order function if it is not.
  15. J. Goldhar and J. R. Murray, “Intensity averaging and four-wave mixing in Raman amplifiers,” IEEE J. Quantum Electron. QE-18, 399 (1982).
    [CrossRef]
  16. G. C. Valley, “Transfer of pump spatial variations to Stokes phase in Raman amplifiers,” IEEE J. Quantum Electron. QE-18, 1370 (1982).
    [CrossRef]
  17. R. S. F. Chang and N. Djeu, “Amplification of a diffraction-limited Stokes beam by a severely distorted pump,” Opt. Lett. 8, 139 (1983).
    [CrossRef] [PubMed]
  18. R. S. F. Chang, R. H. Lemberg, M. T. Duignan, and N. Djeu, “Raman beam cleanup of a severely aberrated pump laser,” IEEE J. Quantum Electron. QE-21, 477 (1985).
    [CrossRef]
  19. Several papers involving Raman beam cleanup and beam combining are included in the feature on stimulated Raman and Brillouin scattering for laser beam control, J. Opt. Soc. Am. B 3, 1330–1496 (1986).
  20. H2and CH4dispersion data taken from Landolt–Börnstein, Zahlenwarte und Functionen aus Physik, Chemie, Astronomie, Geophysik und Technik, Vol. II, Part 8, Optische Konstanten (Springer-Verlag, Berlin, 1962), p. 6–885.
  21. 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]
  22. M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
    [CrossRef]
  23. E. A. Morozova, “Investigation of the spectral distribution of the intensity of the components of the stimulated Raman scattering of light in condensed media,” Tr. Ordena Lenina Fiz. Inst. P. N. Lebedeva 99(1982) [Proc. P. N. Lebedev Phys. Inst. 99, 77 (1982)].
  24. D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the Stimulated-Raman-Scattering linewidth,” Phys. Rev. Lett. 61, 66 (1988).
    [CrossRef] [PubMed]
  25. V. G. Bespalov, D. I. Staselko, and E. Yu. Yutanov, “Fine structure of SRS spectra in compressed hydrogen: the first Stokes component,” Opt. Spektrosk. 62, 763 (1987) [Opt. Spectrosc. (USSR) 62,455 (1987)].
  26. J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. QE-24, 1266 (1988).
    [CrossRef]
  27. J. J. Ottusch and D. A. Rockwell, “Measurement of Raman gain coefficients of hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076 (1988).
    [CrossRef]
  28. D. C. Jones, M. S. Mangir, D. A. Rockwell, and J. O. White, “Stimulated Brillouin scattering gain variation and transient effects in a CH4: He binary gas mixture,” J. Opt. Soc. Am. B 7, 2090 (1990).
    [CrossRef]
  29. N. E. Kornienko, A. M. Steba, and V. L. Strizhevskii, “Theory of generation and amplification of Stokes and anti-Stokes waves in gaseous media,” Kvantovaya Elektron. (Moscow) 9, 2271 (1982) [Sov. J. Quantum Electron. 12, 1475 (1982)].

1990 (1)

1989 (1)

1988 (4)

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]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the Stimulated-Raman-Scattering linewidth,” Phys. Rev. Lett. 61, 66 (1988).
[CrossRef] [PubMed]

J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. QE-24, 1266 (1988).
[CrossRef]

J. J. Ottusch and D. A. Rockwell, “Measurement of Raman gain coefficients of hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076 (1988).
[CrossRef]

1987 (3)

V. G. Bespalov, D. I. Staselko, and E. Yu. Yutanov, “Fine structure of SRS spectra in compressed hydrogen: the first Stokes component,” Opt. Spektrosk. 62, 763 (1987) [Opt. Spectrosc. (USSR) 62,455 (1987)].

