Abstract

Stimulated Raman scattering is considered in the transient limit where the pulse width is small compared with T2. In the case where diffraction, level saturation, anti-Stokes and higher-order Stokes radiation, and quantum noise can all be neglected, we show that there are three distinct evolution regimes: the I regime, where the Stokes pulse is small compared with the pump pulse; the transition regime, where the Stokes and pump pulses are comparable; and the J regime, where the pump pulse is small compared with the Stokes pulse. The characteristic behavior in each of these three regimes is explored by using a combination of analytical and numerical tools.

© 1990 Optical Society of America

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  1. E. J. Woodbury and W. K. Ng, “Ruby laser operation in the near IR,” Proc. Inst. Electr. Eng. 50, 2367 (1962).
  2. R. W. Hellwarth, “Theory of stimulated Raman scattering,” Phys. Rev. 130, 1850–1852 (1963).
    [Crossref]
  3. See, e.g., A. Owyoung and P. Esherick, “Inverse Raman spectroscopy,” in Lasers and Applications, W. O. N. Guimaraes, C.-T. Lin, and A. Mooradian, eds. (Springer-Verlag, Berlin, 1981), pp. 67–76.
    [Crossref]
  4. See, e.g., J. Reintjes, R. H. Lehmberg, R. S. F. Chang, M. T. Duignan, and G. Calame, “Beam cleanup with stimulated Raman scattering in the intensity-averaging regime,” J. Opt. Soc. Am. B 31408–1427 (1986).
    [Crossref]
  5. E. E. Hagenlocker, R. W. Minck, and W. G. Rado, “Effects of phonon lifetime on stimulated optical scattering in gases,” Phys. Rev. 154, 226–233 (1967).
    [Crossref]
  6. C. S. Wang, “Theory of stimulated Raman scattering,” Phys. Rev. 182, 482–494 (1969).
    [Crossref]
  7. R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 260–72 (1970).
    [Crossref]
  8. R. L. Carman, M. E. Mack, F. Shimizu, and N. Bloembergen, “Forward picosecond Stokes-pulse generation in transient stimulated Raman scattering,” Phys. Rev. Lett. 23, 1327–1329 (1969).
    [Crossref]
  9. M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, “Transient stimulated rotational and vibrational Raman scattering in gases,” Appl. Phys. Lett. 16, 209–211 (1970).
    [Crossref]
  10. R. L. Carman and M. E. Mack, “Experimental investigation of transient stimulated Raman scattering in a linearly dispersionless medium,” Phys. Rev. A 5341–348 (1972).
    [Crossref]
  11. M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Control of transient Raman amplifiers,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 200–207 (1988).
    [Crossref]
  12. M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt.Soc. Am. B 5, 37–52 (1988).
    [Crossref]
  13. C. R. Menyuk and G. Hilfer, “Asymptotic evolution of transient pulses undergoing stimulated Raman scattering,”Opt. Lett. 14, 227–229 (1989).
    [Crossref] [PubMed]
  14. C. R. Menyuk, “Transient solitons in stimulated Raman scattering,” Phys. Rev. Lett. 62, 2937–2940 (1989).
    [Crossref] [PubMed]
  15. J. N. Elgin and T. B. O’Hare, “Saturation effects in transient stimulated Raman scattering,” J. Phys. B 12, 159–168 (1979).
    [Crossref]
  16. K. Drühl, R. G. Wenzel, and J. L. Carlsten, “Observation of solitons in stimulated Raman scattering,” Phys. Rev. Lett. 51, 1171–1174 (1983).
    [Crossref]
  17. R. G. Wenzel, J. L. Carlsten, and K. J. Drühl, “Soliton experiments in stimulated Raman scattering,” J. Stat. Phys. 39, 621–632 (1985).
    [Crossref]
  18. See, e.g., 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, 2516–2523 (1988).
    [Crossref] [PubMed]
  19. R. D. Richtmeyer and K. W. Morton, Difference Methods for Initial-Value Problems (Wiley, New York, 1967), pp. 24–25.
  20. See, e.g., W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 550–551.
  21. See, e.g., P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pp. 434–443.
  22. F. Y. F. Chu and A. C. Scott, “Inverse scattering transform for wave–wave scattering,” Phys. Rev. A 12, 2060–2064 (1975).
    [Crossref]
  23. D. J. Kaup, “Creation of a soliton out of dissipation,” Physica 19D, 125–134 (1986).
  24. J. Reintjes, G. Calame, M. D. Duncan, R. Mahon, and L. L. Tankersley, “Multiple pulse effects in transient stimulated Raman amplification,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 87–94 (1988).
    [Crossref]

