Abstract

Using 2.4-nsec pulses at 350 nm, we have observed transverse stimulated Brillouin scattering (SBS) in fused-silica optical components. Transverse SBS sets in when the product of laser fluence and growth time for the scattered optical wave exceeds ∼2.3 J nsec/cm2. An increase in laser bandwidth to 8.3 GHz suppresses SBS losses up to approximately twice the SBS threshold. We review the theory of transverse, broadband SBS and its scaling with experimental parameters.

© 1989 Optical Society of America

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  1. J. L. Emmett, A. L. Schawlow, “Transverse stimulated emission in liquids,” Phys. Rev. 170, 358–362 (1968).
    [CrossRef]
  2. D. Heiman, D. S. Hamilton, R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
    [CrossRef]
  3. N. S. Kurnit, J. R. Ackerhalt, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (personal communications).
  4. J. M. Eggleston, M. J. Kushner, “Stimulated Brillouin scattering parasitics in large optical windows,” Opt. Lett. 12, 410–412 (1987).
    [CrossRef] [PubMed]
  5. In solids there are also some weaker shear-wave Brillouin components, which we shall ignore. See the discussion in Ref. 2.
  6. W. Kaiser, M. Maier, “Stimulated Rayleigh, Brillouin, and Raman spectroscopy,” in Laser Handbook, F. T. Arrechi, E. O. Schulz-Dubois, eds. (North Holland, Amsterdam, 1972), Vol. 2, Chap. E2;A. Penzkofer, L. Laubereau, W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 56–140 (1979).
    [CrossRef]
  7. W. Rother, “Theorie der Lichtverstarkung in absorbierenden Medien,” Z. Naturforsch. 25a, 1120–1135 (1970).
  8. B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985).
    [CrossRef]
  9. J. Schroeder, L. G. Hwa, G. Kendall, C. S. Dumais, M. C. Shyong, D. A. Thompson, “Inelastic light scattering in halide and oxide glasses: intrinsic Brillouin linewidth and stimulated Brillouin gain,” J. Non Cryst. Solids 102, 240–249 (1988).
    [CrossRef]
  10. M. G. Raymer, J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).Note that our τ is l/2Γ in this paper.
    [CrossRef]
  11. N. N. Zhukov, O. P. Zaskal’ko, V. V. Kuz’min, “Self-induced distributed feedback under stimulated Brillouin scattering conditions,” Sov. J. Quantum Electron. 17, 483–486 (1987).
    [CrossRef]
  12. S. A. Akhmanov, Yu. E. D’yakov, L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249–256 (1974).
  13. R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
    [CrossRef]
  14. See, for example, W. R. Trutna, Y. K. Park, R. L. Byer, “The dependence of Raman gain on pump laser bandwidth,” IEEE J. Quantum Electron. QE-15, 648–655 (1979), Eqs. (41) ff;J. M. Eggleston, R. L. Byer, “Steady-state stimulated Raman scattering with a multimode laser,” IEEE J. Quantum Electron. QE-16, 850–853 (1980).
    [CrossRef]
  15. G. C. Valley, “A review of stimulated Brillouin scattering excited with a broad-band pump laser,” IEEE J. Quantum Electron. QE-22, 704–712 (1986).
    [CrossRef]
  16. P. Narum, M. D. Skeldon, R. W. Boyd, “Effect of laser mode structure on stimulated Brillouin scattering,” IEEE J. Quantum Electron. QE-22, 2161–2167 (1986).
    [CrossRef]
  17. R. A. Mullen, R. C. Lind, G. C. Valley, “Observation of stimulated Brillouin scattering with a dual spectral line pump,” Opt. Commun. 63, 123–128 (1987).
    [CrossRef]
  18. M. L. Dlabal, J. Reintjes, R. H. Lehmberg, “Optical phase conjugation of a broad-band laser beam with stimulated Brillouin scattering,” Proc. Soc. Photo-Opt. Instrum. Eng. 739, 22–50 (1987).
  19. E. Lichtman, A. A. Friesem, “Stimulated Brillouin scattering excited by a multimode laser in single-mode optical fibers,” Opt. Commun. 64, 544–548 (1987);E. Lichtman, A. A. Friesem, R. G. Waarts, H. H. Yaffe, “Stimulated Brillouin scattering excited by two pump waves in single-mode fibers,” J. Opt. Soc. Am. B 4, 1397–1403 (1987);J. Opt. Soc. Am. B 5, 259 (1988).Note that our variable P is equivalent to two times these authors’ normalized length parameter Lch/Lcoh.
    [CrossRef]
  20. Y. Aoki, K. Tajima, “Stimulated Brillouin scattering in a long, single-mode fiber excited with a multimode pump laser,” J. Opt. Soc. Am. B 5, 358–363 (1988).
    [CrossRef]
  21. See Eq. (26) of Ref. 12. Note that our variable P is (Scr/S) in that reference.
  22. M. E. Lines, “A possible non-halide route to ultralow loss glasses,” J. Noncryst. Solids 103, 279–288 (1988).
    [CrossRef]
  23. W. W. Simmons, R. O. Godwin, “Nova laser fusion facility—design, engineering, and assembly overview,” Nucl. Technol/Fusion 4, 8–24 (1983).
  24. P. J. Wegner, M. A. Henesian, F. T. Marchi, D. R. Speck, “Demonstration of efficient full-aperture type I/type II third harmonic conversion on Nova,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper MF3.
  25. F. Zernicke, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).
  26. M. A. Henesian, C. D. Swift, J. R. Murray, “Stimulated rotational Raman scattering in nitrogen in long air paths,” Opt. Lett. 10, 565–567 (1985).
    [CrossRef] [PubMed]
  27. M. A. Duguay, J. W. Hansen, “Optical frequency shifting of a mode-locked laser beam,” IEEE J. Quantum Electron. QE-4, 477–481 (1968).
    [CrossRef]
  28. Calculations by D. Eimerl, M. A. Henesian, Lawrence Liver-more National Laboratory, Livermore, California 94550 (personal communication, 1988).
  29. R. C. Eckardt, J. Reintjes, “Phase matching limitations of high efficiency second harmonic generation,” IEEE J. Quantum Electron. QE-20, 1178–1187 (1984).
    [CrossRef]
  30. M. D. Skeldon, T. Kessler, R. S. Craxton, S. Skupsky, W. Seka, J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper WD4.
  31. W. H. Lowdwermilk, “Nd:glass laser technology for ICF research,” Fusion Technol. 15, 339–349 (1989).
  32. J. Nees, S. Williamson, G. Mourou, “100 GHz traveling-wave electro-optic phase modulator,” Appl. Phys. Lett. 54, 1962–1964 (1989).
    [CrossRef]

