Abstract

Theory and measurements are presented for stimulated Brillouin gain spectroscopy in anisotropic media. The coupling between arbitrary pump and Stokes waves and the corresponding acoustic wave is formulated in terms of the elastic displacement vector and the photoelastic tensor. A propagation equation that fully includes transient effects is obtained for the Stokes wave. In the limit of small-signal gains this propagation equation can be solved analytically, yielding expressions that relate experimentally accessible quantities to material properties. Absolute Brillouin steady-state gain coefficients, linewidths, and frequency shifts are thereby determined in a number of optical materials at 532 nm. The Brillouin gain coefficient for fused silica is measured by three techniques, providing the reference for absolute gain measurements. Quantitative agreement is found between theory and experiment for transient effects on stimulated Brillouin scattering.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. M. Eggleson and M. J. Kushner, “Stimulated Brillouin scattering parasitics in large optical windows,” Opt. Lett. 12, 410–412 (1987).
    [Crossref]
  2. J. R. Murray, J. R. Smith, R. B. Ehrlich, D. T. Kyrazis, C. E. Thompson, T. L. Weiland, and R. B. Wilcox, “Experimental observation and suppression of transverse stimulated Brillouin scattering in large optical components,” J. Opt. Soc. Am. B 6, 2402–2411 (1989).
    [Crossref]
  3. E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539–541 (1972).
    [Crossref]
  4. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972).
    [Crossref] [PubMed]
  5. E. J. Bachus, R. P. Braun, W. Eutin, E. Grossmann, H. Foisel, K. M. Heimes, and B. Strebel, “Coherent optical-fibre subscriber line,” Electron. Lett. 21, 1203–1205 (1985).
    [Crossref]
  6. R. G. Waarts and R. P. Braun, “Crosstalk due to stimulated Brillouin scattering in monomode fibre,” Electron. Lett. 21, 1114–1115 (1985).
    [Crossref]
  7. N. A. Olsson and J. P. van der Ziel, “Cancellation of fiber loss by semiconductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48, 1329–1330 (1986).
    [Crossref]
  8. G. W. Faris, L. E. Jusinski, M. J. Dyer, W. K. Bischel, and A. P. Hickman, “High-resolution Brillouin gain spectroscopy in fused silica,” Opt. Lett. 15, 703–705 (1990).
    [Crossref] [PubMed]
  9. G. W. Faris, M. J. Dyer, and A. P. Hickman, “Transient effects on stimulated Brillouin scattering,” Opt. Lett. 17, 1049–1051 (1992).
    [Crossref] [PubMed]
  10. D. Heiman, D. S. Hamilton, and R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
    [Crossref]
  11. J. Schroeder, R. Mohr, P. B. Macedo, and C. J. Montrose, “Rayleigh and Brillouin scattering in K2O–SiO2 glasses,” J. Am. Ceram. Soc. 56, 510–514 (1973).
    [Crossref]
  12. J. Schroeder, L. G. Hwa, M. C. Shyong, G. A. Floudas, D. A. Thompson, and M. G. Drexhage, “Brillouin scattering and phonon attenuation in halide and oxide glasses,” Mater. Sci. Forum 19/20, 653–670 (1987).
    [Crossref]
  13. J. Schroeder, L. G. Hwa, G. Kendall, C. S. Dumais, M. C. Shyong, and D. A. Thompson, “Inelastic light scattering in halide and oxide glasses: intrinsic Brillouin linewidths and stimulated Brillouin gain,” J. Non-Cryst. Solids 102, 240–249 (1988).
    [Crossref]
  14. L. G. Hwa, J. Schroeder, and X. S. Zhao, “Intrinsic Brillouin linewidths and stimulated Brillouin gain coefficients in glasses studied by inelastic light scattering,” J. Opt. Soc. Am. B 6, 833–839 (1989).
    [Crossref]
  15. V. Mazzacurati, M. Nardone, G. Ruocco, and G. Signorelli, “Brillouin scattering intensities in glasses: theory and experiment,” Philos. Mag. B 59, 3–15 (1989).
    [Crossref]
  16. M. Denariez and G. Bret, “Investigation of Rayleigh wings and Brillouin-stimulated scattering in liquids,” Phys. Rev. 171, 160–171 (1968).
    [Crossref]
  17. D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetimes,” Phys. Rev. B 1, 31–43 (1970).
    [Crossref]
  18. A. Owyoung, “Cw stimulated Raman spectroscopy,” in Chemical Applications of Nonlinear Raman Spectroscopy, A. B. Harvey, ed. (Academic, New York, 1981), pp. 281–320.
  19. P. Esherick and A. Owyoung, “High resolution stimulated Raman spectroscopy,” in Advances in Infrared and Raman Spectroscopy, R. J. H. Clark and R. E. Hester, eds. (Heyden, London, 1982), Vol. 9, pp. 130–187.
  20. C. Y. She, G. C. Herring, H. Moosmüller, and S. A. Lee, “Stimulated Rayleigh–Brillouin gain spectroscopy,” Phys. Rev. A 31, 3733–3740 (1985).
    [Crossref] [PubMed]
  21. S. Y. Tang, C. Y. She, and S. A. Lee, “Continuous-wave Rayleigh–Brillouin-gain spectroscopy in SF6,” Opt. Lett. 12, 870–872 (1987).
    [Crossref] [PubMed]
  22. G. C. Herring, M. J. Dyer, and W. K. Bischel, “Cw stimulated Rayleigh–Brillouin spectroscopy,” Bull. Am. Phys. Soc. 32, 1634 (1987).
  23. K. Ratanaphruks, W. T. Grubbs, and R. A. Macphail, “Cw stimulated Brillouin gain spectroscopy of liquids,” Chem. Phys. Lett. 182, 371–378 (1991).
    [Crossref]
  24. M. J. Dyer and W. K. Bischel, “Stimulated Brillouin spectroscopy of liquids,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 182.
  25. N. Shibata, R. G. Waarts, and R. Braun, “Brillouin-gain spectra for single-mode fibers having pure-silica GeO2-doped and P2O5-doped cores,” Opt. Lett. 12, 269–271 (1987).
    [Crossref] [PubMed]
  26. Y. Azuma, N. Shibata, T. Horiguchi, and M. Tateda, “Wavelength dependence of Brillouin-gain spectra for single-mode optical fibres,” Electron. Lett. 24, 250–252 (1988); N. Shibata, Y. Azuma, T. Horiguchi, and M. Tateda, “Identification of longitudinal acoustic modes guided in the core region of a single-mode optical fiber by Brillouin gain spectra measurements,” Opt. Lett. 13, 595–597 (1988).
    [Crossref] [PubMed]
  27. T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1, 107–108 (1989); T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects of Brillouin gain spectra in single-mode fibers,” IEEE Photon. Technol. Lett. 2, 718–720 (1990).
    [Crossref]
  28. N. Shibata, K. Okamoto, and Y. Azuma, “Longitudinal acoustic modes and Brillouin-gain spectra for GeO2-doped-core single-mode fibers,” J. Opt. Soc. Am. B 6, 1167–1174 (1989).
    [Crossref]
  29. Y. Hibina, T. Edahiro, T. Horiguchi, Y. Azuma, and N. Shibata, “Evaluation of residual stress and viscosity in SiO2-core/F-SiO2 clad single-mode optical fibers from Brillouin gain spectra,” J. Appl. Phys. 66, 4049–4052 (1989).
    [Crossref]
  30. T.-O. Tsun, A. Wada, T. Sakai, and R. Yamauchi, “Novel method using white spectral probe signals to measure Brillouin gain spectra of pure silica core fibres,” Electron. Lett. 28, 247–249 (1992).
    [Crossref]
  31. W. Kaiser and M. Maier, “Stimulated Rayleigh, Brillouin, and Raman spectroscopy,” in Laser Handbook, F. T. Arecchi and E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150.
  32. I. L. Fabelinskii, Molecular Scattering of Light (Plenum, New York, 1968), pp. 139–154.
  33. 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]
  34. W. Rother, “Theorie der Lichtverstärkung in Absorbeirenden Medien,” Z. Naturforschung,  25a, 1120–1135 (1970).
  35. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), pp. 187–201.
  36. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), pp. 490–497.
  37. N. M. Kroll, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34–43 (1965).
    [Crossref]
  38. M. J. Damzen and H. Hutchinson, “Laser pulse compression by stimulated Brillouin scattering in tapered waveguides,” IEEE J. Quantum Electron. QE-19, 7–14 (1983).
    [Crossref]
  39. C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
    [Crossref]
  40. G. B. Benedek and K. Fritsch, “Brillouin scattering in cubic crystals,” Phys. Rev. 149, 647–662 (1966).
    [Crossref]
  41. J. F. Nye, Physical Properties of Crystals (Oxford U. Press, London, 1960), pp. 131–149, 235–259.
  42. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon, London, 1959), pp. 36–41.
  43. S. Bhagavantam, Crystal Symmetry and Physical Properties (Academic, London, 1966), pp. 182–187.
  44. D. A. Pinnow, “Electrooptical materials,” in Handbook of Lasers, Robert J. Pressley, ed. (CRC, Cleveland, Ohio, 1971), pp. 478–488.
  45. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, Vol. 55 of National Bureau of Standards Applied Mathematics Series (U.S. Government Printing Office, Washington, D.C., 1972), p. 297.
  46. M. J. Dyer, W. K. Bischel, and D. G. Scerback, “High-power 80-ns transform-limited Nd:YAG laser,” in Pulsed Single-Frequency Lasers: Technology and Applications, W. K. Bischel and L. A. Rahn, eds., Proc. Soc. Photo-Opt. Instrum. Eng.912, 32–36 (1988).
    [Crossref]
  47. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 334–335.
  48. G. W. Faris and M. J. Dyer, “Injection-seeded Nd:YAG laser linewidth measurement using saturation spectroscopy in iodine,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 268.
  49. S. Gerstenkorn and P. Luc, “Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy,” Rev. Phys. Appl. 14, 791–794 (1979); Atlas du Spectre d’Absorption de la Molécule de l’Iode entre 14 800–20 000 cm−1 (Editions du CNRS, Paris, 1978).
    [Crossref]
  50. D. E. Gray, ed., American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, New York, 1972), pp. 6-16, 6-21, 6-28, 6-105, 6-109, 6-236, 2-51, 2-156, 2-164.
  51. W. G. Driscol and W. Vaughan, eds., Handbook of Optics (McGraw Hill, New York, 1978), p. 7–138.
  52. K. W. Kirby and L. G. DeShazer, “Refractive indices of 14 nonlinear crystals isomorphic to KH2PO4,” J. Opt. Soc. Am. B 4, 1072–1078 (1987).
    [Crossref]
  53. Data sheet from Cleveland Crystals, Inc., Cleveland, Ohio.
  54. D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, and G. Kennedy, “Deuterated L-argenine phosphate: a new efficient nonlinear crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
    [Crossref]
  55. Data sheet from Schott Glass Technologies, Inc., Duryea, Pa.
  56. J. Storms, Hoya Optics, Inc., Fremont, Calif. 94538 (personal communication).
  57. Data sheet from Hoya Optics, Inc., Fremont, Calif.
  58. R. C. Weast, ed., Handbook of Chemistry and Physics, 59th ed. (CRC, West Palm Beach, Fla., 1979), p. C-783.
  59. M. Debenham and G. D. Dew, “The refractive index of toluene in the visible region,” J. Phys. E 14, 544–545 (1981).
    [Crossref]
  60. D. L. Wood and K. Nassau, “Optical properties of gadolinium gallium garnet,” Appl. Opt. 29, 3704–3707, (1990).
    [Crossref] [PubMed]
  61. L. J. Graham and R. Chang, “Elastic moduli of single-crystal gadolinium gallium garnet,” J. Appl. Phys. 41, 2247–2248 (1970).
    [Crossref]
  62. P. J. Leonard, “Refractive indices, Verdet constants, and polarizabilities of the inert gases,” At. Data Nucl. Data Tables,  14, 21–37 (1974).
    [Crossref]
  63. J. M. H. L. Sengers, M. Klein, and J. S. Gallagher, “Pressure-volume-temperature relationships of gases; virial coefficients,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 4-204–4-221.
  64. K. Vedam, “The elastic and photoelastic constants of fused quartz,” Phys. Rev. 78, 472–473 (1950).
    [Crossref]
  65. W. Primack and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
    [Crossref]
  66. I. L. Fabelinskii, “Certain problems of molecular scattering of light in liquids,” Usp. Fiz. Nauk 63, 355–410 (1957).
    [Crossref]
  67. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975) p. 155.
  68. D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
    [Crossref]
  69. D. Eimerl, J. Marion, E. K. Graham, H. A. McKinstry, and S. Haussühl, “Elastic constants and thermal fracture of AgGaSe2 and d-LAP,” IEEE J. Quantum Electron. 27, 142–145 (1991).
    [Crossref]

