Abstract

We estimate the effect of Ge doping on the acoustic damping coefficient of silica fibers. We show that an acoustically multimode fiber with a characteristic central index dip, such as that observed in modified chemical-vapor deposition (MCVD)-type fibers, can provide adequate data for a reasonable estimation. This may result from the fact that the scattering integral of each acoustic mode in such a waveguide is strongly position-dependent in the radial direction where there is a varying Ge content.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
  3. C. R. Hammond and S. R. Norman, “Silica based binary glass systems-refractive index behaviour and composition in optical fibres,” Opt. Quantum Electron. 5, 399-409 (1977).
    [CrossRef]
  4. J. W. Fleming, “Dispersion in GeO2-SiO2 glasses,” Appl. Opt. 23, 4486-4493 (1984).
    [CrossRef] [PubMed]
  5. R. E. Youngman, J. Kieffer, J. D. Bass, and L. Duffrène, “Extended structural integrity in network glasses and liquids,” J. Non-Cryst. Solids 222, 190-198 (1997).
    [CrossRef]
  6. A. V. Anan'ev, V. N. Bogdanov, B. Champagnon, M. Ferrari, G. O. Karapetyan, L. V. Maksimov, S. N. Smerdin, and V. A. Solovyev, “Origin of Rayleigh scattering and anomaly of elastic properties in vitreous and molten GeO2,” J. Non-Cryst. Solids 354, 3049-3058 (2008).
    [CrossRef]
  7. P. D. Dragic, “Proposed model for the effect of Ge-doping on the acoustic properties of silica fibers” in Optical Fiber Communication Conference, Vol. 2 of 2009 OSA Technical Digest Series (Optical Society of America, 2009), paper OWU4.
  8. A. Croteau and A. C. J. Poulin, “Photosensitive fibers,” Ch. 9 in Specialty Optical Fibers Handbook, A.Mendex and T.F.Morse, eds. (Academic, 2007).
  9. P. J. Thomas, N. L. Rowell, H. M. van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B 19, 4986-4998 (1979).
    [CrossRef]
  10. Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” J. Lightwave Technol. 22, 631-639 (2004).
    [CrossRef]
  11. A. Kobyakov, S. Kumar, D. Chowdhury, A. B. Ruffin, M. Sauer, S. Bickham, and R. Mishra, “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express 13, 5338-5346 (2005).
    [CrossRef] [PubMed]
  12. T. Nakanishi, M. Tanaka, T. Hasegawa, M. Hirano, T. Okuno, and M. Onishi, “Al2O3-SiO2 core highly nonlinear dispersion-shifted fiber with Brillouin gain suppression improved by 6.1 dB,” in European Conference on Optical Communications (ECOC 2006)(ECOC, 2006), post-deadline paper Th4.2.2.
  13. P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies (CLEO/QELS 2005), Vol. 3, Technical Digest (CD) (Optical Society of America, 2005), paper CThZ3. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2005-CThZ3.
  14. M. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. Demeritt, A. Ruffin, A. Crowley, D. Walton, and L. Zenteno, “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express 15, 8290-8299 (2007).
    [CrossRef] [PubMed]
  15. The index profile is reproduced here with permission from INO of Canada. The index profile was measured at INO.
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    [CrossRef]
  17. 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]
  18. 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]
  19. B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, 1973).
  20. W. P. Mason, Physical Acoustics and the Properties of Solids (Van Nostrand, 1958).
  21. C.-K. Jen and N. Goto, “Backward collinear guided-wave-acousto-optic interactions in single-mode fibers,” J. Lightwave Technol. 7, 2018-2023 (1989).
    [CrossRef]
  22. R. A. Waldron, “Some problems in the theory of guided microsonic waves,” IEEE Trans. Microwave Theory Tech. MTT-17, 893-904 (1969).
    [CrossRef]
  23. C.-K. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634-643 (1986).
  24. R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode fiber characterization,” Electron. Lett. 22, 1101-1113 (1986).
  25. C. Krischer, “Optical measurements of ultrasonic attenuation and reflection losses in fused silica,” J. Acoust. Soc. Am. 48, 1086-1092 (1970).
    [CrossRef]
  26. M. Niklès, L. Thévenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15, 1842-1851 (1997).
    [CrossRef]

