Abstract

We report the first detailed implementation of a 2-D finite-element method (FEM) through a commercial FEM solver that can be universally applied to calculate the Brillouin gain characteristics of optical fibers with arbitrary refractive index profiles and material composition, including radially asymmetric and microstructured optical fibers (MOFs). Experimental results on various fabricated solid and MOFs are presented that demonstrate the widespread applicability and high accuracy of the proposed technique, which should prove to be an invaluable tool for designing novel optical fibers with tailored Brillouin response for a wide range of applications.

© 2010 IEEE

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  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
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  4. C. J. S. de Matos, J. R. Taylor, K. P. Hansen, "All-fibre Brillouin laser based on holey fibre yielding comb-like spectra," Opt. Commun. 238, 185-189 (2004).
  5. Z. Zhu, D. J. Gauthier, R. W. Boyd, "Stored light in an optical fiber via stimulated Brillouin scattering," Science 318, 1748-1750 (2007).
  6. F. Ravet, L. Zou, X. Bao, T. Ozbakkaloglu, M. Saatcioglu, J. Zhou, "Distributed Brillouin sensor for structural health monitoring," Can. J. Civil Eng. 34, 291-297 (2007).
  7. E. Peral, A. Yariv, "Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to a phase shift induced by stimulated Brillouin scattering," IEEE J. Quantum Electron. 35, 1185-1195 (1999).
  8. M. R. Lorenzen, D. Noordegraaf, C. V. Nielsen, O. Odgaard, L. Grüner-Nielsen, K. Rottwitt, "Suppression of Brillouin scattering in fibreoptical parametric amplifier by applying temperature control and phase modulation," Electron. Lett. 45, 125-127 (2009).
  9. M. Laroche, H. Gilles, S. Girard, "Influence of stimulated Brillouin scattering on the temporal dynamics of an actively $Q$-switched double-clad fiber laser," Opt. Commun. 281, 2243-2247 (2008) doi: DOI: 10.1016/j.optcom.2007.11.080.
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  11. A. Liu, "Suppressing stimulated Brillouin scattering in fiber amplifiers using nonuniform fiber and temperature gradient," Opt. Exp. 15, 977-984 (2007).
  12. M.-J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, L. A. Zenteno, "Al/ge co-doped large mode area fiber with high SBS threshold," Opt. Exp. 15, 8290-8299 (2007).
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  14. C. K. Jen, A. Safaaijazi, G. W. Farnell, "Leaky modes in weakly guiding fiber acoustic wave-guides," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 33, 634-643 (1986).
  15. Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, W. Chujo, "Simulating and designing Brillouin gain spectrum in single-mode fibers," J. Lightw. Technol. 22, 631-639 (2004).
  16. A. Kobyakov, S. Kumar, D. Q. Chowdhury, A. B. Ruffin, M. Sauer, S. R. Bickham, R. Mishra, "Design concept for optical fibers with enhanced SBS threshold," Opt. Exp. 13, 5338-5346 (2005).
  17. I. Enomori, K. Saitoh, M. Koshiba, "Fundamental characteristics of localized acoustic modes in photonic crystal fibers," IEICE Trans. Electron. E88-C, 876-882 (2005).
  18. W. W. Zou, Z. Y. He, K. Hotate, "Two-dimensional finite-element modal analysis of Brillouin gain spectra in optical fibers ," IEEE Photon. Technol. Lett. 18, 2487-2489 (2006).
  19. B. Ward, J. Spring, "Finite element analysis of Brillouin gain in SBS-suppressing optical fibers with non-uniform acoustic velocity profiles," Opt. Exp. 17, 15 685-15 699 (2009).
  20. M. D. Mermelstein, "SBS threshold measurements and acoustic beam propagation modeling in guiding and antiguiding single mode optical fibers," Opt. Exp. 17, 16225-16237 (2009).
  21. A. H. McCurdy, "Modeling of stimulated Brillouin scattering in optical fibers with arbitrary radial index profile ," J. Lightw. Technol. 23, 3509 (2005).
  22. P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, A. Khelif, "Stimulated Brillouin scattering from multi-ghz-guided acoustic phonons in nanostructured photonic crystal fibres," Nature Phys. 2, 388-392 (2006).
  23. V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, H. Maillotte, "Phononic bandgap guidance of acoustic modes in photonic crystal fibers," Phys. Rev. B 71, 045107-1-045107-6 (2005).
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  25. [Online]. Available: http://www.nenastran.com/nei-nastran.php.
  26. [Online]. Available: http://www.jcmwave.com/.
  27. J. E. McElhenny, R. K. Pattnaik, J. Toulouse, K. Saitoh, M. Koshiba, "Unique characteristic features of stimulated Brillouin scattering in small-core photonic crystal fibers," J. Opt. Soc. Amer. B 25, 582-593 (2008).
  28. B. A. Auld, Acoustic Fields and Waves in Solids (Krieger, 1973).
  29. J. M. Fini, "Improved symmetry analysis of many-moded microstructure optical fibers," J. Opt. Soc. Amer. B 21, 1431-1436 (2004).
  30. A. Safaai-Jazi, C. Jen, G. W. Farnell, "Analysis of weakly guiding fiber acoustic waveguide," IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 59-68 (1986).
  31. K. Furusawa, Z. Yusoff, F. Poletti, T. M. Monro, N. G. R. Broderick, D. J. Richardson, "Brillouin characterization of holey optical fibers," Opt. Lett. 31, 2541-2543 (2006).
  32. S. Herstrom, L. Gruner-Nielsen, B. Palsdottir, "Acoustic index of ge-doped optical fibers," Opt. Lett. 34, 3689-3691 (2009).
  33. W. Zou, Z. He, K. Hotate, "Experimental study of Brillouin scattering in fluorine-doped single-mode optical fibers ," Opt. Exp. 16, 18804-18812 (2008).
  34. F. Poletti, K. Furusawa, Z. Yusoff, N. G. R. Broderick, D. J. Richardson, "Nonlinear tapered holey fibers with high stimulated Brillouin scattering threshold and controlled dispersion," J. Opt. Soc. Amer. B 24, 2185-2194 (2007).