1992 (3)

G. W. Faris, M. J. Dyer, and A. P. Hickman, “Transient effects on stimulated Brillouin scattering,” Opt. Lett. 17, 1049–1051 (1992).
[Crossref] [PubMed]

T.-O. Tsun, A. Wada, T. Sakai, and R. Yamauchi, “Novel method using white spectral probe signals to measure Brillouin gain spectra of pure silica core fibres,” Electron. Lett. 28, 247–249 (1992).
[Crossref]

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[Crossref]

1991 (2)

D. Eimerl, J. Marion, E. K. Graham, H. A. McKinstry, and S. Haussühl, “Elastic constants and thermal fracture of AgGaSe2 and d-LAP,” IEEE J. Quantum Electron. 27, 142–145 (1991).
[Crossref]

K. Ratanaphruks, W. T. Grubbs, and R. A. Macphail, “Cw stimulated Brillouin gain spectroscopy of liquids,” Chem. Phys. Lett. 182, 371–378 (1991).
[Crossref]

1990 (2)

1989 (7)

L. G. Hwa, J. Schroeder, and X. S. Zhao, “Intrinsic Brillouin linewidths and stimulated Brillouin gain coefficients in glasses studied by inelastic light scattering,” J. Opt. Soc. Am. B 6, 833–839 (1989).
[Crossref]

V. Mazzacurati, M. Nardone, G. Ruocco, and G. Signorelli, “Brillouin scattering intensities in glasses: theory and experiment,” Philos. Mag. B 59, 3–15 (1989).
[Crossref]

J. R. Murray, J. R. Smith, R. B. Ehrlich, D. T. Kyrazis, C. E. Thompson, T. L. Weiland, and R. B. Wilcox, “Experimental observation and suppression of transverse stimulated Brillouin scattering in large optical components,” J. Opt. Soc. Am. B 6, 2402–2411 (1989).
[Crossref]

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1, 107–108 (1989); T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects of Brillouin gain spectra in single-mode fibers,” IEEE Photon. Technol. Lett. 2, 718–720 (1990).
[Crossref]

N. Shibata, K. Okamoto, and Y. Azuma, “Longitudinal acoustic modes and Brillouin-gain spectra for GeO2-doped-core single-mode fibers,” J. Opt. Soc. Am. B 6, 1167–1174 (1989).
[Crossref]

Y. Hibina, T. Edahiro, T. Horiguchi, Y. Azuma, and N. Shibata, “Evaluation of residual stress and viscosity in SiO2-core/F-SiO2 clad single-mode optical fibers from Brillouin gain spectra,” J. Appl. Phys. 66, 4049–4052 (1989).
[Crossref]

D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, and G. Kennedy, “Deuterated L-argenine phosphate: a new efficient nonlinear crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
[Crossref]

1988 (2)

Y. Azuma, N. Shibata, T. Horiguchi, and M. Tateda, “Wavelength dependence of Brillouin-gain spectra for single-mode optical fibres,” Electron. Lett. 24, 250–252 (1988); N. Shibata, Y. Azuma, T. Horiguchi, and M. Tateda, “Identification of longitudinal acoustic modes guided in the core region of a single-mode optical fiber by Brillouin gain spectra measurements,” Opt. Lett. 13, 595–597 (1988).
[Crossref] [PubMed]

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

1987 (6)

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]

N. A. Olsson and J. P. van der Ziel, “Cancellation of fiber loss by semiconductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48, 1329–1330 (1986).
[Crossref]

1985 (3)