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

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

1986 (3)

1985 (1)

R. S. F. Chang, R. H. Lemberg, M. T. Duignan, and N. Djeu, “Raman beam cleanup of a severely aberrated pump laser,” IEEE J. Quantum Electron. QE-21, 477 (1985).
[CrossRef]

1984 (1)

H. F. Döbele, M. Röwenkamp, and B. Rückle, “Amplification of 193 nm radiation in argon fluoride and generation of tunable UV radiation by high-order anti-Stokes Raman scattering,” IEEE J. Quantum Electron. QE-20, 1284 (1984).
[CrossRef]

1983 (2)

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]

R. S. F. Chang and N. Djeu, “Amplification of a diffraction-limited Stokes beam by a severely distorted pump,” Opt. Lett. 8, 139 (1983).
[CrossRef] [PubMed]

1982 (5)

D. J. Brink and D. Proch, “Efficient tunable ultraviolet source based on stimulated Raman scattering of an excimer-pumped dye laser,” Opt. Lett. 7, 494 (1982).
[CrossRef] [PubMed]

J. Goldhar and J. R. Murray, “Intensity averaging and four-wave mixing in Raman amplifiers,” IEEE J. Quantum Electron. QE-18, 399 (1982).
[CrossRef]

G. C. Valley, “Transfer of pump spatial variations to Stokes phase in Raman amplifiers,” IEEE J. Quantum Electron. QE-18, 1370 (1982).
[CrossRef]

E. A. Morozova, “Investigation of the spectral distribution of the intensity of the components of the stimulated Raman scattering of light in condensed media,” Tr. Ordena Lenina Fiz. Inst. P. N. Lebedeva 99(1982) [Proc. P. N. Lebedev Phys. Inst. 99, 77 (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,” Kvantovaya Elektron. (Moscow) 9, 2271 (1982) [Sov. J. Quantum Electron. 12, 1475 (1982)].

1981 (2)

J. R. Ackerhalt, “Novel analytic solutions to general four-wave-mixing problems in a Raman medium,” Phys. Rev. Lett. 46, 922 (1981).
[CrossRef]

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
[CrossRef]

1979 (1)

V. Wilke and W. Schmidt, “Tunable coherent radiation source covering a spectral range from 185 to 880 nm,” Appl. Phys. 18, 177 (1979).
[CrossRef]

1965 (1)

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. A 137, 1787 (1965).

Ackerhalt, J. R.

J. R. Ackerhalt, “Novel analytic solutions to general four-wave-mixing problems in a Raman medium,” Phys. Rev. Lett. 46, 922 (1981).
[CrossRef]

Bespalov, V. G.

V. G. Bespalov, D. I. Staselko, and E. Yu. Yutanov, “Fine structure of SRS spectra in compressed hydrogen: the first Stokes component,” Opt. Spektrosk. 62, 763 (1987) [Opt. Spectrosc. (USSR) 62,455 (1987)].

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]

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]

Bloembergen, N.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. A 137, 1787 (1965).

Brink, D. J.

Bruesselbach, H. W.

In our laboratory, we have achieved gIp0L= 14 in a hydrogen Raman amplifier without self-oscillation, using a 35-nsec, frequency-doubled Nd:YAG pump laser. See M. S. Mangir, J. O. White, J. J. Ottusch, H. W. Bruesselbach, and D. A. Rockwell, “Tunable high energy Raman laser source,” Final Report DAAH01-84-C-A052 (Hughes Research Laboratories, Malibu, Calif., 1988).

Cardimona, D. A.

Carlsten, J. L.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the Stimulated-Raman-Scattering linewidth,” Phys. Rev. Lett. 61, 66 (1988).
[CrossRef] [PubMed]

Chang, R. S. F.

R. S. F. Chang, R. H. Lemberg, M. T. Duignan, and N. Djeu, “Raman beam cleanup of a severely aberrated pump laser,” IEEE J. Quantum Electron. QE-21, 477 (1985).
[CrossRef]

R. S. F. Chang and N. Djeu, “Amplification of a diffraction-limited Stokes beam by a severely distorted pump,” Opt. Lett. 8, 139 (1983).
[CrossRef] [PubMed]

Chen, D.

J. J. Yeh and D. Chen, “Anti-Stokes Raman scattering in H2pumped by an alexandrite laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WM42.

Djeu, N.

R. S. F. Chang, R. H. Lemberg, M. T. Duignan, and N. Djeu, “Raman beam cleanup of a severely aberrated pump laser,” IEEE J. Quantum Electron. QE-21, 477 (1985).
[CrossRef]

R. S. F. Chang and N. Djeu, “Amplification of a diffraction-limited Stokes beam by a severely distorted pump,” Opt. Lett. 8, 139 (1983).
[CrossRef] [PubMed]

Döbele, H. F.