2009 (4)

M. R. Lorenzen, D. Noordegraaf, C. V. Nielsen, O. Odgaard, L. Grüner-Nielsen, K. Rottwitt, "Suppression of Brillouin scattering in fibreoptical parametric amplifier by applying temperature control and phase modulation," Electron. Lett. 45, 125-127 (2009).

B. Ward, J. Spring, "Finite element analysis of Brillouin gain in SBS-suppressing optical fibers with non-uniform acoustic velocity profiles," Opt. Exp. 17, 15 685-15 699 (2009).

M. D. Mermelstein, "SBS threshold measurements and acoustic beam propagation modeling in guiding and antiguiding single mode optical fibers," Opt. Exp. 17, 16225-16237 (2009).

S. Herstrom, L. Gruner-Nielsen, B. Palsdottir, "Acoustic index of ge-doped optical fibers," Opt. Lett. 34, 3689-3691 (2009).

2008 (3)

W. Zou, Z. He, K. Hotate, "Experimental study of Brillouin scattering in fluorine-doped single-mode optical fibers ," Opt. Exp. 16, 18804-18812 (2008).

J. E. McElhenny, R. K. Pattnaik, J. Toulouse, K. Saitoh, M. Koshiba, "Unique characteristic features of stimulated Brillouin scattering in small-core photonic crystal fibers," J. Opt. Soc. Amer. B 25, 582-593 (2008).

M. Laroche, H. Gilles, S. Girard, "Influence of stimulated Brillouin scattering on the temporal dynamics of an actively $Q$-switched double-clad fiber laser," Opt. Commun. 281, 2243-2247 (2008) doi: DOI: 10.1016/j.optcom.2007.11.080.

2007 (6)

A. Liu, "Suppressing stimulated Brillouin scattering in fiber amplifiers using nonuniform fiber and temperature gradient," Opt. Exp. 15, 977-984 (2007).

M.-J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, L. A. Zenteno, "Al/ge co-doped large mode area fiber with high SBS threshold," Opt. Exp. 15, 8290-8299 (2007).

Z. M. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, A. E. Willner, "Broadband SBS slow light in an optical fiber," J. Lightw. Technol. 25, 201-206 (2007).

Z. Zhu, D. J. Gauthier, R. W. Boyd, "Stored light in an optical fiber via stimulated Brillouin scattering," Science 318, 1748-1750 (2007).

F. Ravet, L. Zou, X. Bao, T. Ozbakkaloglu, M. Saatcioglu, J. Zhou, "Distributed Brillouin sensor for structural health monitoring," Can. J. Civil Eng. 34, 291-297 (2007).

F. Poletti, K. Furusawa, Z. Yusoff, N. G. R. Broderick, D. J. Richardson, "Nonlinear tapered holey fibers with high stimulated Brillouin scattering threshold and controlled dispersion," J. Opt. Soc. Amer. B 24, 2185-2194 (2007).