E. J. Bachus, R. P. Braun, W. Eutin, E. Grossmann, H. Foisel, K. M. Heimes, and B. Strebel, “Coherent optical-fibre subscriber line,” Electron. Lett. 21, 1203–1205 (1985).
[Crossref]

R. G. Waarts and R. P. Braun, “Crosstalk due to stimulated Brillouin scattering in monomode fibre,” Electron. Lett. 21, 1114–1115 (1985).
[Crossref]

C. Y. She, G. C. Herring, H. Moosmüller, and S. A. Lee, “Stimulated Rayleigh–Brillouin gain spectroscopy,” Phys. Rev. A 31, 3733–3740 (1985).
[Crossref] [PubMed]

1983 (1)

M. J. Damzen and H. Hutchinson, “Laser pulse compression by stimulated Brillouin scattering in tapered waveguides,” IEEE J. Quantum Electron. QE-19, 7–14 (1983).
[Crossref]

1981 (1)

M. Debenham and G. D. Dew, “The refractive index of toluene in the visible region,” J. Phys. E 14, 544–545 (1981).
[Crossref]

1979 (2)

S. Gerstenkorn and P. Luc, “Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy,” Rev. Phys. Appl. 14, 791–794 (1979); Atlas du Spectre d’Absorption de la Molécule de l’Iode entre 14 800–20 000 cm−1 (Editions du CNRS, Paris, 1978).
[Crossref]

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

1974 (1)

P. J. Leonard, “Refractive indices, Verdet constants, and polarizabilities of the inert gases,” At. Data Nucl. Data Tables,  14, 21–37 (1974).
[Crossref]

1973 (1)

J. Schroeder, R. Mohr, P. B. Macedo, and C. J. Montrose, “Rayleigh and Brillouin scattering in K2O–SiO2 glasses,” J. Am. Ceram. Soc. 56, 510–514 (1973).
[Crossref]

1972 (2)

1970 (3)

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetimes,” Phys. Rev. B 1, 31–43 (1970).
[Crossref]

W. Rother, “Theorie der Lichtverstärkung in Absorbeirenden Medien,” Z. Naturforschung,  25a, 1120–1135 (1970).

L. J. Graham and R. Chang, “Elastic moduli of single-crystal gadolinium gallium garnet,” J. Appl. Phys. 41, 2247–2248 (1970).
[Crossref]

1968 (1)

M. Denariez and G. Bret, “Investigation of Rayleigh wings and Brillouin-stimulated scattering in liquids,” Phys. Rev. 171, 160–171 (1968).
[Crossref]

1966 (2)

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
[Crossref]

G. B. Benedek and K. Fritsch, “Brillouin scattering in cubic crystals,” Phys. Rev. 149, 647–662 (1966).
[Crossref]

1965 (1)

N. M. Kroll, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34–43 (1965).
[Crossref]

1959 (1)

W. Primack and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[Crossref]

1957 (1)

I. L. Fabelinskii, “Certain problems of molecular scattering of light in liquids,” Usp. Fiz. Nauk 63, 355–410 (1957).
[Crossref]

1950 (1)

K. Vedam, “The elastic and photoelastic constants of fused quartz,” Phys. Rev. 78, 472–473 (1950).
[Crossref]

Azuma, Y.

Y. Hibina, T. Edahiro, T. Horiguchi, Y. Azuma, and N. Shibata, “Evaluation of residual stress and viscosity in SiO2-core/F-SiO2 clad single-mode optical fibers from Brillouin gain spectra,” J. Appl. Phys. 66, 4049–4052 (1989).
[Crossref]

N. Shibata, K. Okamoto, and Y. Azuma, “Longitudinal acoustic modes and Brillouin-gain spectra for GeO2-doped-core single-mode fibers,” J. Opt. Soc. Am. B 6, 1167–1174 (1989).
[Crossref]

Y. Azuma, N. Shibata, T. Horiguchi, and M. Tateda, “Wavelength dependence of Brillouin-gain spectra for single-mode optical fibres,” Electron. Lett. 24, 250–252 (1988); N. Shibata, Y. Azuma, T. Horiguchi, and M. Tateda, “Identification of longitudinal acoustic modes guided in the core region of a single-mode optical fiber by Brillouin gain spectra measurements,” Opt. Lett. 13, 595–597 (1988).
[Crossref] [PubMed]

Bachus, E. J.

E. J. Bachus, R. P. Braun, W. Eutin, E. Grossmann, H. Foisel, K. M. Heimes, and B. Strebel, “Coherent optical-fibre subscriber line,” Electron. Lett. 21, 1203–1205 (1985).
[Crossref]

Benedek, G. B.

G. B. Benedek and K. Fritsch, “Brillouin scattering in cubic crystals,” Phys. Rev. 149, 647–662 (1966).
[Crossref]

Bhagavantam, S.

S. Bhagavantam, Crystal Symmetry and Physical Properties (Academic, London, 1966), pp. 182–187.

Bischel, W. K.

G. W. Faris, L. E. Jusinski, M. J. Dyer, W. K. Bischel, and A. P. Hickman, “High-resolution Brillouin gain spectroscopy in fused silica,” Opt. Lett. 15, 703–705 (1990).
[Crossref] [PubMed]

G. C. Herring, M. J. Dyer, and W. K. Bischel, “Cw stimulated Rayleigh–Brillouin spectroscopy,” Bull. Am. Phys. Soc. 32, 1634 (1987).

M. J. Dyer and W. K. Bischel, “Stimulated Brillouin spectroscopy of liquids,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 182.

M. J. Dyer, W. K. Bischel, and D. G. Scerback, “High-power 80-ns transform-limited Nd:YAG laser,” in Pulsed Single-Frequency Lasers: Technology and Applications, W. K. Bischel and L. A. Rahn, eds., Proc. Soc. Photo-Opt. Instrum. Eng.912, 32–36 (1988).
[Crossref]

Braun, R.

Braun, R. P.

E. J. Bachus, R. P. Braun, W. Eutin, E. Grossmann, H. Foisel, K. M. Heimes, and B. Strebel, “Coherent optical-fibre subscriber line,” Electron. Lett. 21, 1203–1205 (1985).
[Crossref]

R. G. Waarts and R. P. Braun, “Crosstalk due to stimulated Brillouin scattering in monomode fibre,” Electron. Lett. 21, 1114–1115 (1985).
[Crossref]

Bret, G.

M. Denariez and G. Bret, “Investigation of Rayleigh wings and Brillouin-stimulated scattering in liquids,” Phys. Rev. 171, 160–171 (1968).
[Crossref]

Chang, R.

L. J. Graham and R. Chang, “Elastic moduli of single-crystal gadolinium gallium garnet,” J. Appl. Phys. 41, 2247–2248 (1970).
[Crossref]

Damzen, M. J.

M. J. Damzen and H. Hutchinson, “Laser pulse compression by stimulated Brillouin scattering in tapered waveguides,” IEEE J. Quantum Electron. QE-19, 7–14 (1983).
[Crossref]

Davis, L.

D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, and G. Kennedy, “Deuterated L-argenine phosphate: a new efficient nonlinear crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
[Crossref]

Debenham, M.

M. Debenham and G. D. Dew, “The refractive index of toluene in the visible region,” J. Phys. E 14, 544–545 (1981).
[Crossref]

Denariez, M.

M. Denariez and G. Bret, “Investigation of Rayleigh wings and Brillouin-stimulated scattering in liquids,” Phys. Rev. 171, 160–171 (1968).
[Crossref]

DeShazer, L. G.

Dew, G. D.

M. Debenham and G. D. Dew, “The refractive index of toluene in the visible region,” J. Phys. E 14, 544–545 (1981).
[Crossref]

Drexhage, M. G.

J. Schroeder, L. G. Hwa, M. C. Shyong, G. A. Floudas, D. A. Thompson, and M. G. Drexhage, “Brillouin scattering and phonon attenuation in halide and oxide glasses,” Mater. Sci. Forum 19/20, 653–670 (1987).
[Crossref]

Dumais, C. S.

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

Dyer, M. J.