1989 (2)

W. H. Lowdwermilk, “Nd:glass laser technology for ICF research,” Fusion Technol. 15, 339–349 (1989).

J. Nees, S. Williamson, G. Mourou, “100 GHz traveling-wave electro-optic phase modulator,” Appl. Phys. Lett. 54, 1962–1964 (1989).
[CrossRef]

1988 (3)

J. Schroeder, L. G. Hwa, G. Kendall, C. S. Dumais, M. C. Shyong, D. A. Thompson, “Inelastic light scattering in halide and oxide glasses: intrinsic Brillouin linewidth and stimulated Brillouin gain,” J. Non Cryst. Solids 102, 240–249 (1988).
[CrossRef]

Y. Aoki, K. Tajima, “Stimulated Brillouin scattering in a long, single-mode fiber excited with a multimode pump laser,” J. Opt. Soc. Am. B 5, 358–363 (1988).
[CrossRef]

M. E. Lines, “A possible non-halide route to ultralow loss glasses,” J. Noncryst. Solids 103, 279–288 (1988).
[CrossRef]

1987 (5)

R. A. Mullen, R. C. Lind, G. C. Valley, “Observation of stimulated Brillouin scattering with a dual spectral line pump,” Opt. Commun. 63, 123–128 (1987).
[CrossRef]

M. L. Dlabal, J. Reintjes, R. H. Lehmberg, “Optical phase conjugation of a broad-band laser beam with stimulated Brillouin scattering,” Proc. Soc. Photo-Opt. Instrum. Eng. 739, 22–50 (1987).

E. Lichtman, A. A. Friesem, “Stimulated Brillouin scattering excited by a multimode laser in single-mode optical fibers,” Opt. Commun. 64, 544–548 (1987);E. Lichtman, A. A. Friesem, R. G. Waarts, H. H. Yaffe, “Stimulated Brillouin scattering excited by two pump waves in single-mode fibers,” J. Opt. Soc. Am. B 4, 1397–1403 (1987);J. Opt. Soc. Am. B 5, 259 (1988).Note that our variable P is equivalent to two times these authors’ normalized length parameter Lch/Lcoh.
[CrossRef]

N. N. Zhukov, O. P. Zaskal’ko, V. V. Kuz’min, “Self-induced distributed feedback under stimulated Brillouin scattering conditions,” Sov. J. Quantum Electron. 17, 483–486 (1987).
[CrossRef]

J. M. Eggleston, M. J. Kushner, “Stimulated Brillouin scattering parasitics in large optical windows,” Opt. Lett. 12, 410–412 (1987).
[CrossRef] [PubMed]

1986 (2)

G. C. Valley, “A review of stimulated Brillouin scattering excited with a broad-band pump laser,” IEEE J. Quantum Electron. QE-22, 704–712 (1986).
[CrossRef]

P. Narum, M. D. Skeldon, R. W. Boyd, “Effect of laser mode structure on stimulated Brillouin scattering,” IEEE J. Quantum Electron. QE-22, 2161–2167 (1986).
[CrossRef]

1985 (1)

1984 (1)

R. C. Eckardt, J. Reintjes, “Phase matching limitations of high efficiency second harmonic generation,” IEEE J. Quantum Electron. QE-20, 1178–1187 (1984).
[CrossRef]

1983 (1)

W. W. Simmons, R. O. Godwin, “Nova laser fusion facility—design, engineering, and assembly overview,” Nucl. Technol/Fusion 4, 8–24 (1983).