2006 (3)

W. W. Zou, Z. Y. He, K. Hotate, "Two-dimensional finite-element modal analysis of Brillouin gain spectra in optical fibers ," IEEE Photon. Technol. Lett. 18, 2487-2489 (2006).

K. Furusawa, Z. Yusoff, F. Poletti, T. M. Monro, N. G. R. Broderick, D. J. Richardson, "Brillouin characterization of holey optical fibers," Opt. Lett. 31, 2541-2543 (2006).

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, A. Khelif, "Stimulated Brillouin scattering from multi-ghz-guided acoustic phonons in nanostructured photonic crystal fibres," Nature Phys. 2, 388-392 (2006).

2005 (4)

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, H. Maillotte, "Phononic bandgap guidance of acoustic modes in photonic crystal fibers," Phys. Rev. B 71, 045107-1-045107-6 (2005).

A. H. McCurdy, "Modeling of stimulated Brillouin scattering in optical fibers with arbitrary radial index profile ," J. Lightw. Technol. 23, 3509 (2005).

A. Kobyakov, S. Kumar, D. Q. Chowdhury, A. B. Ruffin, M. Sauer, S. R. Bickham, R. Mishra, "Design concept for optical fibers with enhanced SBS threshold," Opt. Exp. 13, 5338-5346 (2005).

I. Enomori, K. Saitoh, M. Koshiba, "Fundamental characteristics of localized acoustic modes in photonic crystal fibers," IEICE Trans. Electron. E88-C, 876-882 (2005).

2004 (3)

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, W. Chujo, "Simulating and designing Brillouin gain spectrum in single-mode fibers," J. Lightw. Technol. 22, 631-639 (2004).

C. J. S. de Matos, J. R. Taylor, K. P. Hansen, "All-fibre Brillouin laser based on holey fibre yielding comb-like spectra," Opt. Commun. 238, 185-189 (2004).

J. M. Fini, "Improved symmetry analysis of many-moded microstructure optical fibers," J. Opt. Soc. Amer. B 21, 1431-1436 (2004).

1999 (1)

E. Peral, A. Yariv, "Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to a phase shift induced by stimulated Brillouin scattering," IEEE J. Quantum Electron. 35, 1185-1195 (1999).

1995 (1)

M. T. M. Shiraki, K. Ohashi, "Suppression of stimulated Brillouin scattering in a fiber by changing the core radius ," Electron. Lett. 31, 668-669 (1995).

1986 (2)

C. K. Jen, A. Safaaijazi, G. W. Farnell, "Leaky modes in weakly guiding fiber acoustic wave-guides," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 33, 634-643 (1986).

A. Safaai-Jazi, C. Jen, G. W. Farnell, "Analysis of weakly guiding fiber acoustic waveguide," IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 59-68 (1986).

1979 (1)

P. J. Thomas, N. L. Rowell, H. M. Vandriel, G. I. Stegeman, "Normal acoustic modes and Brillouin scattering in single-mode optical fibers," Phys. Rev. B 19, 4986-4998 (1979).

Can. J. Civil Eng. (1)

F. Ravet, L. Zou, X. Bao, T. Ozbakkaloglu, M. Saatcioglu, J. Zhou, "Distributed Brillouin sensor for structural health monitoring," Can. J. Civil Eng. 34, 291-297 (2007).

Electron. Lett. (2)

M. R. Lorenzen, D. Noordegraaf, C. V. Nielsen, O. Odgaard, L. Grüner-Nielsen, K. Rottwitt, "Suppression of Brillouin scattering in fibreoptical parametric amplifier by applying temperature control and phase modulation," Electron. Lett. 45, 125-127 (2009).

M. T. M. Shiraki, K. Ohashi, "Suppression of stimulated Brillouin scattering in a fiber by changing the core radius ," Electron. Lett. 31, 668-669 (1995).

IEEE J. Quantum Electron. (1)

E. Peral, A. Yariv, "Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to a phase shift induced by stimulated Brillouin scattering," IEEE J. Quantum Electron. 35, 1185-1195 (1999).

IEEE Photon. Technol. Lett. (1)

W. W. Zou, Z. Y. He, K. Hotate, "Two-dimensional finite-element modal analysis of Brillouin gain spectra in optical fibers ," IEEE Photon. Technol. Lett. 18, 2487-2489 (2006).

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (2)

C. K. Jen, A. Safaaijazi, G. W. Farnell, "Leaky modes in weakly guiding fiber acoustic wave-guides," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 33, 634-643 (1986).

A. Safaai-Jazi, C. Jen, G. W. Farnell, "Analysis of weakly guiding fiber acoustic waveguide," IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-33, 59-68 (1986).