2008 (1)

A. V. Anan'ev, V. N. Bogdanov, B. Champagnon, M. Ferrari, G. O. Karapetyan, L. V. Maksimov, S. N. Smerdin, and V. A. Solovyev, “Origin of Rayleigh scattering and anomaly of elastic properties in vitreous and molten GeO2,” J. Non-Cryst. Solids 354, 3049-3058 (2008).
[CrossRef]

2007 (1)

2005 (1)

2004 (1)

1997 (2)

R. E. Youngman, J. Kieffer, J. D. Bass, and L. Duffrène, “Extended structural integrity in network glasses and liquids,” J. Non-Cryst. Solids 222, 190-198 (1997).
[CrossRef]

M. Niklès, L. Thévenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

1993 (1)

C.-K. Jen, C. Neron, A. Shang, K. Abe, L. Bonnell, and J. Kushibiki, “Acoustic characterization of silica glasses,” J. Am. Ceram. Soc. 76, 712-716 (1993).
[CrossRef]

1989 (2)

C.-K. Jen and N. Goto, “Backward collinear guided-wave-acousto-optic interactions in single-mode fibers,” J. Lightwave Technol. 7, 2018-2023 (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]

1988 (1)

1986 (2)

C.-K. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634-643 (1986).

R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode fiber characterization,” Electron. Lett. 22, 1101-1113 (1986).

1984 (1)

1979 (1)

P. J. Thomas, N. L. Rowell, H. M. van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B 19, 4986-4998 (1979).
[CrossRef]

1977 (1)

C. R. Hammond and S. R. Norman, “Silica based binary glass systems-refractive index behaviour and composition in optical fibres,” Opt. Quantum Electron. 5, 399-409 (1977).
[CrossRef]

1972 (1)

1970 (1)

C. Krischer, “Optical measurements of ultrasonic attenuation and reflection losses in fused silica,” J. Acoust. Soc. Am. 48, 1086-1092 (1970).
[CrossRef]

1969 (1)

R. A. Waldron, “Some problems in the theory of guided microsonic waves,” IEEE Trans. Microwave Theory Tech. MTT-17, 893-904 (1969).
[CrossRef]

Abe, K.

C.-K. Jen, C. Neron, A. Shang, K. Abe, L. Bonnell, and J. Kushibiki, “Acoustic characterization of silica glasses,” J. Am. Ceram. Soc. 76, 712-716 (1993).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

Anan'ev, A. V.

A. V. Anan'ev, V. N. Bogdanov, B. Champagnon, M. Ferrari, G. O. Karapetyan, L. V. Maksimov, S. N. Smerdin, and V. A. Solovyev, “Origin of Rayleigh scattering and anomaly of elastic properties in vitreous and molten GeO2,” J. Non-Cryst. Solids 354, 3049-3058 (2008).
[CrossRef]

Auld, B. A.

B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, 1973).

Azuma, Y.

Bass, J. D.

R. E. Youngman, J. Kieffer, J. D. Bass, and L. Duffrène, “Extended structural integrity in network glasses and liquids,” J. Non-Cryst. Solids 222, 190-198 (1997).
[CrossRef]

Bickham, S.

Bogdanov, V. N.

A. V. Anan'ev, V. N. Bogdanov, B. Champagnon, M. Ferrari, G. O. Karapetyan, L. V. Maksimov, S. N. Smerdin, and V. A. Solovyev, “Origin of Rayleigh scattering and anomaly of elastic properties in vitreous and molten GeO2,” J. Non-Cryst. Solids 354, 3049-3058 (2008).
[CrossRef]

Bonnell, L.