G. W. Faris, M. J. Dyer, and A. P. Hickman, “Transient effects on stimulated Brillouin scattering,” Opt. Lett. 17, 1049–1051 (1992).
[Crossref] [PubMed]

G. W. Faris, L. E. Jusinski, M. J. Dyer, W. K. Bischel, and A. P. Hickman, “High-resolution Brillouin gain spectroscopy in fused silica,” Opt. Lett. 15, 703–705 (1990).
[Crossref] [PubMed]

G. C. Herring, M. J. Dyer, and W. K. Bischel, “Cw stimulated Rayleigh–Brillouin spectroscopy,” Bull. Am. Phys. Soc. 32, 1634 (1987).

M. J. Dyer and W. K. Bischel, “Stimulated Brillouin spectroscopy of liquids,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 182.

M. J. Dyer, W. K. Bischel, and D. G. Scerback, “High-power 80-ns transform-limited Nd:YAG laser,” in Pulsed Single-Frequency Lasers: Technology and Applications, W. K. Bischel and L. A. Rahn, eds., Proc. Soc. Photo-Opt. Instrum. Eng.912, 32–36 (1988).
[Crossref]

G. W. Faris and M. J. Dyer, “Injection-seeded Nd:YAG laser linewidth measurement using saturation spectroscopy in iodine,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 268.

Edahiro, T.

Y. Hibina, T. Edahiro, T. Horiguchi, Y. Azuma, and N. Shibata, “Evaluation of residual stress and viscosity in SiO2-core/F-SiO2 clad single-mode optical fibers from Brillouin gain spectra,” J. Appl. Phys. 66, 4049–4052 (1989).
[Crossref]

Eggleson, J. M.

Ehrlich, R. B.

Eimerl, D.

D. Eimerl, J. Marion, E. K. Graham, H. A. McKinstry, and S. Haussühl, “Elastic constants and thermal fracture of AgGaSe2 and d-LAP,” IEEE J. Quantum Electron. 27, 142–145 (1991).
[Crossref]

D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, and G. Kennedy, “Deuterated L-argenine phosphate: a new efficient nonlinear crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
[Crossref]

Esherick, P.

P. Esherick and A. Owyoung, “High resolution stimulated Raman spectroscopy,” in Advances in Infrared and Raman Spectroscopy, R. J. H. Clark and R. E. Hester, eds. (Heyden, London, 1982), Vol. 9, pp. 130–187.

Eutin, W.

E. J. Bachus, R. P. Braun, W. Eutin, E. Grossmann, H. Foisel, K. M. Heimes, and B. Strebel, “Coherent optical-fibre subscriber line,” Electron. Lett. 21, 1203–1205 (1985).
[Crossref]

Fabelinskii, I. L.

I. L. Fabelinskii, “Certain problems of molecular scattering of light in liquids,” Usp. Fiz. Nauk 63, 355–410 (1957).
[Crossref]

I. L. Fabelinskii, Molecular Scattering of Light (Plenum, New York, 1968), pp. 139–154.

Faris, G. W.

G. W. Faris, M. J. Dyer, and A. P. Hickman, “Transient effects on stimulated Brillouin scattering,” Opt. Lett. 17, 1049–1051 (1992).
[Crossref] [PubMed]

G. W. Faris, L. E. Jusinski, M. J. Dyer, W. K. Bischel, and A. P. Hickman, “High-resolution Brillouin gain spectroscopy in fused silica,” Opt. Lett. 15, 703–705 (1990).
[Crossref] [PubMed]

G. W. Faris and M. J. Dyer, “Injection-seeded Nd:YAG laser linewidth measurement using saturation spectroscopy in iodine,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 268.

Floudas, G. A.

J. Schroeder, L. G. Hwa, M. C. Shyong, G. A. Floudas, D. A. Thompson, and M. G. Drexhage, “Brillouin scattering and phonon attenuation in halide and oxide glasses,” Mater. Sci. Forum 19/20, 653–670 (1987).
[Crossref]

Foisel, H.

E. J. Bachus, R. P. Braun, W. Eutin, E. Grossmann, H. Foisel, K. M. Heimes, and B. Strebel, “Coherent optical-fibre subscriber line,” Electron. Lett. 21, 1203–1205 (1985).
[Crossref]

Fritsch, K.

G. B. Benedek and K. Fritsch, “Brillouin scattering in cubic crystals,” Phys. Rev. 149, 647–662 (1966).
[Crossref]

Gallagher, J. S.

J. M. H. L. Sengers, M. Klein, and J. S. Gallagher, “Pressure-volume-temperature relationships of gases; virial coefficients,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 4-204–4-221.

Gerstenkorn, S.

S. Gerstenkorn and P. Luc, “Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy,” Rev. Phys. Appl. 14, 791–794 (1979); Atlas du Spectre d’Absorption de la Molécule de l’Iode entre 14 800–20 000 cm−1 (Editions du CNRS, Paris, 1978).
[Crossref]

Graham, E. K.

D. Eimerl, J. Marion, E. K. Graham, H. A. McKinstry, and S. Haussühl, “Elastic constants and thermal fracture of AgGaSe2 and d-LAP,” IEEE J. Quantum Electron. 27, 142–145 (1991).
[Crossref]

Graham, L. J.

L. J. Graham and R. Chang, “Elastic moduli of single-crystal gadolinium gallium garnet,” J. Appl. Phys. 41, 2247–2248 (1970).
[Crossref]

Grossmann, E.

E. J. Bachus, R. P. Braun, W. Eutin, E. Grossmann, H. Foisel, K. M. Heimes, and B. Strebel, “Coherent optical-fibre subscriber line,” Electron. Lett. 21, 1203–1205 (1985).
[Crossref]

Grubbs, W. T.

K. Ratanaphruks, W. T. Grubbs, and R. A. Macphail, “Cw stimulated Brillouin gain spectroscopy of liquids,” Chem. Phys. Lett. 182, 371–378 (1991).
[Crossref]

Hamilton, D. S.

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

Haussühl, S.

D. Eimerl, J. Marion, E. K. Graham, H. A. McKinstry, and S. Haussühl, “Elastic constants and thermal fracture of AgGaSe2 and d-LAP,” IEEE J. Quantum Electron. 27, 142–145 (1991).
[Crossref]

Heiman, D.

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

Heimes, K. M.

E. J. Bachus, R. P. Braun, W. Eutin, E. Grossmann, H. Foisel, K. M. Heimes, and B. Strebel, “Coherent optical-fibre subscriber line,” Electron. Lett. 21, 1203–1205 (1985).
[Crossref]

Hellwarth, R. W.

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

Herring, G. C.

G. C. Herring, M. J. Dyer, and W. K. Bischel, “Cw stimulated Rayleigh–Brillouin spectroscopy,” Bull. Am. Phys. Soc. 32, 1634 (1987).

C. Y. She, G. C. Herring, H. Moosmüller, and S. A. Lee, “Stimulated Rayleigh–Brillouin gain spectroscopy,” Phys. Rev. A 31, 3733–3740 (1985).
[Crossref] [PubMed]

Hibina, Y.

Y. Hibina, T. Edahiro, T. Horiguchi, Y. Azuma, and N. Shibata, “Evaluation of residual stress and viscosity in SiO2-core/F-SiO2 clad single-mode optical fibers from Brillouin gain spectra,” J. Appl. Phys. 66, 4049–4052 (1989).
[Crossref]

Hickman, A. P.

Horiguchi, T.

Y. Hibina, T. Edahiro, T. Horiguchi, Y. Azuma, and N. Shibata, “Evaluation of residual stress and viscosity in SiO2-core/F-SiO2 clad single-mode optical fibers from Brillouin gain spectra,” J. Appl. Phys. 66, 4049–4052 (1989).
[Crossref]

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1, 107–108 (1989); T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects of Brillouin gain spectra in single-mode fibers,” IEEE Photon. Technol. Lett. 2, 718–720 (1990).
[Crossref]

Y. Azuma, N. Shibata, T. Horiguchi, and M. Tateda, “Wavelength dependence of Brillouin-gain spectra for single-mode optical fibres,” Electron. Lett. 24, 250–252 (1988); N. Shibata, Y. Azuma, T. Horiguchi, and M. Tateda, “Identification of longitudinal acoustic modes guided in the core region of a single-mode optical fiber by Brillouin gain spectra measurements,” Opt. Lett. 13, 595–597 (1988).
[Crossref] [PubMed]

Hutchinson, H.