1981 (1)

M. G. Raymer, J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).Note that our τ is l/2Γ in this paper.
[CrossRef]

1979 (2)

D. Heiman, D. S. Hamilton, R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

See, for example, W. R. Trutna, Y. K. Park, R. L. Byer, “The dependence of Raman gain on pump laser bandwidth,” IEEE J. Quantum Electron. QE-15, 648–655 (1979), Eqs. (41) ff;J. M. Eggleston, R. L. Byer, “Steady-state stimulated Raman scattering with a multimode laser,” IEEE J. Quantum Electron. QE-16, 850–853 (1980).
[CrossRef]

1974 (1)

S. A. Akhmanov, Yu. E. D’yakov, L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249–256 (1974).

1970 (2)

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

W. Rother, “Theorie der Lichtverstarkung in absorbierenden Medien,” Z. Naturforsch. 25a, 1120–1135 (1970).

1968 (2)

J. L. Emmett, A. L. Schawlow, “Transverse stimulated emission in liquids,” Phys. Rev. 170, 358–362 (1968).
[CrossRef]

M. A. Duguay, J. W. Hansen, “Optical frequency shifting of a mode-locked laser beam,” IEEE J. Quantum Electron. QE-4, 477–481 (1968).
[CrossRef]

Ackerhalt, J. R.

N. S. Kurnit, J. R. Ackerhalt, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (personal communications).

Akhmanov, S. A.

S. A. Akhmanov, Yu. E. D’yakov, L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249–256 (1974).

Aoki, Y.

Bloembergen, N.

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

Boyd, R. W.

P. Narum, M. D. Skeldon, R. W. Boyd, “Effect of laser mode structure on stimulated Brillouin scattering,” IEEE J. Quantum Electron. QE-22, 2161–2167 (1986).
[CrossRef]

Byer, R. L.

See, for example, W. R. Trutna, Y. K. Park, R. L. Byer, “The dependence of Raman gain on pump laser bandwidth,” IEEE J. Quantum Electron. QE-15, 648–655 (1979), Eqs. (41) ff;J. M. Eggleston, R. L. Byer, “Steady-state stimulated Raman scattering with a multimode laser,” IEEE J. Quantum Electron. QE-16, 850–853 (1980).
[CrossRef]

Carman, R. L.

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

Craxton, R. S.

M. D. Skeldon, T. Kessler, R. S. Craxton, S. Skupsky, W. Seka, J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper WD4.

D’yakov, Yu. E.

S. A. Akhmanov, Yu. E. D’yakov, L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249–256 (1974).

Dlabal, M. L.

M. L. Dlabal, J. Reintjes, R. H. Lehmberg, “Optical phase conjugation of a broad-band laser beam with stimulated Brillouin scattering,” Proc. Soc. Photo-Opt. Instrum. Eng. 739, 22–50 (1987).

Duguay, M. A.

M. A. Duguay, J. W. Hansen, “Optical frequency shifting of a mode-locked laser beam,” IEEE J. Quantum Electron. QE-4, 477–481 (1968).
[CrossRef]

Dumais, C. S.

J. Schroeder, L. G. Hwa, G. Kendall, C. S. Dumais, M. C. Shyong, D. A. Thompson, “Inelastic light scattering in halide and oxide glasses: intrinsic Brillouin linewidth and stimulated Brillouin gain,” J. Non Cryst. Solids 102, 240–249 (1988).
[CrossRef]

Eckardt, R. C.

R. C. Eckardt, J. Reintjes, “Phase matching limitations of high efficiency second harmonic generation,” IEEE J. Quantum Electron. QE-20, 1178–1187 (1984).
[CrossRef]

Eggleston, J. M.

Eimerl, D.

Calculations by D. Eimerl, M. A. Henesian, Lawrence Liver-more National Laboratory, Livermore, California 94550 (personal communication, 1988).

Emmett, J. L.

J. L. Emmett, A. L. Schawlow, “Transverse stimulated emission in liquids,” Phys. Rev. 170, 358–362 (1968).
[CrossRef]

Friesem, A. A.