C.-K. Jen, C. Neron, A. Shang, K. Abe, L. Bonnell, and J. Kushibiki, “Acoustic characterization of silica glasses,” J. Am. Ceram. Soc. 76, 712-716 (1993).
[CrossRef]

Champagnon, B.

A. V. Anan'ev, V. N. Bogdanov, B. Champagnon, M. Ferrari, G. O. Karapetyan, L. V. Maksimov, S. N. Smerdin, and V. A. Solovyev, “Origin of Rayleigh scattering and anomaly of elastic properties in vitreous and molten GeO2,” J. Non-Cryst. Solids 354, 3049-3058 (2008).
[CrossRef]

Chen, X.

Chowdhury, D.

Chraplyvy, A. R.

R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode fiber characterization,” Electron. Lett. 22, 1101-1113 (1986).

Chujo, W.

Croteau, A.

A. Croteau and A. C. J. Poulin, “Photosensitive fibers,” Ch. 9 in Specialty Optical Fibers Handbook, A.Mendex and T.F.Morse, eds. (Academic, 2007).

Crowley, A.

Demeritt, J.

Derosier, R. M.

R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode fiber characterization,” Electron. Lett. 22, 1101-1113 (1986).

Dragic, P. D.

P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies (CLEO/QELS 2005), Vol. 3, Technical Digest (CD) (Optical Society of America, 2005), paper CThZ3. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2005-CThZ3.

P. D. Dragic, “Proposed model for the effect of Ge-doping on the acoustic properties of silica fibers” in Optical Fiber Communication Conference, Vol. 2 of 2009 OSA Technical Digest Series (Optical Society of America, 2009), paper OWU4.

Duffrène, L.

R. E. Youngman, J. Kieffer, J. D. Bass, and L. Duffrène, “Extended structural integrity in network glasses and liquids,” J. Non-Cryst. Solids 222, 190-198 (1997).
[CrossRef]

Farnell, G. W.

C.-K. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634-643 (1986).

Ferrari, M.

A. V. Anan'ev, V. N. Bogdanov, B. Champagnon, M. Ferrari, G. O. Karapetyan, L. V. Maksimov, S. N. Smerdin, and V. A. Solovyev, “Origin of Rayleigh scattering and anomaly of elastic properties in vitreous and molten GeO2,” J. Non-Cryst. Solids 354, 3049-3058 (2008).
[CrossRef]

Fleming, J. W.

Galvanauskas, A.

P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies (CLEO/QELS 2005), Vol. 3, Technical Digest (CD) (Optical Society of America, 2005), paper CThZ3. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2005-CThZ3.

Goto, N.

C.-K. Jen and N. Goto, “Backward collinear guided-wave-acousto-optic interactions in single-mode fibers,” J. Lightwave Technol. 7, 2018-2023 (1989).
[CrossRef]

Gray, S.

Hammond, C. R.

C. R. Hammond and S. R. Norman, “Silica based binary glass systems-refractive index behaviour and composition in optical fibres,” Opt. Quantum Electron. 5, 399-409 (1977).
[CrossRef]

Hasegawa, T.

T. Nakanishi, M. Tanaka, T. Hasegawa, M. Hirano, T. Okuno, and M. Onishi, “Al2O3-SiO2 core highly nonlinear dispersion-shifted fiber with Brillouin gain suppression improved by 6.1 dB,” in European Conference on Optical Communications (ECOC 2006)(ECOC, 2006), post-deadline paper Th4.2.2.

Hirano, M.

T. Nakanishi, M. Tanaka, T. Hasegawa, M. Hirano, T. Okuno, and M. Onishi, “Al2O3-SiO2 core highly nonlinear dispersion-shifted fiber with Brillouin gain suppression improved by 6.1 dB,” in European Conference on Optical Communications (ECOC 2006)(ECOC, 2006), post-deadline paper Th4.2.2.

Horiguchi, T.

Jen, C.-K.