M. J. Damzen and H. Hutchinson, “Laser pulse compression by stimulated Brillouin scattering in tapered waveguides,” IEEE J. Quantum Electron. QE-19, 7–14 (1983).
[Crossref]

Hwa, L. G.

L. G. Hwa, J. Schroeder, and X. S. Zhao, “Intrinsic Brillouin linewidths and stimulated Brillouin gain coefficients in glasses studied by inelastic light scattering,” J. Opt. Soc. Am. B 6, 833–839 (1989).
[Crossref]

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

J. Schroeder, L. G. Hwa, M. C. Shyong, G. A. Floudas, D. A. Thompson, and M. G. Drexhage, “Brillouin scattering and phonon attenuation in halide and oxide glasses,” Mater. Sci. Forum 19/20, 653–670 (1987).
[Crossref]

Ippen, E. P.

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539–541 (1972).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975) p. 155.

Jusinski, L. E.

Kaiser, W.

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetimes,” Phys. Rev. B 1, 31–43 (1970).
[Crossref]

W. Kaiser and M. Maier, “Stimulated Rayleigh, Brillouin, and Raman spectroscopy,” in Laser Handbook, F. T. Arecchi and E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150.

Kendall, G.

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

Kennedy, G.

D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, and G. Kennedy, “Deuterated L-argenine phosphate: a new efficient nonlinear crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
[Crossref]

Kirby, K. W.

Klein, M.

J. M. H. L. Sengers, M. Klein, and J. S. Gallagher, “Pressure-volume-temperature relationships of gases; virial coefficients,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 4-204–4-221.

Kroll, N. M.

N. M. Kroll, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34–43 (1965).
[Crossref]

Kurashima, T.

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1, 107–108 (1989); T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects of Brillouin gain spectra in single-mode fibers,” IEEE Photon. Technol. Lett. 2, 718–720 (1990).
[Crossref]

Kushner, M. J.

Kyrazis, D. T.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon, London, 1959), pp. 36–41.

Lee, S. A.

S. Y. Tang, C. Y. She, and S. A. Lee, “Continuous-wave Rayleigh–Brillouin-gain spectroscopy in SF6,” Opt. Lett. 12, 870–872 (1987).
[Crossref] [PubMed]

C. Y. She, G. C. Herring, H. Moosmüller, and S. A. Lee, “Stimulated Rayleigh–Brillouin gain spectroscopy,” Phys. Rev. A 31, 3733–3740 (1985).
[Crossref] [PubMed]

Leonard, P. J.

P. J. Leonard, “Refractive indices, Verdet constants, and polarizabilities of the inert gases,” At. Data Nucl. Data Tables,  14, 21–37 (1974).
[Crossref]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon, London, 1959), pp. 36–41.

Loiacono, G.

D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, and G. Kennedy, “Deuterated L-argenine phosphate: a new efficient nonlinear crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
[Crossref]

Luc, P.

S. Gerstenkorn and P. Luc, “Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy,” Rev. Phys. Appl. 14, 791–794 (1979); Atlas du Spectre d’Absorption de la Molécule de l’Iode entre 14 800–20 000 cm−1 (Editions du CNRS, Paris, 1978).
[Crossref]

Macedo, P. B.

J. Schroeder, R. Mohr, P. B. Macedo, and C. J. Montrose, “Rayleigh and Brillouin scattering in K2O–SiO2 glasses,” J. Am. Ceram. Soc. 56, 510–514 (1973).
[Crossref]

Macphail, R. A.

K. Ratanaphruks, W. T. Grubbs, and R. A. Macphail, “Cw stimulated Brillouin gain spectroscopy of liquids,” Chem. Phys. Lett. 182, 371–378 (1991).
[Crossref]

Maier, M.

W. Kaiser and M. Maier, “Stimulated Rayleigh, Brillouin, and Raman spectroscopy,” in Laser Handbook, F. T. Arecchi and E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150.

Marion, J.

D. Eimerl, J. Marion, E. K. Graham, H. A. McKinstry, and S. Haussühl, “Elastic constants and thermal fracture of AgGaSe2 and d-LAP,” IEEE J. Quantum Electron. 27, 142–145 (1991).
[Crossref]

Mazzacurati, V.

V. Mazzacurati, M. Nardone, G. Ruocco, and G. Signorelli, “Brillouin scattering intensities in glasses: theory and experiment,” Philos. Mag. B 59, 3–15 (1989).
[Crossref]

McKinstry, H. A.

D. Eimerl, J. Marion, E. K. Graham, H. A. McKinstry, and S. Haussühl, “Elastic constants and thermal fracture of AgGaSe2 and d-LAP,” IEEE J. Quantum Electron. 27, 142–145 (1991).
[Crossref]

Mohr, R.

J. Schroeder, R. Mohr, P. B. Macedo, and C. J. Montrose, “Rayleigh and Brillouin scattering in K2O–SiO2 glasses,” J. Am. Ceram. Soc. 56, 510–514 (1973).
[Crossref]

Montrose, C. J.

J. Schroeder, R. Mohr, P. B. Macedo, and C. J. Montrose, “Rayleigh and Brillouin scattering in K2O–SiO2 glasses,” J. Am. Ceram. Soc. 56, 510–514 (1973).
[Crossref]

Moosmüller, H.

C. Y. She, G. C. Herring, H. Moosmüller, and S. A. Lee, “Stimulated Rayleigh–Brillouin gain spectroscopy,” Phys. Rev. A 31, 3733–3740 (1985).
[Crossref] [PubMed]

Murray, J. R.

Nardone, M.

V. Mazzacurati, M. Nardone, G. Ruocco, and G. Signorelli, “Brillouin scattering intensities in glasses: theory and experiment,” Philos. Mag. B 59, 3–15 (1989).
[Crossref]

Nassau, K.

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford U. Press, London, 1960), pp. 131–149, 235–259.

Okamoto, K.

Olsson, N. A.

N. A. Olsson and J. P. van der Ziel, “Cancellation of fiber loss by semiconductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48, 1329–1330 (1986).
[Crossref]

Owyoung, A.

A. Owyoung, “Cw stimulated Raman spectroscopy,” in Chemical Applications of Nonlinear Raman Spectroscopy, A. B. Harvey, ed. (Academic, New York, 1981), pp. 281–320.

P. Esherick and A. Owyoung, “High resolution stimulated Raman spectroscopy,” in Advances in Infrared and Raman Spectroscopy, R. J. H. Clark and R. E. Hester, eds. (Heyden, London, 1982), Vol. 9, pp. 130–187.

Pinnow, D. A.

D. A. Pinnow, “Electrooptical materials,” in Handbook of Lasers, Robert J. Pressley, ed. (CRC, Cleveland, Ohio, 1971), pp. 478–488.

Pohl, D.

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetimes,” Phys. Rev. B 1, 31–43 (1970).
[Crossref]

Post, D.

W. Primack and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[Crossref]

Primack, W.

W. Primack and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[Crossref]

Ratanaphruks, K.

K. Ratanaphruks, W. T. Grubbs, and R. A. Macphail, “Cw stimulated Brillouin gain spectroscopy of liquids,” Chem. Phys. Lett. 182, 371–378 (1991).
[Crossref]

Roberts, D. A.

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[Crossref]

Rother, W.

W. Rother, “Theorie der Lichtverstärkung in Absorbeirenden Medien,” Z. Naturforschung,  25a, 1120–1135 (1970).

Ruocco, G.

V. Mazzacurati, M. Nardone, G. Ruocco, and G. Signorelli, “Brillouin scattering intensities in glasses: theory and experiment,” Philos. Mag. B 59, 3–15 (1989).
[Crossref]

Sakai, T.

T.-O. Tsun, A. Wada, T. Sakai, and R. Yamauchi, “Novel method using white spectral probe signals to measure Brillouin gain spectra of pure silica core fibres,” Electron. Lett. 28, 247–249 (1992).
[Crossref]

Scerback, D. G.

M. J. Dyer, W. K. Bischel, and D. G. Scerback, “High-power 80-ns transform-limited Nd:YAG laser,” in Pulsed Single-Frequency Lasers: Technology and Applications, W. K. Bischel and L. A. Rahn, eds., Proc. Soc. Photo-Opt. Instrum. Eng.912, 32–36 (1988).
[Crossref]

Schroeder, J.