E. Lichtman, A. A. Friesem, “Stimulated Brillouin scattering excited by a multimode laser in single-mode optical fibers,” Opt. Commun. 64, 544–548 (1987);E. Lichtman, A. A. Friesem, R. G. Waarts, H. H. Yaffe, “Stimulated Brillouin scattering excited by two pump waves in single-mode fibers,” J. Opt. Soc. Am. B 4, 1397–1403 (1987);J. Opt. Soc. Am. B 5, 259 (1988).Note that our variable P is equivalent to two times these authors’ normalized length parameter Lch/Lcoh.
[CrossRef]

Godwin, R. O.

W. W. Simmons, R. O. Godwin, “Nova laser fusion facility—design, engineering, and assembly overview,” Nucl. Technol/Fusion 4, 8–24 (1983).

Hamilton, D. S.

D. Heiman, D. S. Hamilton, R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

Hansen, J. W.

M. A. Duguay, J. W. Hansen, “Optical frequency shifting of a mode-locked laser beam,” IEEE J. Quantum Electron. QE-4, 477–481 (1968).
[CrossRef]

Heiman, D.

D. Heiman, D. S. Hamilton, R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

Hellwarth, R. W.

D. Heiman, D. S. Hamilton, R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

Henesian, M. A.

M. A. Henesian, C. D. Swift, J. R. Murray, “Stimulated rotational Raman scattering in nitrogen in long air paths,” Opt. Lett. 10, 565–567 (1985).
[CrossRef] [PubMed]

P. J. Wegner, M. A. Henesian, F. T. Marchi, D. R. Speck, “Demonstration of efficient full-aperture type I/type II third harmonic conversion on Nova,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper MF3.

Calculations by D. Eimerl, M. A. Henesian, Lawrence Liver-more National Laboratory, Livermore, California 94550 (personal communication, 1988).

Hwa, L. G.

J. Schroeder, L. G. Hwa, G. Kendall, C. S. Dumais, M. C. Shyong, D. A. Thompson, “Inelastic light scattering in halide and oxide glasses: intrinsic Brillouin linewidth and stimulated Brillouin gain,” J. Non Cryst. Solids 102, 240–249 (1988).
[CrossRef]

Kaiser, W.

W. Kaiser, M. Maier, “Stimulated Rayleigh, Brillouin, and Raman spectroscopy,” in Laser Handbook, F. T. Arrechi, E. O. Schulz-Dubois, eds. (North Holland, Amsterdam, 1972), Vol. 2, Chap. E2;A. Penzkofer, L. Laubereau, W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 56–140 (1979).
[CrossRef]

Kendall, G.

J. Schroeder, L. G. Hwa, G. Kendall, C. S. Dumais, M. C. Shyong, D. A. Thompson, “Inelastic light scattering in halide and oxide glasses: intrinsic Brillouin linewidth and stimulated Brillouin gain,” J. Non Cryst. Solids 102, 240–249 (1988).
[CrossRef]

Kessler, T.

M. D. Skeldon, T. Kessler, R. S. Craxton, S. Skupsky, W. Seka, J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper WD4.

Kurnit, N. S.

N. S. Kurnit, J. R. Ackerhalt, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (personal communications).

Kushner, M. J.

Kuz’min, V. V.

N. N. Zhukov, O. P. Zaskal’ko, V. V. Kuz’min, “Self-induced distributed feedback under stimulated Brillouin scattering conditions,” Sov. J. Quantum Electron. 17, 483–486 (1987).
[CrossRef]

Lehmberg, R. H.

M. L. Dlabal, J. Reintjes, R. H. Lehmberg, “Optical phase conjugation of a broad-band laser beam with stimulated Brillouin scattering,” Proc. Soc. Photo-Opt. Instrum. Eng. 739, 22–50 (1987).

Lichtman, E.

E. Lichtman, A. A. Friesem, “Stimulated Brillouin scattering excited by a multimode laser in single-mode optical fibers,” Opt. Commun. 64, 544–548 (1987);E. Lichtman, A. A. Friesem, R. G. Waarts, H. H. Yaffe, “Stimulated Brillouin scattering excited by two pump waves in single-mode fibers,” J. Opt. Soc. Am. B 4, 1397–1403 (1987);J. Opt. Soc. Am. B 5, 259 (1988).Note that our variable P is equivalent to two times these authors’ normalized length parameter Lch/Lcoh.
[CrossRef]

Lind, R. C.

R. A. Mullen, R. C. Lind, G. C. Valley, “Observation of stimulated Brillouin scattering with a dual spectral line pump,” Opt. Commun. 63, 123–128 (1987).
[CrossRef]

Lines, M. E.

M. E. Lines, “A possible non-halide route to ultralow loss glasses,” J. Noncryst. Solids 103, 279–288 (1988).
[CrossRef]

Lowdwermilk, W. H.