1989 (2)

1988 (2)

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt.Soc. Am. B 5, 37–52 (1988).
[Crossref]

See, e.g., 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, 2516–2523 (1988).
[Crossref] [PubMed]

1986 (2)

1985 (1)

R. G. Wenzel, J. L. Carlsten, and K. J. Drühl, “Soliton experiments in stimulated Raman scattering,” J. Stat. Phys. 39, 621–632 (1985).
[Crossref]

1983 (1)

K. Drühl, R. G. Wenzel, and J. L. Carlsten, “Observation of solitons in stimulated Raman scattering,” Phys. Rev. Lett. 51, 1171–1174 (1983).
[Crossref]

1979 (1)

J. N. Elgin and T. B. O’Hare, “Saturation effects in transient stimulated Raman scattering,” J. Phys. B 12, 159–168 (1979).
[Crossref]

1975 (1)

F. Y. F. Chu and A. C. Scott, “Inverse scattering transform for wave–wave scattering,” Phys. Rev. A 12, 2060–2064 (1975).
[Crossref]

1972 (1)

R. L. Carman and M. E. Mack, “Experimental investigation of transient stimulated Raman scattering in a linearly dispersionless medium,” Phys. Rev. A 5341–348 (1972).
[Crossref]

1970 (2)

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, “Transient stimulated rotational and vibrational Raman scattering in gases,” Appl. Phys. Lett. 16, 209–211 (1970).
[Crossref]

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 260–72 (1970).
[Crossref]

1969 (2)

R. L. Carman, M. E. Mack, F. Shimizu, and N. Bloembergen, “Forward picosecond Stokes-pulse generation in transient stimulated Raman scattering,” Phys. Rev. Lett. 23, 1327–1329 (1969).
[Crossref]

C. S. Wang, “Theory of stimulated Raman scattering,” Phys. Rev. 182, 482–494 (1969).
[Crossref]

1967 (1)

E. E. Hagenlocker, R. W. Minck, and W. G. Rado, “Effects of phonon lifetime on stimulated optical scattering in gases,” Phys. Rev. 154, 226–233 (1967).
[Crossref]

1963 (1)

R. W. Hellwarth, “Theory of stimulated Raman scattering,” Phys. Rev. 130, 1850–1852 (1963).
[Crossref]

1962 (1)

E. J. Woodbury and W. K. Ng, “Ruby laser operation in the near IR,” Proc. Inst. Electr. Eng. 50, 2367 (1962).

Bischel, W. K.

See, e.g., 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, 2516–2523 (1988).
[Crossref] [PubMed]

Bloembergen, N.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 260–72 (1970).
[Crossref]

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, “Transient stimulated rotational and vibrational Raman scattering in gases,” Appl. Phys. Lett. 16, 209–211 (1970).
[Crossref]

R. L. Carman, M. E. Mack, F. Shimizu, and N. Bloembergen, “Forward picosecond Stokes-pulse generation in transient stimulated Raman scattering,” Phys. Rev. Lett. 23, 1327–1329 (1969).
[Crossref]

Calame, G.

See, e.g., J. Reintjes, R. H. Lehmberg, R. S. F. Chang, M. T. Duignan, and G. Calame, “Beam cleanup with stimulated Raman scattering in the intensity-averaging regime,” J. Opt. Soc. Am. B 31408–1427 (1986).
[Crossref]

J. Reintjes, G. Calame, M. D. Duncan, R. Mahon, and L. L. Tankersley, “Multiple pulse effects in transient stimulated Raman amplification,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 87–94 (1988).
[Crossref]

Carlsten, J. L.