H. F. Döbele, M. Röwenkamp, and B. Rückle, “Amplification of 193 nm radiation in argon fluoride and generation of tunable UV radiation by high-order anti-Stokes Raman scattering,” IEEE J. Quantum Electron. QE-20, 1284 (1984).
[CrossRef]

Duignan, M. T.

R. S. F. Chang, R. H. Lemberg, M. T. Duignan, and N. Djeu, “Raman beam cleanup of a severely aberrated pump laser,” IEEE J. Quantum Electron. QE-21, 477 (1985).
[CrossRef]

Duncan, M. D.

Dyer, M. J.

Gavrieledes, A.

Gelbwachs, J. A.

J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. QE-24, 1266 (1988).
[CrossRef]

Goldhar, J.

J. Goldhar and J. R. Murray, “Intensity averaging and four-wave mixing in Raman amplifiers,” IEEE J. Quantum Electron. QE-18, 399 (1982).
[CrossRef]

Hickman, A. P.

C. Reuser, 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]

Jones, D. C.

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,” Kvantovaya Elektron. (Moscow) 9, 2271 (1982) [Sov. J. Quantum Electron. 12, 1475 (1982)].

Landolt–Börnstein,

H2and CH4dispersion data taken from Landolt–Börnstein, Zahlenwarte und Functionen aus Physik, Chemie, Astronomie, Geophysik und Technik, Vol. II, Part 8, Optische Konstanten (Springer-Verlag, Berlin, 1962), p. 6–885.

Lemberg, R. H.

R. S. F. Chang, R. H. Lemberg, M. T. Duignan, and N. Djeu, “Raman beam cleanup of a severely aberrated pump laser,” IEEE J. Quantum Electron. QE-21, 477 (1985).
[CrossRef]

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.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the Stimulated-Raman-Scattering linewidth,” Phys. Rev. Lett. 61, 66 (1988).
[CrossRef] [PubMed]

Mahon, R.

Mangir, M. S.

D. C. Jones, M. S. Mangir, D. A. Rockwell, and J. O. White, “Stimulated Brillouin scattering gain variation and transient effects in a CH4: He binary gas mixture,” J. Opt. Soc. Am. B 7, 2090 (1990).
[CrossRef]

In our laboratory, we have achieved gIp0L= 14 in a hydrogen Raman amplifier without self-oscillation, using a 35-nsec, frequency-doubled Nd:YAG pump laser. See M. S. Mangir, J. O. White, J. J. Ottusch, H. W. Bruesselbach, and D. A. Rockwell, “Tunable high energy Raman laser source,” Final Report DAAH01-84-C-A052 (Hughes Research Laboratories, Malibu, Calif., 1988).

Michie, R. B.

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]

Morozova, E. A.

E. A. Morozova, “Investigation of the spectral distribution of the intensity of the components of the stimulated Raman scattering of light in condensed media,” Tr. Ordena Lenina Fiz. Inst. P. N. Lebedeva 99(1982) [Proc. P. N. Lebedev Phys. Inst. 99, 77 (1982)].

Mostowski, J.

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
[CrossRef]

Murray, J. R.

J. Goldhar and J. R. Murray, “Intensity averaging and four-wave mixing in Raman amplifiers,” IEEE J. Quantum Electron. QE-18, 399 (1982).
[CrossRef]

Ottusch, J. J.

J. J. Ottusch and D. A. Rockwell, “Measurement of Raman gain coefficients of hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076 (1988).
[CrossRef]

In our laboratory, we have achieved gIp0L= 14 in a hydrogen Raman amplifier without self-oscillation, using a 35-nsec, frequency-doubled Nd:YAG pump laser. See M. S. Mangir, J. O. White, J. J. Ottusch, H. W. Bruesselbach, and D. A. Rockwell, “Tunable high energy Raman laser source,” Final Report DAAH01-84-C-A052 (Hughes Research Laboratories, Malibu, Calif., 1988).

Peterson, P. R.

Proch, D.

Raymer, M. G.

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
[CrossRef]

Raymond, T. D.

Reintjes, J.

Reuser, C.

Ritchie, B.

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

Rockwell, D. A.