W. H. Lowdwermilk, “Nd:glass laser technology for ICF research,” Fusion Technol. 15, 339–349 (1989).

Maier, M.

W. Kaiser, M. Maier, “Stimulated Rayleigh, Brillouin, and Raman spectroscopy,” in Laser Handbook, F. T. Arrechi, E. O. Schulz-Dubois, eds. (North Holland, Amsterdam, 1972), Vol. 2, Chap. E2;A. Penzkofer, L. Laubereau, W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 56–140 (1979).
[CrossRef]

Marchi, F. T.

P. J. Wegner, M. A. Henesian, F. T. Marchi, D. R. Speck, “Demonstration of efficient full-aperture type I/type II third harmonic conversion on Nova,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper MF3.

Midwinter, J. E.

F. Zernicke, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).

Mostowski, J.

M. G. Raymer, J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).Note that our τ is l/2Γ in this paper.
[CrossRef]

Mourou, G.

J. Nees, S. Williamson, G. Mourou, “100 GHz traveling-wave electro-optic phase modulator,” Appl. Phys. Lett. 54, 1962–1964 (1989).
[CrossRef]

Mullen, R. A.

R. A. Mullen, R. C. Lind, G. C. Valley, “Observation of stimulated Brillouin scattering with a dual spectral line pump,” Opt. Commun. 63, 123–128 (1987).
[CrossRef]

Murray, J. R.

Narum, P.

P. Narum, M. D. Skeldon, R. W. Boyd, “Effect of laser mode structure on stimulated Brillouin scattering,” IEEE J. Quantum Electron. QE-22, 2161–2167 (1986).
[CrossRef]

Nees, J.

J. Nees, S. Williamson, G. Mourou, “100 GHz traveling-wave electro-optic phase modulator,” Appl. Phys. Lett. 54, 1962–1964 (1989).
[CrossRef]

Park, Y. K.

See, for example, W. R. Trutna, Y. K. Park, R. L. Byer, “The dependence of Raman gain on pump laser bandwidth,” IEEE J. Quantum Electron. QE-15, 648–655 (1979), Eqs. (41) ff;J. M. Eggleston, R. L. Byer, “Steady-state stimulated Raman scattering with a multimode laser,” IEEE J. Quantum Electron. QE-16, 850–853 (1980).
[CrossRef]

Pavlov, L. I.

S. A. Akhmanov, Yu. E. D’yakov, L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249–256 (1974).

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985).
[CrossRef]

Raymer, M. G.

M. G. Raymer, J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).Note that our τ is l/2Γ in this paper.
[CrossRef]

Reintjes, J.

M. L. Dlabal, J. Reintjes, R. H. Lehmberg, “Optical phase conjugation of a broad-band laser beam with stimulated Brillouin scattering,” Proc. Soc. Photo-Opt. Instrum. Eng. 739, 22–50 (1987).

R. C. Eckardt, J. Reintjes, “Phase matching limitations of high efficiency second harmonic generation,” IEEE J. Quantum Electron. QE-20, 1178–1187 (1984).
[CrossRef]

Rother, W.

W. Rother, “Theorie der Lichtverstarkung in absorbierenden Medien,” Z. Naturforsch. 25a, 1120–1135 (1970).

Schawlow, A. L.

J. L. Emmett, A. L. Schawlow, “Transverse stimulated emission in liquids,” Phys. Rev. 170, 358–362 (1968).
[CrossRef]

Schroeder, J.

J. Schroeder, L. G. Hwa, G. Kendall, C. S. Dumais, M. C. Shyong, D. A. Thompson, “Inelastic light scattering in halide and oxide glasses: intrinsic Brillouin linewidth and stimulated Brillouin gain,” J. Non Cryst. Solids 102, 240–249 (1988).
[CrossRef]

Seka, W.

M. D. Skeldon, T. Kessler, R. S. Craxton, S. Skupsky, W. Seka, J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper WD4.

Shimizu, F.

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985).
[CrossRef]

Shyong, M. C.

J. Schroeder, L. G. Hwa, G. Kendall, C. S. Dumais, M. C. Shyong, D. A. Thompson, “Inelastic light scattering in halide and oxide glasses: intrinsic Brillouin linewidth and stimulated Brillouin gain,” J. Non Cryst. Solids 102, 240–249 (1988).
[CrossRef]

Simmons, W. W.

W. W. Simmons, R. O. Godwin, “Nova laser fusion facility—design, engineering, and assembly overview,” Nucl. Technol/Fusion 4, 8–24 (1983).

Skeldon, M. D.

P. Narum, M. D. Skeldon, R. W. Boyd, “Effect of laser mode structure on stimulated Brillouin scattering,” IEEE J. Quantum Electron. QE-22, 2161–2167 (1986).
[CrossRef]

M. D. Skeldon, T. Kessler, R. S. Craxton, S. Skupsky, W. Seka, J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper WD4.