L. G. Hwa, J. Schroeder, and X. S. Zhao, “Intrinsic Brillouin linewidths and stimulated Brillouin gain coefficients in glasses studied by inelastic light scattering,” J. Opt. Soc. Am. B 6, 833–839 (1989).
[Crossref]

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

J. Schroeder, L. G. Hwa, M. C. Shyong, G. A. Floudas, D. A. Thompson, and M. G. Drexhage, “Brillouin scattering and phonon attenuation in halide and oxide glasses,” Mater. Sci. Forum 19/20, 653–670 (1987).
[Crossref]

J. Schroeder, R. Mohr, P. B. Macedo, and C. J. Montrose, “Rayleigh and Brillouin scattering in K2O–SiO2 glasses,” J. Am. Ceram. Soc. 56, 510–514 (1973).
[Crossref]

Sengers, J. M. H. L.

J. M. H. L. Sengers, M. Klein, and J. S. Gallagher, “Pressure-volume-temperature relationships of gases; virial coefficients,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 4-204–4-221.

She, C. Y.

S. Y. Tang, C. Y. She, and S. A. Lee, “Continuous-wave Rayleigh–Brillouin-gain spectroscopy in SF6,” Opt. Lett. 12, 870–872 (1987).
[Crossref] [PubMed]

C. Y. She, G. C. Herring, H. Moosmüller, and S. A. Lee, “Stimulated Rayleigh–Brillouin gain spectroscopy,” Phys. Rev. A 31, 3733–3740 (1985).
[Crossref] [PubMed]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), pp. 187–201.

Shibata, N.

Y. Hibina, T. Edahiro, T. Horiguchi, Y. Azuma, and N. Shibata, “Evaluation of residual stress and viscosity in SiO2-core/F-SiO2 clad single-mode optical fibers from Brillouin gain spectra,” J. Appl. Phys. 66, 4049–4052 (1989).
[Crossref]

N. Shibata, K. Okamoto, and Y. Azuma, “Longitudinal acoustic modes and Brillouin-gain spectra for GeO2-doped-core single-mode fibers,” J. Opt. Soc. Am. B 6, 1167–1174 (1989).
[Crossref]

Y. Azuma, N. Shibata, T. Horiguchi, and M. Tateda, “Wavelength dependence of Brillouin-gain spectra for single-mode optical fibres,” Electron. Lett. 24, 250–252 (1988); N. Shibata, Y. Azuma, T. Horiguchi, and M. Tateda, “Identification of longitudinal acoustic modes guided in the core region of a single-mode optical fiber by Brillouin gain spectra measurements,” Opt. Lett. 13, 595–597 (1988).
[Crossref] [PubMed]

N. Shibata, R. G. Waarts, and R. Braun, “Brillouin-gain spectra for single-mode fibers having pure-silica GeO2-doped and P2O5-doped cores,” Opt. Lett. 12, 269–271 (1987).
[Crossref] [PubMed]

Shyong, M. C.

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

J. Schroeder, L. G. Hwa, M. C. Shyong, G. A. Floudas, D. A. Thompson, and M. G. Drexhage, “Brillouin scattering and phonon attenuation in halide and oxide glasses,” Mater. Sci. Forum 19/20, 653–670 (1987).
[Crossref]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 334–335.

Signorelli, G.

V. Mazzacurati, M. Nardone, G. Ruocco, and G. Signorelli, “Brillouin scattering intensities in glasses: theory and experiment,” Philos. Mag. B 59, 3–15 (1989).
[Crossref]

Smith, J. R.

Smith, R. G.

Stolen, R. H.

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539–541 (1972).
[Crossref]

Storms, J.

J. Storms, Hoya Optics, Inc., Fremont, Calif. 94538 (personal communication).

Strebel, B.

E. J. Bachus, R. P. Braun, W. Eutin, E. Grossmann, H. Foisel, K. M. Heimes, and B. Strebel, “Coherent optical-fibre subscriber line,” Electron. Lett. 21, 1203–1205 (1985).
[Crossref]

Tang, C. L.

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
[Crossref]

Tang, S. Y.

Tateda, M.

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1, 107–108 (1989); T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects of Brillouin gain spectra in single-mode fibers,” IEEE Photon. Technol. Lett. 2, 718–720 (1990).
[Crossref]

Y. Azuma, N. Shibata, T. Horiguchi, and M. Tateda, “Wavelength dependence of Brillouin-gain spectra for single-mode optical fibres,” Electron. Lett. 24, 250–252 (1988); N. Shibata, Y. Azuma, T. Horiguchi, and M. Tateda, “Identification of longitudinal acoustic modes guided in the core region of a single-mode optical fiber by Brillouin gain spectra measurements,” Opt. Lett. 13, 595–597 (1988).
[Crossref] [PubMed]

Thompson, C. E.

Thompson, D. A.

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

J. Schroeder, L. G. Hwa, M. C. Shyong, G. A. Floudas, D. A. Thompson, and M. G. Drexhage, “Brillouin scattering and phonon attenuation in halide and oxide glasses,” Mater. Sci. Forum 19/20, 653–670 (1987).
[Crossref]

Tsun, T.-O.

T.-O. Tsun, A. Wada, T. Sakai, and R. Yamauchi, “Novel method using white spectral probe signals to measure Brillouin gain spectra of pure silica core fibres,” Electron. Lett. 28, 247–249 (1992).
[Crossref]

Valley, G. C.

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]

van der Ziel, J. P.

N. A. Olsson and J. P. van der Ziel, “Cancellation of fiber loss by semiconductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48, 1329–1330 (1986).
[Crossref]

Vedam, K.

K. Vedam, “The elastic and photoelastic constants of fused quartz,” Phys. Rev. 78, 472–473 (1950).
[Crossref]

Velsko, S.

D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, and G. Kennedy, “Deuterated L-argenine phosphate: a new efficient nonlinear crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
[Crossref]

Waarts, R. G.

N. Shibata, R. G. Waarts, and R. Braun, “Brillouin-gain spectra for single-mode fibers having pure-silica GeO2-doped and P2O5-doped cores,” Opt. Lett. 12, 269–271 (1987).
[Crossref] [PubMed]

R. G. Waarts and R. P. Braun, “Crosstalk due to stimulated Brillouin scattering in monomode fibre,” Electron. Lett. 21, 1114–1115 (1985).
[Crossref]

Wada, A.

T.-O. Tsun, A. Wada, T. Sakai, and R. Yamauchi, “Novel method using white spectral probe signals to measure Brillouin gain spectra of pure silica core fibres,” Electron. Lett. 28, 247–249 (1992).
[Crossref]

Wang, F.

D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, and G. Kennedy, “Deuterated L-argenine phosphate: a new efficient nonlinear crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
[Crossref]

Weiland, T. L.

Wilcox, R. B.

Wood, D. L.

Yamauchi, R.

T.-O. Tsun, A. Wada, T. Sakai, and R. Yamauchi, “Novel method using white spectral probe signals to measure Brillouin gain spectra of pure silica core fibres,” Electron. Lett. 28, 247–249 (1992).
[Crossref]

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), pp. 490–497.

Zhao, X. S.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

N. A. Olsson and J. P. van der Ziel, “Cancellation of fiber loss by semiconductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48, 1329–1330 (1986).
[Crossref]

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539–541 (1972).
[Crossref]

At. Data Nucl. Data Tables (1)

P. J. Leonard, “Refractive indices, Verdet constants, and polarizabilities of the inert gases,” At. Data Nucl. Data Tables,  14, 21–37 (1974).
[Crossref]

Bull. Am. Phys. Soc. (1)

G. C. Herring, M. J. Dyer, and W. K. Bischel, “Cw stimulated Rayleigh–Brillouin spectroscopy,” Bull. Am. Phys. Soc. 32, 1634 (1987).