D. C. Jones, M. S. Mangir, D. A. Rockwell, and J. O. White, “Stimulated Brillouin scattering gain variation and transient effects in a CH4: He binary gas mixture,” J. Opt. Soc. Am. B 7, 2090 (1990).
[CrossRef]

J. J. Ottusch and D. A. Rockwell, “Measurement of Raman gain coefficients of hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076 (1988).
[CrossRef]

In our laboratory, we have achieved gIp0L= 14 in a hydrogen Raman amplifier without self-oscillation, using a 35-nsec, frequency-doubled Nd:YAG pump laser. See M. S. Mangir, J. O. White, J. J. Ottusch, H. W. Bruesselbach, and D. A. Rockwell, “Tunable high energy Raman laser source,” Final Report DAAH01-84-C-A052 (Hughes Research Laboratories, Malibu, Calif., 1988).

Röwenkamp, M.

H. F. Döbele, M. Röwenkamp, and B. Rückle, “Amplification of 193 nm radiation in argon fluoride and generation of tunable UV radiation by high-order anti-Stokes Raman scattering,” IEEE J. Quantum Electron. QE-20, 1284 (1984).
[CrossRef]

Rückle, B.

H. F. Döbele, M. Röwenkamp, and B. Rückle, “Amplification of 193 nm radiation in argon fluoride and generation of tunable UV radiation by high-order anti-Stokes Raman scattering,” IEEE J. Quantum Electron. QE-20, 1284 (1984).
[CrossRef]

Schmidt, W.

V. Wilke and W. Schmidt, “Tunable coherent radiation source covering a spectral range from 185 to 880 nm,” Appl. Phys. 18, 177 (1979).
[CrossRef]

Shen, Y. R.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. A 137, 1787 (1965).

Staselko, D. I.

V. G. Bespalov, D. I. Staselko, and E. Yu. Yutanov, “Fine structure of SRS spectra in compressed hydrogen: the first Stokes component,” Opt. Spektrosk. 62, 763 (1987) [Opt. Spectrosc. (USSR) 62,455 (1987)].

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,” Kvantovaya Elektron. (Moscow) 9, 2271 (1982) [Sov. J. Quantum Electron. 12, 1475 (1982)].

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,” Kvantovaya Elektron. (Moscow) 9, 2271 (1982) [Sov. J. Quantum Electron. 12, 1475 (1982)].

Swanson, R. C.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the Stimulated-Raman-Scattering linewidth,” Phys. Rev. Lett. 61, 66 (1988).
[CrossRef] [PubMed]

Tankersley, L. L.

Valley, G. C.

G. C. Valley, “Transfer of pump spatial variations to Stokes phase in Raman amplifiers,” IEEE J. Quantum Electron. QE-18, 1370 (1982).
[CrossRef]

White, J. O.

D. C. Jones, M. S. Mangir, D. A. Rockwell, and J. O. White, “Stimulated Brillouin scattering gain variation and transient effects in a CH4: He binary gas mixture,” J. Opt. Soc. Am. B 7, 2090 (1990).
[CrossRef]

In our laboratory, we have achieved gIp0L= 14 in a hydrogen Raman amplifier without self-oscillation, using a 35-nsec, frequency-doubled Nd:YAG pump laser. See M. S. Mangir, J. O. White, J. J. Ottusch, H. W. Bruesselbach, and D. A. Rockwell, “Tunable high energy Raman laser source,” Final Report DAAH01-84-C-A052 (Hughes Research Laboratories, Malibu, Calif., 1988).

Wilke, V.

V. Wilke and W. Schmidt, “Tunable coherent radiation source covering a spectral range from 185 to 880 nm,” Appl. Phys. 18, 177 (1979).
[CrossRef]

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]

Yeh, J. J.

J. J. Yeh and D. Chen, “Anti-Stokes Raman scattering in H2pumped by an alexandrite laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WM42.

Yutanov, E. Yu.

V. G. Bespalov, D. I. Staselko, and E. Yu. Yutanov, “Fine structure of SRS spectra in compressed hydrogen: the first Stokes component,” Opt. Spektrosk. 62, 763 (1987) [Opt. Spectrosc. (USSR) 62,455 (1987)].