R. G. Wenzel, J. L. Carlsten, and K. J. Drühl, “Soliton experiments in stimulated Raman scattering,” J. Stat. Phys. 39, 621–632 (1985).
[Crossref]

K. Drühl, R. G. Wenzel, and J. L. Carlsten, “Observation of solitons in stimulated Raman scattering,” Phys. Rev. Lett. 51, 1171–1174 (1983).
[Crossref]

Carman, R. L.

R. L. Carman and M. E. Mack, “Experimental investigation of transient stimulated Raman scattering in a linearly dispersionless medium,” Phys. Rev. A 5341–348 (1972).
[Crossref]

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, “Transient stimulated rotational and vibrational Raman scattering in gases,” Appl. Phys. Lett. 16, 209–211 (1970).
[Crossref]

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 260–72 (1970).
[Crossref]

R. L. Carman, M. E. Mack, F. Shimizu, and N. Bloembergen, “Forward picosecond Stokes-pulse generation in transient stimulated Raman scattering,” Phys. Rev. Lett. 23, 1327–1329 (1969).
[Crossref]

Chang, R. S. F.

Chu, F. Y. F.

F. Y. F. Chu and A. C. Scott, “Inverse scattering transform for wave–wave scattering,” Phys. Rev. A 12, 2060–2064 (1975).
[Crossref]

Drühl, K.

K. Drühl, R. G. Wenzel, and J. L. Carlsten, “Observation of solitons in stimulated Raman scattering,” Phys. Rev. Lett. 51, 1171–1174 (1983).
[Crossref]

Drühl, K. J.

R. G. Wenzel, J. L. Carlsten, and K. J. Drühl, “Soliton experiments in stimulated Raman scattering,” J. Stat. Phys. 39, 621–632 (1985).
[Crossref]

Duignan, M. T.

Duncan, M. D.

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt.Soc. Am. B 5, 37–52 (1988).
[Crossref]

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Control of transient Raman amplifiers,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 200–207 (1988).
[Crossref]

J. Reintjes, G. Calame, M. D. Duncan, R. Mahon, and L. L. Tankersley, “Multiple pulse effects in transient stimulated Raman amplification,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 87–94 (1988).
[Crossref]

Elgin, J. N.

J. N. Elgin and T. B. O’Hare, “Saturation effects in transient stimulated Raman scattering,” J. Phys. B 12, 159–168 (1979).
[Crossref]

Esherick, P.

See, e.g., A. Owyoung and P. Esherick, “Inverse Raman spectroscopy,” in Lasers and Applications, W. O. N. Guimaraes, C.-T. Lin, and A. Mooradian, eds. (Springer-Verlag, Berlin, 1981), pp. 67–76.
[Crossref]

Feshbach, H.

See, e.g., P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pp. 434–443.

Flannery, B. P.

See, e.g., W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 550–551.

Hagenlocker, E. E.

E. E. Hagenlocker, R. W. Minck, and W. G. Rado, “Effects of phonon lifetime on stimulated optical scattering in gases,” Phys. Rev. 154, 226–233 (1967).
[Crossref]

Hellwarth, R. W.

R. W. Hellwarth, “Theory of stimulated Raman scattering,” Phys. Rev. 130, 1850–1852 (1963).
[Crossref]

Hickman, A. P.

See, e.g., 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, 2516–2523 (1988).
[Crossref] [PubMed]

Hilfer, G.

Kaup, D. J.

D. J. Kaup, “Creation of a soliton out of dissipation,” Physica 19D, 125–134 (1986).

Lehmberg, R. H.

Mack, M. E.

R. L. Carman and M. E. Mack, “Experimental investigation of transient stimulated Raman scattering in a linearly dispersionless medium,” Phys. Rev. A 5341–348 (1972).
[Crossref]

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, “Transient stimulated rotational and vibrational Raman scattering in gases,” Appl. Phys. Lett. 16, 209–211 (1970).
[Crossref]

R. L. Carman, M. E. Mack, F. Shimizu, and N. Bloembergen, “Forward picosecond Stokes-pulse generation in transient stimulated Raman scattering,” Phys. Rev. Lett. 23, 1327–1329 (1969).
[Crossref]

Mahon, R.