Chem. Phys. Lett. (1)

K. Ratanaphruks, W. T. Grubbs, and R. A. Macphail, “Cw stimulated Brillouin gain spectroscopy of liquids,” Chem. Phys. Lett. 182, 371–378 (1991).
[Crossref]

Electron. Lett. (4)

Y. Azuma, N. Shibata, T. Horiguchi, and M. Tateda, “Wavelength dependence of Brillouin-gain spectra for single-mode optical fibres,” Electron. Lett. 24, 250–252 (1988); N. Shibata, Y. Azuma, T. Horiguchi, and M. Tateda, “Identification of longitudinal acoustic modes guided in the core region of a single-mode optical fiber by Brillouin gain spectra measurements,” Opt. Lett. 13, 595–597 (1988).
[Crossref] [PubMed]

T.-O. Tsun, A. Wada, T. Sakai, and R. Yamauchi, “Novel method using white spectral probe signals to measure Brillouin gain spectra of pure silica core fibres,” Electron. Lett. 28, 247–249 (1992).
[Crossref]

E. J. Bachus, R. P. Braun, W. Eutin, E. Grossmann, H. Foisel, K. M. Heimes, and B. Strebel, “Coherent optical-fibre subscriber line,” Electron. Lett. 21, 1203–1205 (1985).
[Crossref]

R. G. Waarts and R. P. Braun, “Crosstalk due to stimulated Brillouin scattering in monomode fibre,” Electron. Lett. 21, 1114–1115 (1985).
[Crossref]

IEEE J. Quantum Electron. (5)

M. J. Damzen and H. Hutchinson, “Laser pulse compression by stimulated Brillouin scattering in tapered waveguides,” IEEE J. Quantum Electron. QE-19, 7–14 (1983).
[Crossref]

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[Crossref]

D. Eimerl, J. Marion, E. K. Graham, H. A. McKinstry, and S. Haussühl, “Elastic constants and thermal fracture of AgGaSe2 and d-LAP,” IEEE J. Quantum Electron. 27, 142–145 (1991).
[Crossref]

D. Eimerl, S. Velsko, L. Davis, F. Wang, G. Loiacono, and G. Kennedy, “Deuterated L-argenine phosphate: a new efficient nonlinear crystal,” IEEE J. Quantum Electron. 25, 179–193 (1989).
[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]

IEEE Photon. Technol. Lett. (1)

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1, 107–108 (1989); T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects of Brillouin gain spectra in single-mode fibers,” IEEE Photon. Technol. Lett. 2, 718–720 (1990).
[Crossref]

J. Am. Ceram. Soc. (1)

J. Schroeder, R. Mohr, P. B. Macedo, and C. J. Montrose, “Rayleigh and Brillouin scattering in K2O–SiO2 glasses,” J. Am. Ceram. Soc. 56, 510–514 (1973).
[Crossref]

J. Appl. Phys. (5)

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
[Crossref]

Y. Hibina, T. Edahiro, T. Horiguchi, Y. Azuma, and N. Shibata, “Evaluation of residual stress and viscosity in SiO2-core/F-SiO2 clad single-mode optical fibers from Brillouin gain spectra,” J. Appl. Phys. 66, 4049–4052 (1989).
[Crossref]

N. M. Kroll, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34–43 (1965).
[Crossref]

L. J. Graham and R. Chang, “Elastic moduli of single-crystal gadolinium gallium garnet,” J. Appl. Phys. 41, 2247–2248 (1970).
[Crossref]

W. Primack and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[Crossref]

J. Non-Cryst. Solids (1)

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

J. Opt. Soc. Am. B (4)

J. Phys. E (1)

M. Debenham and G. D. Dew, “The refractive index of toluene in the visible region,” J. Phys. E 14, 544–545 (1981).
[Crossref]

Mater. Sci. Forum (1)

J. Schroeder, L. G. Hwa, M. C. Shyong, G. A. Floudas, D. A. Thompson, and M. G. Drexhage, “Brillouin scattering and phonon attenuation in halide and oxide glasses,” Mater. Sci. Forum 19/20, 653–670 (1987).
[Crossref]

Opt. Lett. (5)

Philos. Mag. B (1)

V. Mazzacurati, M. Nardone, G. Ruocco, and G. Signorelli, “Brillouin scattering intensities in glasses: theory and experiment,” Philos. Mag. B 59, 3–15 (1989).
[Crossref]

Phys. Rev. (3)

M. Denariez and G. Bret, “Investigation of Rayleigh wings and Brillouin-stimulated scattering in liquids,” Phys. Rev. 171, 160–171 (1968).
[Crossref]

G. B. Benedek and K. Fritsch, “Brillouin scattering in cubic crystals,” Phys. Rev. 149, 647–662 (1966).
[Crossref]

K. Vedam, “The elastic and photoelastic constants of fused quartz,” Phys. Rev. 78, 472–473 (1950).
[Crossref]

Phys. Rev. A (1)

C. Y. She, G. C. Herring, H. Moosmüller, and S. A. Lee, “Stimulated Rayleigh–Brillouin gain spectroscopy,” Phys. Rev. A 31, 3733–3740 (1985).
[Crossref] [PubMed]

Phys. Rev. B (2)

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetimes,” Phys. Rev. B 1, 31–43 (1970).
[Crossref]

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

Rev. Phys. Appl. (1)

S. Gerstenkorn and P. Luc, “Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy,” Rev. Phys. Appl. 14, 791–794 (1979); Atlas du Spectre d’Absorption de la Molécule de l’Iode entre 14 800–20 000 cm−1 (Editions du CNRS, Paris, 1978).
[Crossref]

Usp. Fiz. Nauk (1)

I. L. Fabelinskii, “Certain problems of molecular scattering of light in liquids,” Usp. Fiz. Nauk 63, 355–410 (1957).
[Crossref]

Z. Naturforschung (1)

W. Rother, “Theorie der Lichtverstärkung in Absorbeirenden Medien,” Z. Naturforschung,  25a, 1120–1135 (1970).

Other (24)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), pp. 187–201.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), pp. 490–497.

D. E. Gray, ed., American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, New York, 1972), pp. 6-16, 6-21, 6-28, 6-105, 6-109, 6-236, 2-51, 2-156, 2-164.

W. G. Driscol and W. Vaughan, eds., Handbook of Optics (McGraw Hill, New York, 1978), p. 7–138.

Data sheet from Cleveland Crystals, Inc., Cleveland, Ohio.

Data sheet from Schott Glass Technologies, Inc., Duryea, Pa.

J. Storms, Hoya Optics, Inc., Fremont, Calif. 94538 (personal communication).

Data sheet from Hoya Optics, Inc., Fremont, Calif.

R. C. Weast, ed., Handbook of Chemistry and Physics, 59th ed. (CRC, West Palm Beach, Fla., 1979), p. C-783.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975) p. 155.

J. M. H. L. Sengers, M. Klein, and J. S. Gallagher, “Pressure-volume-temperature relationships of gases; virial coefficients,” in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 4-204–4-221.

A. Owyoung, “Cw stimulated Raman spectroscopy,” in Chemical Applications of Nonlinear Raman Spectroscopy, A. B. Harvey, ed. (Academic, New York, 1981), pp. 281–320.

P. Esherick and A. Owyoung, “High resolution stimulated Raman spectroscopy,” in Advances in Infrared and Raman Spectroscopy, R. J. H. Clark and R. E. Hester, eds. (Heyden, London, 1982), Vol. 9, pp. 130–187.

J. F. Nye, Physical Properties of Crystals (Oxford U. Press, London, 1960), pp. 131–149, 235–259.

L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon, London, 1959), pp. 36–41.

S. Bhagavantam, Crystal Symmetry and Physical Properties (Academic, London, 1966), pp. 182–187.

D. A. Pinnow, “Electrooptical materials,” in Handbook of Lasers, Robert J. Pressley, ed. (CRC, Cleveland, Ohio, 1971), pp. 478–488.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, Vol. 55 of National Bureau of Standards Applied Mathematics Series (U.S. Government Printing Office, Washington, D.C., 1972), p. 297.

M. J. Dyer, W. K. Bischel, and D. G. Scerback, “High-power 80-ns transform-limited Nd:YAG laser,” in Pulsed Single-Frequency Lasers: Technology and Applications, W. K. Bischel and L. A. Rahn, eds., Proc. Soc. Photo-Opt. Instrum. Eng.912, 32–36 (1988).
[Crossref]

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 334–335.

G. W. Faris and M. J. Dyer, “Injection-seeded Nd:YAG laser linewidth measurement using saturation spectroscopy in iodine,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 268.

M. J. Dyer and W. K. Bischel, “Stimulated Brillouin spectroscopy of liquids,” in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 182.