C.-K. Jen, C. Neron, A. Shang, K. Abe, L. Bonnell, and J. Kushibiki, “Acoustic characterization of silica glasses,” J. Am. Ceram. Soc. 76, 712-716 (1993).
[CrossRef]

C.-K. Jen and N. Goto, “Backward collinear guided-wave-acousto-optic interactions in single-mode fibers,” J. Lightwave Technol. 7, 2018-2023 (1989).
[CrossRef]

C.-K. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634-643 (1986).

Karapetyan, G. O.

A. V. Anan'ev, V. N. Bogdanov, B. Champagnon, M. Ferrari, G. O. Karapetyan, L. V. Maksimov, S. N. Smerdin, and V. A. Solovyev, “Origin of Rayleigh scattering and anomaly of elastic properties in vitreous and molten GeO2,” J. Non-Cryst. Solids 354, 3049-3058 (2008).
[CrossRef]

Kieffer, J.

R. E. Youngman, J. Kieffer, J. D. Bass, and L. Duffrène, “Extended structural integrity in network glasses and liquids,” J. Non-Cryst. Solids 222, 190-198 (1997).
[CrossRef]

Kobyakov, A.

Koyamada, Y.

Krischer, C.

C. Krischer, “Optical measurements of ultrasonic attenuation and reflection losses in fused silica,” J. Acoust. Soc. Am. 48, 1086-1092 (1970).
[CrossRef]

Kumar, S.

Kushibiki, J.

C.-K. Jen, C. Neron, A. Shang, K. Abe, L. Bonnell, and J. Kushibiki, “Acoustic characterization of silica glasses,” J. Am. Ceram. Soc. 76, 712-716 (1993).
[CrossRef]

Li, M.

Liu, A.

Liu, C.-H.

P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies (CLEO/QELS 2005), Vol. 3, Technical Digest (CD) (Optical Society of America, 2005), paper CThZ3. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2005-CThZ3.

Maksimov, L. V.

A. V. Anan'ev, V. N. Bogdanov, B. Champagnon, M. Ferrari, G. O. Karapetyan, L. V. Maksimov, S. N. Smerdin, and V. A. Solovyev, “Origin of Rayleigh scattering and anomaly of elastic properties in vitreous and molten GeO2,” J. Non-Cryst. Solids 354, 3049-3058 (2008).
[CrossRef]

Mason, W. P.

W. P. Mason, Physical Acoustics and the Properties of Solids (Van Nostrand, 1958).

Mishra, R.

Nakamura, S.

Nakanishi, T.

T. Nakanishi, M. Tanaka, T. Hasegawa, M. Hirano, T. Okuno, and M. Onishi, “Al2O3-SiO2 core highly nonlinear dispersion-shifted fiber with Brillouin gain suppression improved by 6.1 dB,” in European Conference on Optical Communications (ECOC 2006)(ECOC, 2006), post-deadline paper Th4.2.2.

Neron, C.

C.-K. Jen, C. Neron, A. Shang, K. Abe, L. Bonnell, and J. Kushibiki, “Acoustic characterization of silica glasses,” J. Am. Ceram. Soc. 76, 712-716 (1993).
[CrossRef]

Niklès, M.

M. Niklès, L. Thévenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

Norman, S. R.

C. R. Hammond and S. R. Norman, “Silica based binary glass systems-refractive index behaviour and composition in optical fibres,” Opt. Quantum Electron. 5, 399-409 (1977).
[CrossRef]

Okamoto, K.

Okuno, T.

T. Nakanishi, M. Tanaka, T. Hasegawa, M. Hirano, T. Okuno, and M. Onishi, “Al2O3-SiO2 core highly nonlinear dispersion-shifted fiber with Brillouin gain suppression improved by 6.1 dB,” in European Conference on Optical Communications (ECOC 2006)(ECOC, 2006), post-deadline paper Th4.2.2.

Onishi, M.