Appl. Phys. (1)

V. Wilke and W. Schmidt, “Tunable coherent radiation source covering a spectral range from 185 to 880 nm,” Appl. Phys. 18, 177 (1979).
[CrossRef]

Appl. Phys. B (1)

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]

IEEE J. Quantum Electron. (6)

H. F. Döbele, M. Röwenkamp, and B. Rückle, “Amplification of 193 nm radiation in argon fluoride and generation of tunable UV radiation by high-order anti-Stokes Raman scattering,” IEEE J. Quantum Electron. QE-20, 1284 (1984).
[CrossRef]

J. Goldhar and J. R. Murray, “Intensity averaging and four-wave mixing in Raman amplifiers,” IEEE J. Quantum Electron. QE-18, 399 (1982).
[CrossRef]

G. C. Valley, “Transfer of pump spatial variations to Stokes phase in Raman amplifiers,” IEEE J. Quantum Electron. QE-18, 1370 (1982).
[CrossRef]

R. S. F. Chang, R. H. Lemberg, M. T. Duignan, and N. Djeu, “Raman beam cleanup of a severely aberrated pump laser,” IEEE J. Quantum Electron. QE-21, 477 (1985).
[CrossRef]

J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. QE-24, 1266 (1988).
[CrossRef]

J. J. Ottusch and D. A. Rockwell, “Measurement of Raman gain coefficients of hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076 (1988).
[CrossRef]

J. Opt. Soc. Am. B (5)

Kvantovaya Elektron. (Moscow) (1)

N. E. Kornienko, A. M. Steba, and V. L. Strizhevskii, “Theory of generation and amplification of Stokes and anti-Stokes waves in gaseous media,” Kvantovaya Elektron. (Moscow) 9, 2271 (1982) [Sov. J. Quantum Electron. 12, 1475 (1982)].

Opt. Lett. (3)

Opt. Spektrosk. (1)

V. G. Bespalov, D. I. Staselko, and E. Yu. Yutanov, “Fine structure of SRS spectra in compressed hydrogen: the first Stokes component,” Opt. Spektrosk. 62, 763 (1987) [Opt. Spectrosc. (USSR) 62,455 (1987)].

Phys. Rev. A (4)

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
[CrossRef]

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. A 137, 1787 (1965).

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

Phys. Rev. Lett. (2)

J. R. Ackerhalt, “Novel analytic solutions to general four-wave-mixing problems in a Raman medium,” Phys. Rev. Lett. 46, 922 (1981).
[CrossRef]

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Quantum fluctuations in the Stimulated-Raman-Scattering linewidth,” Phys. Rev. Lett. 61, 66 (1988).
[CrossRef] [PubMed]

Tr. Ordena Lenina Fiz. Inst. P. N. Lebedeva (1)

E. A. Morozova, “Investigation of the spectral distribution of the intensity of the components of the stimulated Raman scattering of light in condensed media,” Tr. Ordena Lenina Fiz. Inst. P. N. Lebedeva 99(1982) [Proc. P. N. Lebedev Phys. Inst. 99, 77 (1982)].

Other (4)

In our laboratory, we have achieved gIp0L= 14 in a hydrogen Raman amplifier without self-oscillation, using a 35-nsec, frequency-doubled Nd:YAG pump laser. See M. S. Mangir, J. O. White, J. J. Ottusch, H. W. Bruesselbach, and D. A. Rockwell, “Tunable high energy Raman laser source,” Final Report DAAH01-84-C-A052 (Hughes Research Laboratories, Malibu, Calif., 1988).

Expanding the pump and Stokes seed beams in the plane defined by their k vectors has two benefits: (a) it facilitates better beam overlap throughout the interaction region (less beam walk-off) and (b) it reduces the diffraction divergence of each beam in the direction to which the phase-matching condition is most sensitive. To clarify the second point, we consider a diffracted component of the Stokes beam whose wave vector is ks+ Δks. The deviation angle from perfect phase matching θ for this component is a first-order function of Δk if Δks is in the plane of the interaction and is a second-order function if it is not.

H2and CH4dispersion data taken from Landolt–Börnstein, Zahlenwarte und Functionen aus Physik, Chemie, Astronomie, Geophysik und Technik, Vol. II, Part 8, Optische Konstanten (Springer-Verlag, Berlin, 1962), p. 6–885.

J. J. Yeh and D. Chen, “Anti-Stokes Raman scattering in H2pumped by an alexandrite laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WM42.