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt.Soc. Am. B 5, 37–52 (1988).
[Crossref]

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Control of transient Raman amplifiers,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 200–207 (1988).
[Crossref]

J. Reintjes, G. Calame, M. D. Duncan, R. Mahon, and L. L. Tankersley, “Multiple pulse effects in transient stimulated Raman amplification,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 87–94 (1988).
[Crossref]

Menyuk, C. R.

Minck, R. W.

E. E. Hagenlocker, R. W. Minck, and W. G. Rado, “Effects of phonon lifetime on stimulated optical scattering in gases,” Phys. Rev. 154, 226–233 (1967).
[Crossref]

Morse, P. M.

See, e.g., P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pp. 434–443.

Morton, K. W.

R. D. Richtmeyer and K. W. Morton, Difference Methods for Initial-Value Problems (Wiley, New York, 1967), pp. 24–25.

Ng, W. K.

E. J. Woodbury and W. K. Ng, “Ruby laser operation in the near IR,” Proc. Inst. Electr. Eng. 50, 2367 (1962).

O’Hare, T. B.

J. N. Elgin and T. B. O’Hare, “Saturation effects in transient stimulated Raman scattering,” J. Phys. B 12, 159–168 (1979).
[Crossref]

Owyoung, A.

See, e.g., A. Owyoung and P. Esherick, “Inverse Raman spectroscopy,” in Lasers and Applications, W. O. N. Guimaraes, C.-T. Lin, and A. Mooradian, eds. (Springer-Verlag, Berlin, 1981), pp. 67–76.
[Crossref]

Press, W. H.

See, e.g., W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 550–551.

Rado, W. G.

E. E. Hagenlocker, R. W. Minck, and W. G. Rado, “Effects of phonon lifetime on stimulated optical scattering in gases,” Phys. Rev. 154, 226–233 (1967).
[Crossref]

Reintjes, J.

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt.Soc. Am. B 5, 37–52 (1988).
[Crossref]

See, e.g., J. Reintjes, R. H. Lehmberg, R. S. F. Chang, M. T. Duignan, and G. Calame, “Beam cleanup with stimulated Raman scattering in the intensity-averaging regime,” J. Opt. Soc. Am. B 31408–1427 (1986).
[Crossref]

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, “Transient stimulated rotational and vibrational Raman scattering in gases,” Appl. Phys. Lett. 16, 209–211 (1970).
[Crossref]

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Control of transient Raman amplifiers,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 200–207 (1988).
[Crossref]

J. Reintjes, G. Calame, M. D. Duncan, R. Mahon, and L. L. Tankersley, “Multiple pulse effects in transient stimulated Raman amplification,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 87–94 (1988).
[Crossref]

Richtmeyer, R. D.

R. D. Richtmeyer and K. W. Morton, Difference Methods for Initial-Value Problems (Wiley, New York, 1967), pp. 24–25.

Scott, A. C.

F. Y. F. Chu and A. C. Scott, “Inverse scattering transform for wave–wave scattering,” Phys. Rev. A 12, 2060–2064 (1975).
[Crossref]

Shimizu, F.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 260–72 (1970).
[Crossref]

R. L. Carman, M. E. Mack, F. Shimizu, and N. Bloembergen, “Forward picosecond Stokes-pulse generation in transient stimulated Raman scattering,” Phys. Rev. Lett. 23, 1327–1329 (1969).
[Crossref]

Tankersley, L. L.

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt.Soc. Am. B 5, 37–52 (1988).
[Crossref]

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Control of transient Raman amplifiers,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 200–207 (1988).
[Crossref]

J. Reintjes, G. Calame, M. D. Duncan, R. Mahon, and L. L. Tankersley, “Multiple pulse effects in transient stimulated Raman amplification,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 87–94 (1988).
[Crossref]

Teukolsky, S. A.

See, e.g., W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 550–551.

Vetterling, W. T.