T. Nakanishi, M. Tanaka, T. Hasegawa, M. Hirano, T. Okuno, and M. Onishi, “Al2O3-SiO2 core highly nonlinear dispersion-shifted fiber with Brillouin gain suppression improved by 6.1 dB,” in European Conference on Optical Communications (ECOC 2006)(ECOC, 2006), post-deadline paper Th4.2.2.

Papen, G. C.

P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies (CLEO/QELS 2005), Vol. 3, Technical Digest (CD) (Optical Society of America, 2005), paper CThZ3. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2005-CThZ3.

Poulin, A. C. J.

A. Croteau and A. C. J. Poulin, “Photosensitive fibers,” Ch. 9 in Specialty Optical Fibers Handbook, A.Mendex and T.F.Morse, eds. (Academic, 2007).

Robert, P. A.

M. Niklès, L. Thévenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

Rowell, N. L.

P. J. Thomas, N. L. Rowell, H. M. van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B 19, 4986-4998 (1979).
[CrossRef]

Ruffin, A.

Ruffin, A. B.

Safaai-Jazi, A.

C.-K. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634-643 (1986).

Sato, S.

Sauer, M.

Shang, A.

C.-K. Jen, C. Neron, A. Shang, K. Abe, L. Bonnell, and J. Kushibiki, “Acoustic characterization of silica glasses,” J. Am. Ceram. Soc. 76, 712-716 (1993).
[CrossRef]

Shibata, N.

Smerdin, S. N.

A. V. Anan'ev, V. N. Bogdanov, B. Champagnon, M. Ferrari, G. O. Karapetyan, L. V. Maksimov, S. N. Smerdin, and V. A. Solovyev, “Origin of Rayleigh scattering and anomaly of elastic properties in vitreous and molten GeO2,” J. Non-Cryst. Solids 354, 3049-3058 (2008).
[CrossRef]

Smith, R. G.

Solovyev, V. A.

A. V. Anan'ev, V. N. Bogdanov, B. Champagnon, M. Ferrari, G. O. Karapetyan, L. V. Maksimov, S. N. Smerdin, and V. A. Solovyev, “Origin of Rayleigh scattering and anomaly of elastic properties in vitreous and molten GeO2,” J. Non-Cryst. Solids 354, 3049-3058 (2008).
[CrossRef]

Sotobayashi, H.

Stegeman, G. I.

P. J. Thomas, N. L. Rowell, H. M. van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B 19, 4986-4998 (1979).
[CrossRef]

Tanaka, M.

T. Nakanishi, M. Tanaka, T. Hasegawa, M. Hirano, T. Okuno, and M. Onishi, “Al2O3-SiO2 core highly nonlinear dispersion-shifted fiber with Brillouin gain suppression improved by 6.1 dB,” in European Conference on Optical Communications (ECOC 2006)(ECOC, 2006), post-deadline paper Th4.2.2.

Tateda, M.

Thévenaz, L.

M. Niklès, L. Thévenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

Thomas, P. J.

P. J. Thomas, N. L. Rowell, H. M. van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B 19, 4986-4998 (1979).
[CrossRef]

Tkach, R. W.

R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode fiber characterization,” Electron. Lett. 22, 1101-1113 (1986).

van Driel, H. M.

P. J. Thomas, N. L. Rowell, H. M. van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B 19, 4986-4998 (1979).
[CrossRef]

Waldron, R. A.

R. A. Waldron, “Some problems in the theory of guided microsonic waves,” IEEE Trans. Microwave Theory Tech. MTT-17, 893-904 (1969).
[CrossRef]

Walton, D.

Wang, J.

Youngman, R. E.

R. E. Youngman, J. Kieffer, J. D. Bass, and L. Duffrène, “Extended structural integrity in network glasses and liquids,” J. Non-Cryst. Solids 222, 190-198 (1997).
[CrossRef]

Zenteno, L.

Appl. Opt. (2)

Electron. Lett. (1)

R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode fiber characterization,” Electron. Lett. 22, 1101-1113 (1986).