Skupsky, S.

M. D. Skeldon, T. Kessler, R. S. Craxton, S. Skupsky, W. Seka, J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper WD4.

Soures, J. M.

M. D. Skeldon, T. Kessler, R. S. Craxton, S. Skupsky, W. Seka, J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper WD4.

Speck, D. R.

P. J. Wegner, M. A. Henesian, F. T. Marchi, D. R. Speck, “Demonstration of efficient full-aperture type I/type II third harmonic conversion on Nova,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper MF3.

Swift, C. D.

Tajima, K.

Thompson, D. A.

J. Schroeder, L. G. Hwa, G. Kendall, C. S. Dumais, M. C. Shyong, D. A. Thompson, “Inelastic light scattering in halide and oxide glasses: intrinsic Brillouin linewidth and stimulated Brillouin gain,” J. Non Cryst. Solids 102, 240–249 (1988).
[CrossRef]

Trutna, W. R.

See, for example, W. R. Trutna, Y. K. Park, R. L. Byer, “The dependence of Raman gain on pump laser bandwidth,” IEEE J. Quantum Electron. QE-15, 648–655 (1979), Eqs. (41) ff;J. M. Eggleston, R. L. Byer, “Steady-state stimulated Raman scattering with a multimode laser,” IEEE J. Quantum Electron. QE-16, 850–853 (1980).
[CrossRef]

Valley, G. C.

R. A. Mullen, R. C. Lind, G. C. Valley, “Observation of stimulated Brillouin scattering with a dual spectral line pump,” Opt. Commun. 63, 123–128 (1987).
[CrossRef]

G. C. Valley, “A review of stimulated Brillouin scattering excited with a broad-band pump laser,” IEEE J. Quantum Electron. QE-22, 704–712 (1986).
[CrossRef]

Wang, C. S.

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

Wegner, P. J.

P. J. Wegner, M. A. Henesian, F. T. Marchi, D. R. Speck, “Demonstration of efficient full-aperture type I/type II third harmonic conversion on Nova,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper MF3.

Williamson, S.

J. Nees, S. Williamson, G. Mourou, “100 GHz traveling-wave electro-optic phase modulator,” Appl. Phys. Lett. 54, 1962–1964 (1989).
[CrossRef]

Zaskal’ko, O. P.

N. N. Zhukov, O. P. Zaskal’ko, V. V. Kuz’min, “Self-induced distributed feedback under stimulated Brillouin scattering conditions,” Sov. J. Quantum Electron. 17, 483–486 (1987).
[CrossRef]

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985).
[CrossRef]

Zernicke, F.

F. Zernicke, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).

Zhukov, N. N.

N. N. Zhukov, O. P. Zaskal’ko, V. V. Kuz’min, “Self-induced distributed feedback under stimulated Brillouin scattering conditions,” Sov. J. Quantum Electron. 17, 483–486 (1987).
[CrossRef]

Appl. Phys. Lett. (1)

J. Nees, S. Williamson, G. Mourou, “100 GHz traveling-wave electro-optic phase modulator,” Appl. Phys. Lett. 54, 1962–1964 (1989).
[CrossRef]

Fusion Technol. (1)

W. H. Lowdwermilk, “Nd:glass laser technology for ICF research,” Fusion Technol. 15, 339–349 (1989).

IEEE J. Quantum Electron. (5)

R. C. Eckardt, J. Reintjes, “Phase matching limitations of high efficiency second harmonic generation,” IEEE J. Quantum Electron. QE-20, 1178–1187 (1984).
[CrossRef]

M. A. Duguay, J. W. Hansen, “Optical frequency shifting of a mode-locked laser beam,” IEEE J. Quantum Electron. QE-4, 477–481 (1968).
[CrossRef]

See, for example, W. R. Trutna, Y. K. Park, R. L. Byer, “The dependence of Raman gain on pump laser bandwidth,” IEEE J. Quantum Electron. QE-15, 648–655 (1979), Eqs. (41) ff;J. M. Eggleston, R. L. Byer, “Steady-state stimulated Raman scattering with a multimode laser,” IEEE J. Quantum Electron. QE-16, 850–853 (1980).
[CrossRef]

G. C. Valley, “A review of stimulated Brillouin scattering excited with a broad-band pump laser,” IEEE J. Quantum Electron. QE-22, 704–712 (1986).
[CrossRef]

P. Narum, M. D. Skeldon, R. W. Boyd, “Effect of laser mode structure on stimulated Brillouin scattering,” IEEE J. Quantum Electron. QE-22, 2161–2167 (1986).
[CrossRef]

J. Non Cryst. Solids (1)

J. Schroeder, L. G. Hwa, G. Kendall, C. S. Dumais, M. C. Shyong, D. A. Thompson, “Inelastic light scattering in halide and oxide glasses: intrinsic Brillouin linewidth and stimulated Brillouin gain,” J. Non Cryst. Solids 102, 240–249 (1988).
[CrossRef]

J. Noncryst. Solids (1)

M. E. Lines, “A possible non-halide route to ultralow loss glasses,” J. Noncryst. Solids 103, 279–288 (1988).
[CrossRef]

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

Nucl. Technol/Fusion (1)

W. W. Simmons, R. O. Godwin, “Nova laser fusion facility—design, engineering, and assembly overview,” Nucl. Technol/Fusion 4, 8–24 (1983).