See, e.g., W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 550–551.

Wang, C. S.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 260–72 (1970).
[Crossref]

C. S. Wang, “Theory of stimulated Raman scattering,” Phys. Rev. 182, 482–494 (1969).
[Crossref]

Wenzel, R. G.

R. G. Wenzel, J. L. Carlsten, and K. J. Drühl, “Soliton experiments in stimulated Raman scattering,” J. Stat. Phys. 39, 621–632 (1985).
[Crossref]

K. Drühl, R. G. Wenzel, and J. L. Carlsten, “Observation of solitons in stimulated Raman scattering,” Phys. Rev. Lett. 51, 1171–1174 (1983).
[Crossref]

Woodbury, E. J.

E. J. Woodbury and W. K. Ng, “Ruby laser operation in the near IR,” Proc. Inst. Electr. Eng. 50, 2367 (1962).

Appl. Phys. Lett. (1)

M. E. Mack, R. L. Carman, J. Reintjes, and N. Bloembergen, “Transient stimulated rotational and vibrational Raman scattering in gases,” Appl. Phys. Lett. 16, 209–211 (1970).
[Crossref]

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

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

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt.Soc. Am. B 5, 37–52 (1988).
[Crossref]

J. Phys. B (1)

J. N. Elgin and T. B. O’Hare, “Saturation effects in transient stimulated Raman scattering,” J. Phys. B 12, 159–168 (1979).
[Crossref]

J. Stat. Phys. (1)

R. G. Wenzel, J. L. Carlsten, and K. J. Drühl, “Soliton experiments in stimulated Raman scattering,” J. Stat. Phys. 39, 621–632 (1985).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (3)

E. E. Hagenlocker, R. W. Minck, and W. G. Rado, “Effects of phonon lifetime on stimulated optical scattering in gases,” Phys. Rev. 154, 226–233 (1967).
[Crossref]

C. S. Wang, “Theory of stimulated Raman scattering,” Phys. Rev. 182, 482–494 (1969).
[Crossref]

R. W. Hellwarth, “Theory of stimulated Raman scattering,” Phys. Rev. 130, 1850–1852 (1963).
[Crossref]

Phys. Rev. A (4)

R. L. Carman and M. E. Mack, “Experimental investigation of transient stimulated Raman scattering in a linearly dispersionless medium,” Phys. Rev. A 5341–348 (1972).
[Crossref]

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 260–72 (1970).
[Crossref]

See, e.g., 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, 2516–2523 (1988).
[Crossref] [PubMed]

F. Y. F. Chu and A. C. Scott, “Inverse scattering transform for wave–wave scattering,” Phys. Rev. A 12, 2060–2064 (1975).
[Crossref]

Phys. Rev. Lett. (3)

C. R. Menyuk, “Transient solitons in stimulated Raman scattering,” Phys. Rev. Lett. 62, 2937–2940 (1989).
[Crossref] [PubMed]

K. Drühl, R. G. Wenzel, and J. L. Carlsten, “Observation of solitons in stimulated Raman scattering,” Phys. Rev. Lett. 51, 1171–1174 (1983).
[Crossref]

R. L. Carman, M. E. Mack, F. Shimizu, and N. Bloembergen, “Forward picosecond Stokes-pulse generation in transient stimulated Raman scattering,” Phys. Rev. Lett. 23, 1327–1329 (1969).
[Crossref]

Physica (1)

D. J. Kaup, “Creation of a soliton out of dissipation,” Physica 19D, 125–134 (1986).

Proc. Inst. Electr. Eng. (1)

E. J. Woodbury and W. K. Ng, “Ruby laser operation in the near IR,” Proc. Inst. Electr. Eng. 50, 2367 (1962).

Other (6)

J. Reintjes, G. Calame, M. D. Duncan, R. Mahon, and L. L. Tankersley, “Multiple pulse effects in transient stimulated Raman amplification,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 87–94 (1988).
[Crossref]

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Control of transient Raman amplifiers,” in Nonlinear Optical Beam Manipulation, Beam Combining, and Atmospheric Manipulation, R. A. Fisher, ed., Proc. Soc. Photo-Opt. Instrum. Eng.874, 200–207 (1988).
[Crossref]