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Figures (13)

Fig. 1
Fig. 1

Block diagram of an anti-Stokes converter using collimated pump and first-order Stokes seed beams, slightly crossed within a Raman-active medium, to produce a collimated anti-Stokes output. In this implementation, a single laser supplies the energy to pump the Stokes seed generator as well as the anti-Stokes converter.

Fig. 2
Fig. 2

Schematic diagram defining the wave-vector mismatch Δ for the four-wave mixing process by which two pump photons are converted to Stokes and anti-Stokes photons. The dashed lines indicate the phase-matching condition (θ = 0) for which Δ = 0.

Fig. 3
Fig. 3

Pump, Stokes, and anti-Stokes intensities as a function of distance in an amplifier under phase-matched conditions (Δ = 0). The calculation assumes λp = 527 nm, Δ ν ¯ R = 4155 cm−1, g = 2.5 cm/GW, Ip0 = 200 MW/cm2, Ia0 = 0, and Is0/Ip0 = 5% (a) or 10% (b).

Fig. 4
Fig. 4

Pump, Stokes, and anti-Stokes intensity ratios in the z → ∞ limit. The peak anti-Stokes conversion of 51% occurs when the Stokes seed fraction is 6.8%. Below this value the Stokes and anti-Stokes limiting intensities are equal. Above it, they diverge and the pump is exhausted. Note that the limiting Stokes intensity includes the contribution from the input Stokes seed, so it can sometimes exceed the input pump intensity.

Fig. 5
Fig. 5

Contours of constant anti-Stokes conversion efficiency Ia/Ip0, in the phase-matched case (Δ = 0). (a) Conversion efficiency contours for anti-Stokes converter only (the pump energy used to generate the Stokes seed is not included). (b) System efficiency contours assuming a 50% conversion efficiency from pump light to Stokes light in the Stokes seed generator.

Fig. 6
Fig. 6

Pump, Stokes, and anti-Stokes intensities in a non-phase-matched situation (Δ = 120 mrad/cm). All other conditions are the same as those for Fig. 3(b). For small angles, Δ and θ are proportional. In H2 gas at 35 atm and λp = 527 nm, dΔ/dθ = 1.2 × 103 cm−1,21 so θ = 100 μrad in this case.

Fig. 7
Fig. 7

Anti-Stokes conversion efficiency as a function of phase mismatch for gIp0L = 15 and two values of f = Is0/Ip0. The units on the θ axis are appropriate for a 30-cm-long cell. The conversion efficiency hump in the f = 5% curve becomes more pronounced at lower input Stokes seed fractions and shifts to higher values of Δ. For input Stokes seed fractions higher than 10%, the peak of the efficiency curve decreases, but it also becomes increasingly insensitive to Δ, i.e., flatter. For reference, the diffraction divergence of a 1-cm-wide diffraction-limited beam at λ = 527: nm is ~50 μrad.

Fig. 8
Fig. 8

Contours of constant anti-Stokes conversion efficiency as a function of input Stokes seed fraction and phase mismatch for gIp0L = 5 (a) and 15 (b). The units on the Δ/gIp0 axis are appropriate for H2 gas at 35 atm and λp = 527 nm. The units on the θ axis are appropriate for cell lengths of 10 cm (a) and 30 cm (b). For other cell lengths the units on the θ axis must be rescaled in proportion to L−1.

Fig. 9
Fig. 9

Contours of (total heating rate)/(input pump intensity) as a function of input Stokes seed fraction and phase mismatch angle in the limit as gIp0L → ∞. For comparison, the total heat generated in a saturated Raman amplifier is (Δω/ωp)Ip0 = 0.22Ip0 (assuming that the Raman medium is H2 gas and λp = 527 nm).

Fig. 10
Fig. 10

Schematic diagram of the anti-Stokes generation optical setup.

Fig. 11
Fig. 11

Typical temporal pulse shapes of (a) the input pump, (b) the input Stokes seed, and (c) the output anti-Stokes beams monitored by a fast (τ ~ 0.2 nsec) photodiode and digitizing oscilloscope. Each pulse was recorded on a different laser shot. There was little pulse-to-pulse change in the transform-limited pump pulses, but some small temporal fluctuations in the Stokes seed pulse generated in the backward-Raman oscillator are evident. The anti-Stokes pulse showed greater pulse-to-pulse variability, but the 10–20% deep, ~200-MHz ripples were evident on all the pulses. The value of Is0/Ip0 (≃10%) was quite steady throughout the pulse. The dashed curve in (c) is the anti-Stokes pulse shape predicted by the plane-wave, steady-state model from the pump and Stokes intensities given in (a) and (b).