IEEE Trans. Microwave Theory Tech. (1)

R. A. Waldron, “Some problems in the theory of guided microsonic waves,” IEEE Trans. Microwave Theory Tech. MTT-17, 893-904 (1969).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

C.-K. Jen, A. Safaai-Jazi, and G. W. Farnell, “Leaky modes in weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 634-643 (1986).

J. Acoust. Soc. Am. (1)

C. Krischer, “Optical measurements of ultrasonic attenuation and reflection losses in fused silica,” J. Acoust. Soc. Am. 48, 1086-1092 (1970).
[CrossRef]

J. Am. Ceram. Soc. (1)

C.-K. Jen, C. Neron, A. Shang, K. Abe, L. Bonnell, and J. Kushibiki, “Acoustic characterization of silica glasses,” J. Am. Ceram. Soc. 76, 712-716 (1993).
[CrossRef]

J. Lightwave Technol. (3)

C.-K. Jen and N. Goto, “Backward collinear guided-wave-acousto-optic interactions in single-mode fibers,” J. Lightwave Technol. 7, 2018-2023 (1989).
[CrossRef]

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” J. Lightwave Technol. 22, 631-639 (2004).
[CrossRef]

M. Niklès, L. Thévenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

J. Non-Cryst. Solids (2)

R. E. Youngman, J. Kieffer, J. D. Bass, and L. Duffrène, “Extended structural integrity in network glasses and liquids,” J. Non-Cryst. Solids 222, 190-198 (1997).
[CrossRef]

A. V. Anan'ev, V. N. Bogdanov, B. Champagnon, M. Ferrari, G. O. Karapetyan, L. V. Maksimov, S. N. Smerdin, and V. A. Solovyev, “Origin of Rayleigh scattering and anomaly of elastic properties in vitreous and molten GeO2,” J. Non-Cryst. Solids 354, 3049-3058 (2008).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

C. R. Hammond and S. R. Norman, “Silica based binary glass systems-refractive index behaviour and composition in optical fibres,” Opt. Quantum Electron. 5, 399-409 (1977).
[CrossRef]

Phys. Rev. B (1)

P. J. Thomas, N. L. Rowell, H. M. van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B 19, 4986-4998 (1979).
[CrossRef]

Other (8)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

The index profile is reproduced here with permission from INO of Canada. The index profile was measured at INO.

T. Nakanishi, M. Tanaka, T. Hasegawa, M. Hirano, T. Okuno, and M. Onishi, “Al2O3-SiO2 core highly nonlinear dispersion-shifted fiber with Brillouin gain suppression improved by 6.1 dB,” in European Conference on Optical Communications (ECOC 2006)(ECOC, 2006), post-deadline paper Th4.2.2.

P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies (CLEO/QELS 2005), Vol. 3, Technical Digest (CD) (Optical Society of America, 2005), paper CThZ3. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2005-CThZ3.

B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, 1973).

W. P. Mason, Physical Acoustics and the Properties of Solids (Van Nostrand, 1958).

P. D. Dragic, “Proposed model for the effect of Ge-doping on the acoustic properties of silica fibers” in Optical Fiber Communication Conference, Vol. 2 of 2009 OSA Technical Digest Series (Optical Society of America, 2009), paper OWU4.

A. Croteau and A. C. J. Poulin, “Photosensitive fibers,” Ch. 9 in Specialty Optical Fibers Handbook, A.Mendex and T.F.Morse, eds. (Academic, 2007).

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Figures (6)

Fig. 1
Fig. 1

(a) Measured and approximate steplike index of refraction profile. (b) Estimated [Ge] doping profile associated with the approximate index profile. (c) Longitudinal acoustic velocity profile. (d) Shear acoustic velocity profile. (e) Mass density profile.

Fig. 2
Fig. 2

Block diagram of the experimental setup used to measure the BGS for the test fiber. A heterodyne apparatus was used with the master oscillator signal provided by cleaving the test fiber to a slight angle for a small feedback. The seed laser is isolated, twice amplified, and passed through a circulator and into a 15     m test segment. The back-reflected LO and Stokes’ waves are both preamplified before heterodyning.