See, e.g., A. Owyoung and P. Esherick, “Inverse Raman spectroscopy,” in Lasers and Applications, W. O. N. Guimaraes, C.-T. Lin, and A. Mooradian, eds. (Springer-Verlag, Berlin, 1981), pp. 67–76.
[Crossref]

R. D. Richtmeyer and K. W. Morton, Difference Methods for Initial-Value Problems (Wiley, New York, 1967), pp. 24–25.

See, e.g., W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 550–551.

See, e.g., P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pp. 434–443.

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Figures (17)

Fig. 1
Fig. 1

Schematic illustration of the three regimes of evolution. The sum of photon numbers in both waves is conserved. In the I regime the Stokes pulse grows exponentially while the pump pulse remains essentially constant. In the transition regime, the Stokes and pump pulses have comparable amplitudes. Finally, in the J regime the pump pulse undergoes a weak algebraic decay while the Stokes pulse grows correspondingly.

Fig. 2
Fig. 2

Normalized integrand μ of Eq. (11b) versus t′ and s when AL ∝ sech2αst. The maximum intensity is 0.1 GW/cm2. The FWHM is 40 psec.

Fig. 3
Fig. 3

Normalized integrand μ of Eq. (11b) versus t′ and s when AL ∝ exp(−αg|t|4). The maximum intensity is 0.1 GW/cm2. The FWHM is 44.3 psec.

Fig. 4
Fig. 4

The maximum of the integrand of Eq. (11b), t0, is shown as a function of s for three different offsets: (a).−20 psec, (b) 0 psec, (c) 20 psec. Other parameters are the same as in Fig. 2. The exact result is shown as a solid curve and the analytic approximation from Eq. (18) is shown as a dashed curve. The logarithmic variation is evident.

Fig. 5
Fig. 5

A comparison between the exact and approximate analytic results for the full time variation is shown. Parameters are the same as in Fig. 2. The two results agree to within a factor of 2.

Fig. 6
Fig. 6

Linear Stokes gain versus offset (in picoseconds) shown for (a) a symmetric pump pulse and a Stokes pulse of 40 psec FWHM and (b) a symmetric pump pulse of 40 psec FWHM and an asymmetric Stokes pulse, which rises more rapidly than the pump pulse but conforms to it thereafter. The Stokes profile in (b) mimics the profile in the NRL experiments. The maximum pump intensity is 4 GW/cm2, and the propagation distance is 100 cm.

Fig. 7
Fig. 7

Linear Stokes gain versus offset (in picoseconds) shown for three different pulse shapes: (a) sech2αst, (b) exp(−αg|t|4), and (c) square. Parameters are the same as in Fig. 6. The maximum pump intensity is 4 GW/cm2.

Fig. 8
Fig. 8

Phase difference ϕLϕS shown versus time (in picoseconds) for three different Stokes offsets: (a) −20 psec, (b) 0 psec, and (c) 20 psec. In all cases ASAL ∝ sech2αst. The FWHM is 40 psec, the maximum pump intensity is 1 GW/cm2, and the propagation distance is 100 cm. The maximum chirp is π. Phase locking is evident in all cases.

Fig. 9
Fig. 9

Phase difference ϕLϕS shown versus time (in picoseconds) for three different pump chirp amplitudes: (a) π, (b) 2π, and (c) 5π. The Stokes phase locks to the pump phase slightly before t = 0 in all three cases.

Fig. 10
Fig. 10

Pump intensity profile versus time (in picoseconds) at (a) 0 cm, (b) 100 cm, and (c) 200 cm. An initial profile of ASAL ∝ sech2αst is used in which the maximum pump intensity is 40 GW/ cm2, the maximum Stokes intensity is 0.04 GW/cm2, and the FWHM is 40 psec.

Fig. 11
Fig. 11

Stokes intensity profile versus time. Parameters are the same as in Fig. 10.

Fig. 12
Fig. 12

Material excitation |Q|2 versus time. Parameters are the same as in Fig. 10.