IEICE Trans. Electron. (1)

I. Enomori, K. Saitoh, M. Koshiba, "Fundamental characteristics of localized acoustic modes in photonic crystal fibers," IEICE Trans. Electron. E88-C, 876-882 (2005).

J. Lightw. Technol. (3)

A. H. McCurdy, "Modeling of stimulated Brillouin scattering in optical fibers with arbitrary radial index profile ," J. Lightw. Technol. 23, 3509 (2005).

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, W. Chujo, "Simulating and designing Brillouin gain spectrum in single-mode fibers," J. Lightw. Technol. 22, 631-639 (2004).

Z. M. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, A. E. Willner, "Broadband SBS slow light in an optical fiber," J. Lightw. Technol. 25, 201-206 (2007).

J. Opt. Soc. Amer. B (3)

J. M. Fini, "Improved symmetry analysis of many-moded microstructure optical fibers," J. Opt. Soc. Amer. B 21, 1431-1436 (2004).

J. E. McElhenny, R. K. Pattnaik, J. Toulouse, K. Saitoh, M. Koshiba, "Unique characteristic features of stimulated Brillouin scattering in small-core photonic crystal fibers," J. Opt. Soc. Amer. B 25, 582-593 (2008).

F. Poletti, K. Furusawa, Z. Yusoff, N. G. R. Broderick, D. J. Richardson, "Nonlinear tapered holey fibers with high stimulated Brillouin scattering threshold and controlled dispersion," J. Opt. Soc. Amer. B 24, 2185-2194 (2007).

Nature Phys. (1)

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, A. Khelif, "Stimulated Brillouin scattering from multi-ghz-guided acoustic phonons in nanostructured photonic crystal fibres," Nature Phys. 2, 388-392 (2006).

Opt. Commun. (2)

C. J. S. de Matos, J. R. Taylor, K. P. Hansen, "All-fibre Brillouin laser based on holey fibre yielding comb-like spectra," Opt. Commun. 238, 185-189 (2004).

M. Laroche, H. Gilles, S. Girard, "Influence of stimulated Brillouin scattering on the temporal dynamics of an actively $Q$-switched double-clad fiber laser," Opt. Commun. 281, 2243-2247 (2008) doi: DOI: 10.1016/j.optcom.2007.11.080.

Opt. Exp. (6)

A. Kobyakov, S. Kumar, D. Q. Chowdhury, A. B. Ruffin, M. Sauer, S. R. Bickham, R. Mishra, "Design concept for optical fibers with enhanced SBS threshold," Opt. Exp. 13, 5338-5346 (2005).

B. Ward, J. Spring, "Finite element analysis of Brillouin gain in SBS-suppressing optical fibers with non-uniform acoustic velocity profiles," Opt. Exp. 17, 15 685-15 699 (2009).

M. D. Mermelstein, "SBS threshold measurements and acoustic beam propagation modeling in guiding and antiguiding single mode optical fibers," Opt. Exp. 17, 16225-16237 (2009).

A. Liu, "Suppressing stimulated Brillouin scattering in fiber amplifiers using nonuniform fiber and temperature gradient," Opt. Exp. 15, 977-984 (2007).

M.-J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, L. A. Zenteno, "Al/ge co-doped large mode area fiber with high SBS threshold," Opt. Exp. 15, 8290-8299 (2007).

W. Zou, Z. He, K. Hotate, "Experimental study of Brillouin scattering in fluorine-doped single-mode optical fibers ," Opt. Exp. 16, 18804-18812 (2008).

Opt. Lett. (2)

Phys. Rev. B (2)

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, H. Maillotte, "Phononic bandgap guidance of acoustic modes in photonic crystal fibers," Phys. Rev. B 71, 045107-1-045107-6 (2005).

P. J. Thomas, N. L. Rowell, H. M. Vandriel, G. I. Stegeman, "Normal acoustic modes and Brillouin scattering in single-mode optical fibers," Phys. Rev. B 19, 4986-4998 (1979).

Science (1)

Z. Zhu, D. J. Gauthier, R. W. Boyd, "Stored light in an optical fiber via stimulated Brillouin scattering," Science 318, 1748-1750 (2007).

Other (6)

R. W. Boyd, Nonlinear Optics (Academic, 2008).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

Modeling Guide, COMSOL Version 3.5a 9 and 13 [Online]. Available: http://www.comsol.com/.

[Online]. Available: http://www.nenastran.com/nei-nastran.php.

[Online]. Available: http://www.jcmwave.com/.

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

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