Fig. 12
Fig. 12

Anti-Stokes conversion efficiency as a function of phase mismatch for conditions appropriate to our experiment: f = 10%, gIp0L = 3.6 (solid curve) and 1.8 (dashed curve). The units on the θ axis are appropriate for our 60-cm-long converter cell. For comparison, the half-height diffraction divergences of the pump and Stokes seed beams are both ~100 μrad.

Fig. 13
Fig. 13

Variation of the measured anti-Stokes energy with angle between the pump and Stokes seed beams. The calculated phase-matching angle is 7.9 ± 0.4 mrad. The angular separation between the pump and Stokes seed beams at the peak of the anti-Stokes conversion efficiency curve was measured with an accuracy no better than ±0.5 mrad; deviations from this angle were measured with ±0.025-mrad accuracy. The stated uncertainty in the calculated phase-matching angle stems from a 10% uncertainty in the conversion cell pressure. The curve is a visual guide.

Tables (1)

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Table 1 Comparison of Raman Amplifier and Anti-Stokes Converter Characteristics

Equations (15)

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d A p d z = g 2 ω s ω p ( A a 2 - A s 2 ) A p , d A s d z = g 2 ω s ω s [ - A a * A p exp ( i Δ z ) + A p * A s ] A p , d A a d z = g 2 ω s ω a [ - A a A p * + A p A s * exp ( i Δ z ) ] A p .
ϕ [ 2 k a ( k a + k s - 2 k p ) k s ( k a + k s ) ] 1 / 2
d Δ d θ = k s ϕ ( 1 + k s k a ) .
d H d z = Δ ω d d z ( N s - N a ) = Δ ω d d z ( A s 2 ω s - A a 2 ω a ) = g Δ ω ω s { A p 2 ( A s 2 + A a 2 ) - 2 Re [ A s * A a * A p 2 exp ( i Δ z ) ] } .
d H d z = g Δ ω ω s A p 2 ( A s - A a ) 2 .
d Θ d z = g 2 ω p ω s ( - A a A p + A p A s ) .
d A p d Θ = - 1 2 ( A s + A a ) , d A s d Θ = 1 2 ω s ω p A p , d A a d Θ = 1 2 ω a ω p A p .
A p = r cos Θ - s sin Θ , A s = 1 2 ω s ω p ( r sin Θ + s cos Θ ) + t , A a = 1 2 ω a ω p ( r sin Θ + s cos Θ ) - t .
A p ( Θ ) = I p 0 cos ( χ + Θ ) cos χ , A s ( Θ ) = I p 0 2 [ ω s sin ( χ + Θ ) + ω a sin χ ω p cos χ ] , A a ( Θ ) = I p 0 2 ω a ω p [ sin ( χ + Θ ) - sin χ cos χ ] .
d Θ d z = g I p 0 cos 2 χ [ ω a ω s sin χ - Δ ω ω s sin ( χ + Θ ) ] cos ( χ + Θ ) ,
g I p 0 z = ( ω s / ω a ) cos 2 χ ( Δ ω / ω a ) 2 - sin 2 χ × ( Δ ω ω a ln [ ( ω p / ω a ) tan χ cos ( χ + Θ ) sin χ - ( Δ ω / ω a ) sin ( χ + Θ ) ] - sin χ ln { tan [ π / 4 + ( χ + Θ ) / 2 ] tan ( π / 4 + χ / 2 ) } ) .
I p = I p 0 - 0.5 [ ( ω a / Δ ω ) 2 - 1 ] I s 0 , I a = I s = 0.25 ( ω a / Δ ω ) 2 I s 0 ,
I p = 0 , I s = 0.5 [ ( ω s / ω p ) tan ( π / 4 - χ / 2 ) + 2 tan χ ] 2 I p 0 , I a = 0.5 ( ω a / ω p ) 2 tan 2 ( π / 4 - χ / 2 ) I p 0 ,
I a = 0.5 I p 0 / [ 1 - ( Δ ω / ω a ) 2 ] ,
N a / N p 0 = 0.5 / ( 1 + Δ ω / ω a ) ,

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