Fig. 3
Fig. 3

Measured BGS at 1555 nm showing the presence of three L 0 m modes (solid curve). The dashed curve is a simple Lorentzian fit to the data. The fit and measured data are nearly indistinguishable. The vertical lines represent the locations of the calculated acoustic modes using the theory applied to the profiles of Fig. 1. These calculated acoustic modes were used in the acousto-optic scattering calculations.

Fig. 4
Fig. 4

Plots of the (a) L 01 , (b) L 02 , and (c) L 03 acoustic modes using the profiles in Fig. 1 and neglecting the shear wave components. The acoustic velocity profile is overlaid on each mode as a visual aid (dashed line).

Fig. 5
Fig. 5

Extracted Brillouin spectral width versus [Ge] for a constant acoustic frequency of 9.967 GHz (lower curve) and a constant optical wavelength (upper curve). The constant-wavelength plot appears to be nonlinear.

Fig. 6
Fig. 6

Model from [7] fit to the constant-wavelength data of Fig. 5. The extrapolated spectral width of silica is consistent with fictive bulk material. The rollover at large [Ge] is due to a decreasing acoustic velocity with increasing [Ge].

Tables (1)

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Table 1 Measured and Calculated Values for the Fiber of this Investigation

Equations (25)

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g B ( ν B ) = 2 π n 7 p 12 2 c λ 2 ρ V a Δ ν B ,
Δ ν B = V a α π .
D p , q = Vol E p * δ ε p , q E i q d V ,
δ ε r r = ε 0 n 4 ( p 11 S r r + p 12 S ϕ ϕ + p 12 S z z ) ,
δ ε ϕ ϕ = ε 0 n 4 ( p 11 S ϕ ϕ + p 12 S r r + p 12 S z z ) ,
δ ε ϕ r = ε 0 n 4 2 p 44 S ϕ r ,
S p q = 1 2 ( u q p + u p q ) .
ρ u ̈ ¯ [ c ̿ ¯ u + η ¯ ̿ u ̇ ] = 1 2 ¯ [ γ ̿ E k E l ] ,
U = φ + × Ψ ,
( t + h 2 ) φ = 0 ,
( t + k 2 ) Ψ = 0 ,
h i = ± ( 2 π ν B V L i ) 2 β 2 ,
k i = ± ( 2 π ν B V S i ) 2 β 2 ,
V L i = λ i + 2 μ i ρ i ,
V S i = μ i ρ i .
u r 1 ( r = a ) = u r 2 ( r = a ) ,
u z 1 ( r = a ) = u z 2 ( r = a ) ,
T r r = T 1 = ( λ 1 + 2 μ 1 ) u r 1 r r = a + λ 1 u r 1 r r = a + λ 1 u z 1 z r = a = ( λ 2 + 2 μ 2 ) u r 2 r r = a + λ 2 u r 2 r r = a + λ 2 u z 2 z r = a ,
T r z = μ S r z = μ S 5 = μ 1 ( u r 1 z + u z 1 r ) r = a = μ 2 ( u r 2 z + u z 2 r ) r = a .
u r ( r ) = A h X l ( h r ) + B β Z l ( k r ) ,
u ϕ ( r ) = 0 ,
u z ( r ) = j A β X l ( h r ) + j B k Z l ( k r ) ,
m g B ( ν ) ( Δ ν B m 2 ) ( ν ν a m ) 2 + ( Δ ν B m 2 ) 2 Γ m ,
α m = 1 = D ̂ 2 D ̂ 2 + D ̂ 3 α i = 2 + D ̂ 3 D ̂ 2 + D ̂ 3 X .
α m = 3 = D ̂ 1 D ̂ 1 + D ̂ 2 X + D ̂ 2 D ̂ 1 + D ̂ 2 α i = 2 ,

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