Opt. Commun. (2)

R. A. Mullen, R. C. Lind, G. C. Valley, “Observation of stimulated Brillouin scattering with a dual spectral line pump,” Opt. Commun. 63, 123–128 (1987).
[CrossRef]

E. Lichtman, A. A. Friesem, “Stimulated Brillouin scattering excited by a multimode laser in single-mode optical fibers,” Opt. Commun. 64, 544–548 (1987);E. Lichtman, A. A. Friesem, R. G. Waarts, H. H. Yaffe, “Stimulated Brillouin scattering excited by two pump waves in single-mode fibers,” J. Opt. Soc. Am. B 4, 1397–1403 (1987);J. Opt. Soc. Am. B 5, 259 (1988).Note that our variable P is equivalent to two times these authors’ normalized length parameter Lch/Lcoh.
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

J. L. Emmett, A. L. Schawlow, “Transverse stimulated emission in liquids,” Phys. Rev. 170, 358–362 (1968).
[CrossRef]

Phys. Rev. A (2)

M. G. Raymer, J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).Note that our τ is l/2Γ in this paper.
[CrossRef]

R. L. Carman, F. Shimizu, C. S. Wang, N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

Phys. Rev. B (1)

D. Heiman, D. S. Hamilton, R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

M. L. Dlabal, J. Reintjes, R. H. Lehmberg, “Optical phase conjugation of a broad-band laser beam with stimulated Brillouin scattering,” Proc. Soc. Photo-Opt. Instrum. Eng. 739, 22–50 (1987).

Sov. J. Quantum Electron. (1)

N. N. Zhukov, O. P. Zaskal’ko, V. V. Kuz’min, “Self-induced distributed feedback under stimulated Brillouin scattering conditions,” Sov. J. Quantum Electron. 17, 483–486 (1987).
[CrossRef]

Sov. Phys. JETP (1)

S. A. Akhmanov, Yu. E. D’yakov, L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249–256 (1974).

Z. Naturforsch. (1)

W. Rother, “Theorie der Lichtverstarkung in absorbierenden Medien,” Z. Naturforsch. 25a, 1120–1135 (1970).

Other (9)

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985).
[CrossRef]

N. S. Kurnit, J. R. Ackerhalt, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (personal communications).

In solids there are also some weaker shear-wave Brillouin components, which we shall ignore. See the discussion in Ref. 2.

W. Kaiser, M. Maier, “Stimulated Rayleigh, Brillouin, and Raman spectroscopy,” in Laser Handbook, F. T. Arrechi, E. O. Schulz-Dubois, eds. (North Holland, Amsterdam, 1972), Vol. 2, Chap. E2;A. Penzkofer, L. Laubereau, W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 56–140 (1979).
[CrossRef]

M. D. Skeldon, T. Kessler, R. S. Craxton, S. Skupsky, W. Seka, J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper WD4.

P. J. Wegner, M. A. Henesian, F. T. Marchi, D. R. Speck, “Demonstration of efficient full-aperture type I/type II third harmonic conversion on Nova,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper MF3.

F. Zernicke, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).

See Eq. (26) of Ref. 12. Note that our variable P is (Scr/S) in that reference.

Calculations by D. Eimerl, M. A. Henesian, Lawrence Liver-more National Laboratory, Livermore, California 94550 (personal communication, 1988).

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Figures (8)

Fig. 1
Fig. 1

Scattering geometry for transverse SBS in an optical component. The pump and Stokes waves are polarized perpendicular to the plane of the figure.

Fig. 2
Fig. 2

Effect of pulse length on the growth of transverse SBS. The scattered light at A grows for the full pulse length t in the direction perpendicular to the pump polarization where the gain is largest. The scattered light at B can grow only for the propagation time to the edge of the aperture t′ < t. No side-scattered light can grow for a time greater than ta (assuming no reflection at the edge of the beam or component).

Fig. 3
Fig. 3

Setup for transverse SBS experiments using a test station on a beam line of the Nova fusion laser.