Fig. 13
Fig. 13

R versus ζ for different Stokes offsets: (a) −20 psec, (b) 0 psec, and (c) 20 psec. Other parameters are the same as in Fig. 10.

Fig. 14
Fig. 14

N versus ζ plotted on a parabolic scale for different Stokes offsets. Parameters are the same as in Fig. 13.

Fig. 15
Fig. 15

R versus ζ for different pump and Stokes shapes: (a) ASAL ∝ sech2αst, FWHM 40 psec; (b) AsAL ∝ exp(αg|t|4), FWHM 44.3 psec; (c) a square profile, FWHM 44.0 psec. The maximum pump intensity is 40 GW/cm2, and the maximum Stokes intensity is 0.04 GW/cm2.

Fig. 16
Fig. 16

N versus ζ plotted on a parabolic scale for different pump and Stokes shapes. Parameters are the same as in Fig. 15.

Fig. 17
Fig. 17

R versus ζ for different initial chirps: (a) no chirp, (b) a maximum chirp of π on the pump, (c) a maximum chirp of 5π on the pump. Other parameters are the same as in Fig. 10.

Equations (53)

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A L z = i k L k S κ 2 Q A S ,
A S z = i κ 2 Q * A L ,
Q t + Γ Q = i κ 1 A S * A L ,
K ( t ) = | A L ( z , t ) | 2 + k L k S | A S ( z , t ) | 2 .
I regime transition regime J regime .
Q ( z , t ) = i κ 1 t A L ( z , t ) A S * ( z , t ) exp [ Γ ( t t ) ] d t .
A L ( z + Δ z 2 ) A L ( z ) = i k L k S κ 2 Q ( z ) A S ( z ) Δ z 2 ,
A S ( z + Δ z 2 ) A S ( z ) = i κ 2 Q * ( z ) A L ( z ) Δ z 2 .
A L ( z + Δ z ) A L ( z ) = i k L k S κ 2 Q ( z + Δ z 2 ) A S ( z + Δ z 2 ) Δ z ,
A S ( z + Δ z ) A S ( z ) = i κ 2 Q * ( z + Δ z 2 ) A L ( z + Δ z 2 ) Δ z ,
κ 2 = 4 π ω S 2 ( ω L ω S ) c 2 k S κ 1
g s s = 16 π κ 1 κ 2 c Γ ,
A 1 χ = X A 2 , A 2 χ = X * A 1 , X τ + γ X = A 2 * A 1 ,
K ( τ ) = | A 1 ( χ , τ ) | 2 + | A 2 ( χ , τ ) | 2
B 1 χ = X B 2 , B 2 χ = X * B 1 , X T + X = B 2 * B 1 ,
A L ( z , t ) = A L 0 ( t ) ,
A S ( z , t ) = A S 0 ( t ) + 2 κ 1 κ 2 z A L 0 ( t ) × t exp [ Γ ( t t ) ] A L 0 * ( t ) A S 0 ( t ) I 1 ( s 1 / 2 ) s 1 / 2 d t ,
Q ( z , t ) = i κ 1 t exp [ Γ ( t t ) ] A L 0 ( t ) A S 0 * ( t ) I 0 ( s 1 / 2 ) d t ,
s ( t , t ) = 4 κ 1 κ 2 z [ τ ( t ) τ ( t ) ]
τ ( t ) = t K ( t ) d t t | A L 0 ( t ) | 2 d t .
A S ( z , t ) = A S 0 I 0 ( s 1 / 2 ) ,
Q ( z , t ) = A S 0 * ( t ) A L 0 * ( t ) s 1 / 2 I 1 ( s 1 / 2 ) 2 i κ 2 z ,