W. Kaiser and M. Maier, “Stimulated Rayleigh, Brillouin, and Raman spectroscopy,” in Laser Handbook, F. T. Arecchi and E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150.

I. L. Fabelinskii, Molecular Scattering of Light (Plenum, New York, 1968), pp. 139–154.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Transient temporal response for the Brillouin-gain signal, normalized to the peak steady-state gain, for Γtp = 10. The dashed curve is the response in the steady-state limit (on resonance).

Fig. 2
Fig. 2

Transient temporal response for the Brillouin-gain signal, normalized to the peak steady-state gain, for Γtp = 1. The dashed curve is the response in the steady-state limit (on resonance).

Fig. 3
Fig. 3

Delay for the peak of the Brillouin-gain signal at line center (Δω = 0) as a function of degree of transiency, Γtp. The point shown is an experimental measurement in gadolinium gallium garnet (GGG).

Fig. 4
Fig. 4

Brillouin-gain signal at the line center (Δω = 0) for the peak of the Brillouin signal (solid curve) and the peak of the pump pulse (dashed curve) as a function of degree of transiency, Γtp. The point shown is an experimental measurement in fused silica.

Fig. 5
Fig. 5

Experimental arrangement for stimulated Brillouin-gain spectroscopy in counterpropagating geometry: λ/2, half-wave plate; Pol, polarizer.

Fig. 6
Fig. 6

Brillouin-gain spectrum for a transverse acoustic wave in GGG.

Tables (5)

Tables Icon

Table 1 Comparison of Measurements of the Brillouin Gain Coefficient for Fused Silica

Tables Icon

Table 2 Brillouin Measurements at 532 nm

Tables Icon

Table 3 Measurements of the Elasto-optic Coefficient p12 for Fused Silica

Tables Icon

Table 4 Elastic Constants

Tables Icon

Table 5 Elasto-optic Coefficients

Equations (51)

Equations on this page are rendered with MathJax. Learn more.

u t + [ Γ B 2 - i ( ω a 2 - ω B 2 2 ω a ) ] u + v a · u = - k a p 16 π ρ ω a D p D s * ,
D s t + v s · D s = c 2 k s 2 k a p 4 ω s D p u * ,
u = 1 2 { u ( r , t ) ^ a exp [ i ( k a · r - ω a t ) ] + c . c . } , D p = 1 2 { D p ( t ) ^ p exp [ i ( k p · r - ω p t ) ] + c . c . } , D s = 1 2 { [ D s ( r , t ) ^ s + i k s ^ s · D s k s 2 ] × exp [ i ( k s · r - ω s t ) ] + c . c . } , ^ p · k p = 0             ^ s · k s = 0.
k p = k s ± k a , ω p = ω s ± ω a .
ρ ω B 2 a i - c i j l m k a j k a l a m = 0 ,
ω p 2 c 2 p i - ν i j k p 2 p j + ν m j k p i k p m p j = 0 ,
ω s 2 c 2 s i - ν i j k s 2 s j + ν m j k s i k s m s j = 0.
κ ^ a = k a / k a
Q i m a m = ( ρ ω B 2 / k a 2 ) a i ,
Q i m = c i j l m κ a j κ a l .
k a = ω B / v ,
k p = n p ω p / c , k s = n s ω s / c ,
v a m = c i j l m k a j a i a l ρ ω a , v s = c 2 ω s ( ν i j s i s j k s - ν i j s i k s j ^ s ) .
Γ B = 2 π Δ ν B = 1 τ B = η i j a i a j ρ ,
p = p i j l m p i s j κ a l a m ,
δ ν i j = p i j l m u l x m ,
D i = i j E j .
u ( r , t ) = - k a p 16 π ρ ω a - t D p ( t ) D s * ( r , t ) × exp { - [ Γ B 2 - i ( ω a 2 - ω B 2 2 ω a ) ] ( t - t ) } d t .
ω a 2 - ω B 2 2 ω a ( ω a - ω B ) = - 2 ω a Δ ω ,
t ^ = t - ( z / v s ) .
D p n p 2 E p ,             D s n s 2 E s ,             v s c n s = ω s k s ,             v a ω a k a ,
E s z = n p c 32 π Γ B g E p ( t ^ ) - t ^ E p * ( t ) E s ( r , t ) × exp [ - ( Γ B 2 - i Δ ω ) ( t ^ - t ) ] d t ,
g = k s k a n s 2 n p 3 p 2 2 c p v a Γ B .
k a = ( k s 2 - 2 k s k p cos θ + k p 2 ) 1 / 2 ,
I s ( z , t ^ ) = I s ( 0 , t ^ ) exp [ g I p ( t ^ ) z 1 + ( 2 Δ ω / Γ B ) 2 ] ,
I s = n s c 8 π E s 2 , I p = n p c 8 π E p 2 .
p = p 11 p m s m κ a n δ m n + p 12 p m s m κ a n a n ( 1 - δ m n ) + p 44 ( p m s n κ a m a n + p m s n κ a n a m ) ( 1 - δ m n ) .
p = p 12 p m s m κ a n a n + p 44 ( p m s n κ a m a n + p m s n κ a n a m ) = p 12 ( ^ p · ^ s ) ( κ ^ a · ^ a ) + p 44 [ ( ^ p · κ ^ a ) ( ^ s · ^ a ) + ( ^ p · ^ a ) ( ^ s · κ ^ a ) ] .
p = p 12 ( ^ p · ^ s ) + p 14 [ ( ^ p · κ ^ a ) ( ^ s · ^ a ) + ( ^ p · ^ a ) ( ^ s · κ ^ a ) ]
p = p 14 [ ( ^ p · κ ^ a ) ( ^ s · ^ a ) + ( ^ p · ^ a ) ( ^ s · κ ^ a ) ] .
k a = 2 k s sin ( θ / 2 ) ,
ω B = 2 n v a c ω s sin ( θ / 2 ) .
g = k s 2 n 5 p 12 2 c ρ v a Γ B sin θ 2 = 2 π γ 2 λ s 2 n c ρ v a Δ ν sin θ 2 ,
γ = ρ ( / ρ )
v a 2 = ( ω B k a ) 2 = c i i ρ ,
E s ( z , t ^ ) E s ( 0 , t ^ ) + z E s z ( 0 , t ^ ) .
E s ( z , t ^ ) = E s ( 0 , t ) { 1 + n p c 8 π Γ B g z 4 E p ( t ^ ) - t ^ E p * ( t ) × exp [ - ( Γ B 2 - i Δ ω ) ( t ^ - t ) ] d t } .
s ( Δ ω , t ^ ) = I ( L , t ^ ) - I ( 0 , t ^ ) I ( 0 , t ^ ) = n p c 8 π Γ B g L 2 Re { E p ( t ^ ) - t ^ E p * ( t ) × exp [ - ( Γ B 2 - i Δ ω ) ( t ^ - t ) d t ] } .
S ( Δ ω ) = - s ( Δ ω , t ^ ) d t ^ .
E p ( t ) = 1 ( 2 π ) 1 / 2 - exp ( - i ω t ) F p ( ω ) d ω , F p ( ω ) = 1 ( 2 π ) 1 / 2 - exp ( i ω t ) E p ( t ) d t ,
P ( ω ) = n p c 8 π F p ( ω ) 2
- P ( ω ) d ω = - I ( t ) d t .
S ( Δ ω ) = g L - P ( ω ) d ω 1 + [ 2 ( Δ ω - ω ) / Γ B ] 2 .
- S ( Δ ω ) d Δ ω = π 2 Γ B g L - I ( t ) d t .
E p ( t ) = E p o exp [ - ( t / t p ) 2 ]
s ( Δ ω , t ^ ) g I p o L = π 1 / 2 4 Γ B t p exp [ - 2 ( t ^ / t p ) 2 ] × Re w [ Δ ω t p 2 + i ( Γ B t p 4 - t ^ t p ) ] ,
Γ B t p = 2 [ τ + 1 π 1 / 2 Re w ( i τ ) ] ,
τ = Γ B t p 4 - t delay t p .
n 2 - 1 n 2 + 2 = 4 π 3 N α ,
γ = ρ ρ = 1 3 ( n 2 - 1 ) ( n 2 + 2 )
p = ( 1 / 4 ) ( p 11 - p 12 - 2 p 44 ) sin ( 4 θ ) ,

Metrics