Fig. 4
Fig. 4

Beam profile of the Nova laser and the expected pattern of transverse SBS radiation. The test sample has a diameter of 80 cm, and the beam (shaded regions) has a diameter of 69 cm with a 6-cm-wide dark split in the center. The polarization of the 350-nm beam is perpendicular to the disk split for Type I–II frequency conversion and is tipped at an angle of 35 deg for Type II–II conversion (heavy arrows at window periphery). We expect transverse SBS radiation to grow perpendicular to the polarization. The laser pulse length is comparable with the transit time across the aperture, so only limited areas of the beam can go over SBS threshold at a fixed time into the pulse. The heavily shaded area can see radiation growing perpendicular to the pulse for the full 2.4-nsec pulse length: this will be the area that goes over threshold when the parameter H just reaches its threshold value at that time. The medium-shaded area is the additional area that goes over threshold if the time to threshold is 1.6 nsec. The obscuration in the center of the beam causes a significant reduction in these areas for Type II–II conversion.

Fig. 5
Fig. 5

Shape of the incident (reflected) and transmitted pulse within the heavily shaded region of Fig. 4A for a shot that reaches threshold at ∼1.6 nsec into the pulse (5750 J, 2.4 nsec). The transmission predicted by a simple threshold model [Eq. (5)] as a function of the threshold parameter H is shown at the top of the figure, with the experimental data below. The transmission begins to drop rapidly for H slightly greater than 2. The high-frequency noise on the top of the pulse is typical of the streak cameras used to measure these pulse shapes. The recovery of transmission at the end of the pulse is discussed in Subsection 3.C.

Fig. 6
Fig. 6

Transmitted versus incident energy for the fused-silica window and lens. The points marked with small dots are shots at 1-nsec pulse length, for which SBS is always below threshold. The scatter in these points shows the typical scatter in data taken on this test station. The other data points are coded as follows: ○, window, type I–II conversion, narrow-band; ●, window, type I–II conversion, broadband; △, window, type II–II conversion, narrow-band; ×, lens, type I–II conversion, narrow-band. The point indicated by the arrow is the point for which pulse shapes are shown in Fig. 5. Energy loss sets in more slowly than predicted by the simple model of Eq. (6) because of the finite pulse-length effects shown in Fig. 4; also, losses are less for type II–II conversion, as suggested by that figure.

Fig. 7
Fig. 7

Relative peak intensity of side-scattered light versus incident energy. The data points are coded as described in the caption to Fig. 6. Curve A shows the expected exponential growth of transverse SBS intensity from relation (4) and the gain parameters discussed in Subsection 2.E. Curve B shows a linear growth in intensity as expected for simple linear scattering. These curves and the data are normalized to a value of unity at 2 kJ. The data are consistent with a sum of contributions varying as A (with gain saturation) and B. Note that the broadband side-scattered radiation shows only linear growth.

Fig. 8
Fig. 8

Waveform of the frequency modulation that was used to study the effect of laser bandwidth on transverse SBS. The frequency deviation is a 2.2-GHz sinusoid damped with a ∼1-nsec exponential and commences ∼0.5 nsec after the beginning of the pulse. The average bandwidth over the 2.4-nsec laser pulse is either 5.5 or 2.75 GHz: the peak-to-peak deviation of the exponential envelope is approximately three times these values.

Equations (24)

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γ = k s k b γ e 2 τ 2 n 3 c υ s ρ = 4 π 2 γ e 2 τ λ p 2 n c υ s ρ sin ( θ / 2 ) .
τ = ρ η k b 2 = ρ 4 η k p 2 sin 2 ( θ / 2 ) ,
ν b = 2 υ s n λ p sin ( θ / 2 ) .
G ( t ) 2 ( γ I L t τ ) 1 / 2 .
H ( t ) = I t t g = G ( t ) 2 n τ 4 c γ .
T = ( H T φ t p ) 1 / 2 .
G ( t ) = γ I L = γ I c t a n .
H T s = φ t a = G T n c γ t p .
H T H T s = ( G T / 4 ) ( t p / τ ) .
k p k s = k b , k p k s = k b ,
L d ( k b k b ) π .
L df = c 4 Δ n Δ ν ,
L db = c 4 n Δ ν .
L dt c 2 n Δ ν .
α = γ I 2 π Δ ν n c ,
F = α α 0 = 1 π 2 P ,
F = Δ ν b Δ ν b + Δ ν p ,
F = 1 ( 1 + d ) P 2 ± { [ 1 ( 1 + d ) P 2 ] 2 + d P } 1 / 2 ,
F = d d + 1 = Δ ν b Δ ν b + Δ ν p ,
F = 1 P ,
1 d = Δ ν p Δ ν b = ( 1 F ) ( 1 F + 1 P b ) ,
F = α α 0 = γ γ 0 .
ν b θ = ν b 2 cos ( θ / 2 ) ,
γ τ n 7 λ p 2 sin ( θ / 2 ) .

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