s ( t ) = 4 κ 1 κ 2 τ ( t ) .
C ( t , t ) = exp [ Γ ( t t ) ] A L 0 * ( t ) A S 0 ( t ) I 1 ( s 1 / 2 ) s 1 / 2 ,
μ = C ( 0 , t ) max [ C ( 0 , t ) ] .
A L ( t ) = C L exp ( Γ ω t ) exp [ i ϕ L ( t ) ]
A S ( t ) = C S exp ( Γ ω t ) exp [ i ϕ S ( t ) ]
t 0 = 1 2 Γ ω In [ 2 ( 2 Γ ω + Γ ) τ ( t ) / C L 2 s 1 / 2 3 / 2 ] .
A S ( t ) = C S exp [ i ϕ S ( t ) ] ,
A S ( t ) = E S exp [ i ϕ S ( t ) ] sech 2 [ α s ( t t off ) ] .
t 0 = 1 2 Γ ω In [ 2 ( Γ ω + Γ ) τ ( t ) / C L 2 s 1 / 2 3 / 2 ] .
A S ( z , t ) = 2 κ 1 κ 2 z [ π Γ ω 2 ( 2 + Γ / Γ ω ) ] 1 / 2 A L 0 ( t ) A S 0 ( t 0 ) A L 0 * ( t 0 ) × exp [ Γ ( t t 0 ) ] exp ( s 1 / 2 ) ( 2 π s 3 / 2 ) 1 / 2 .
A S 0 ( t ) = E S sech 2 [ α s g ( t ) t ] ,
g ( t ) = 1 + 1.5 exp ( 5 α s t ) exp ( 5 α s t ) + exp ( 5 α s t ) ,
A L 0 ( t ) = f ( t ) exp ( i β | f ( t ) | 2 ) ,
A L = [ K ( t ) ] 1 / 2 sech [ α z κ 1 κ 2 α 0 t K ( t ) d t ] , A S = ( k S k L ) 1 / 2 [ K ( t ) ] 1 / 2 tanh [ α z κ 1 κ 2 α 0 t [ K ( t ) ] d t ] , Q = i α κ 2 ( k S k L ) 1 / 2 sech [ α z κ 1 κ 2 α 0 t [ K ( t ) ] d t ] ,
z = κ 1 κ 2 α 2 K ( t ) d t
A L = [ K ( t ) ] 1 / 2 cn [ α z κ 1 κ 2 m α 0 t K ( t ) d t ] , A S = ( k S k L ) 1 / 2 [ K ( t ) ] 1 / 2 sn [ α z κ 1 κ 2 m α 0 t K ( t ) d t ] , Q = i α κ 2 ( k S k L ) 1 / 2 dn [ α z κ 1 κ 2 m α 0 t K ( t ) d t ] ,
S z = k L k S κ 2 κ 1 | Q | 2 2 Γ k L k S κ 2 κ 1 0 t | Q | 2 d t k L k S κ 2 κ 1 | Q | 2 ,
S = t | A L | 2 d t .
z | Q | 2 d z 0
K ( t ) d t = τ ,
| d | Q | 2 d z | < κ 1 κ 2 τ 3 2
A L ( z , t ) = A L 0 ( t ) 2 κ 1 κ 2 ( z z 0 ) k L k S A S 0 ( t ) × t exp [ Γ ( t t ) ] A S 0 * ( t ) A L 0 ( t ) J 1 ( s 1 / 2 ) s 1 / 2 d t ,
A S ( z , t ) = A S 0 ( t ) ,
Q ( z , t ) = i κ 1 t exp [ Γ ( t t ) ] × A S 0 * ( t ) A L 0 ( t ) J 0 ( s 1 / 2 ) d t ,
s = 4 κ 1 κ 2 ( z z 0 ) [ τ ( t ) τ ( t ) ] .
τ ( t ) = t K ( t ) d t k L k S t | A S 0 ( t ) | 2 d t .
J n ( x ) = ( 2 π x ) 1 / 2 cos ( x 1 2 n π 1 4 π ) .
A L ( z , t ) = A L 0 ( t ) A S 0 ( t ) × t exp [ Γ ( t t ) ] A L 0 ( t ) A S 0 ( t ) d [ J 0 ( s 1 / 2 ) ] d t d t ,
I L = c 8 π | A L | 2 d t
ζ = κ 1 κ 2 z τ ,
R = [ I L ( 0 ) / I L ( ζ ) ] 2

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