Abstract

A new way to suppress stimulated Brillouin scattering by using an all-solid chalcogenide-tellurite photonic bandgap fiber is presented in the paper. The compositions of the chalcogenide and the tellurite glass are As2Se3 and TeO2-ZnO-Li2O-Bi2O3. The light and the acoustic wave are confined in the fiber by photonic bandgap and acoustic bandgap mechanism, respectively. When the pump wavelength is within the photonic bandgap and the acoustic wave generated by the pump light is outside the acoustic bandgap, the interaction between the optical and the acoustic modes is very weak, thus stimulated Brillouin scattering is suppressed in the photonic bandgap fiber.

© 2012 OSA

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2012

2011

S. Dasgupta, F. Poletti, S. Liu, P. Petropoulos, D. J. Richardson, L. Grüner-Nielsen, and S. Herstrøm, “Modeling Brillouin Gain Spectrum of Solid and Microstructured Optical Fibers Using a Finite Element Method,” J. Lightwave Technol.29(1), 22–30 (2011).
[CrossRef]

R. Parvizi, H. Arof, N. M. Ali, H. Ahmad, and S. W. Harun, “0.16 nm spaced multi-wavelength Brillouin fiber laser in a figure-of-eight configuration,” Opt. Laser Technol.43(4), 866–869 (2011).
[CrossRef]

2010

R. Parvizi, S. W. Harun, N. S. Shahabuddin, Z. Yusoff, and H. Ahmad, “Multi-wavelength bismuth-based erbium-doped fiber laser based on four-wave mixing effect in photonic crystal fiber,” Opt. Laser Technol.42(8), 1250–1252 (2010).
[CrossRef]

S. Chin, L. Thévenaz, J. Sancho, S. Sales, J. Capmany, P. Berger, J. Bourderionnet, and D. Dolfi, “Broadband true time delay for microwave signal processing, using slow light based on stimulated Brillouin scattering in optical fibers,” Opt. Express18(21), 22599–22613 (2010).
[CrossRef] [PubMed]

2009

2008

2007

2006

K. S. Abedin, “Stimulated Brillouin scattering in single-mode tellurite glass fiber,” Opt. Express14(24), 11766–11772 (2006).
[CrossRef] [PubMed]

C. Florea, M. Bashkansky, Z. Dutton, J. Sanghera, P. Pureza, and I. Aggarwal, “Stimulated Brillouin scattering in single-mode As2S3 and As2Se3 chalcogenide fibers,” Opt. Express14(25), 12063–12070 (2006).
[CrossRef] [PubMed]

W. W. Zou, Z. Y. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett.18(23), 2487–2489 (2006).
[CrossRef]

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecher, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys.2(6), 388–392 (2006).
[CrossRef]

2005

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Photonic bandgap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B71(4), 045107 (2005).
[CrossRef]

I. Enomori, K. Saitoh, and M. Koshiba, “Fundamental characteristics of localized acoustic modes in photonic crystal fibers,”IEICE Trans. Electron,” E88-C(2), 876–882 (2005).

2003

2002

2001

1997

M. M. Sigalas, “Elastic wave band gaps and defect states in two-dimensional composites,” J. Acoust. Soc. Am.101(3), 1256–1261 (1997).
[CrossRef]

1996

K. Shiraki, M. Ohashi, and M. Tateda, “Performance of strain-free stimulated Brillouin scattering suppression fiber,” J. Lightwave Technol.14(4), 549–554 (1996).
[CrossRef]

1995

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett.31(8), 668–669 (1995).
[CrossRef]

1988

C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett.24(23), 1419–1420 (1988).
[CrossRef]

1986

M. A. Duguay, Y. Kukubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multiplayer structures,” Appl. Phys. Lett.49(1), 13–15 (1986).
[CrossRef]

1979

P. J. Thomas, N. L. Rowell, H. M. Vandriel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B19(10), 4986–4998 (1979).
[CrossRef]

1972

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett.21(11), 539–541 (1972).
[CrossRef]

Abe, K.

C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett.24(23), 1419–1420 (1988).
[CrossRef]

Abedin, K. S.

Abeeluck, A. K.

Aggarwal, I.

Agrawal, G. P.

Ahmad, H.

R. Parvizi, H. Arof, N. M. Ali, H. Ahmad, and S. W. Harun, “0.16 nm spaced multi-wavelength Brillouin fiber laser in a figure-of-eight configuration,” Opt. Laser Technol.43(4), 866–869 (2011).
[CrossRef]

R. Parvizi, S. W. Harun, N. S. Shahabuddin, Z. Yusoff, and H. Ahmad, “Multi-wavelength bismuth-based erbium-doped fiber laser based on four-wave mixing effect in photonic crystal fiber,” Opt. Laser Technol.42(8), 1250–1252 (2010).
[CrossRef]

Ali, N. M.

R. Parvizi, H. Arof, N. M. Ali, H. Ahmad, and S. W. Harun, “0.16 nm spaced multi-wavelength Brillouin fiber laser in a figure-of-eight configuration,” Opt. Laser Technol.43(4), 866–869 (2011).
[CrossRef]

Andrekson, P. A.

Arof, H.

R. Parvizi, H. Arof, N. M. Ali, H. Ahmad, and S. W. Harun, “0.16 nm spaced multi-wavelength Brillouin fiber laser in a figure-of-eight configuration,” Opt. Laser Technol.43(4), 866–869 (2011).
[CrossRef]

Bao, X. Y.

Bashkansky, M.

Benchabane, S.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Photonic bandgap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B71(4), 045107 (2005).
[CrossRef]

Berger, P.

Bourderionnet, J.

Byrnes, A.

Cahill, J. P.

Capmany, J.

Chaudhari, C.

Chen, L.

Chen, X.

Cherif, R.

R. Cherif, M. Zghal, and L. Tartara, “Characterization of stimulated Brillouin scattering in small core microstructured chalcogenide fiber,” Opt. Commun.285(3), 341–346 (2012).
[CrossRef]

Chin, S.

Choi, D. Y.

Crowley, A. M.

Dainese, P.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecher, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys.2(6), 388–392 (2006).
[CrossRef]

Dasgupta, S.

Demeritt, J. A.

Dolfi, D.

Dross, F.

Dudley, J. M.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Photonic bandgap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B71(4), 045107 (2005).
[CrossRef]

Duguay, M. A.

M. A. Duguay, Y. Kukubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multiplayer structures,” Appl. Phys. Lett.49(1), 13–15 (1986).
[CrossRef]

Dutton, Z.

Eggleton, B. J.

Enomori, I.

I. Enomori, K. Saitoh, and M. Koshiba, “Fundamental characteristics of localized acoustic modes in photonic crystal fibers,”IEICE Trans. Electron,” E88-C(2), 876–882 (2005).

Florea, C.

Fragnito, H. L.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecher, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys.2(6), 388–392 (2006).
[CrossRef]

Goto, N.

C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett.24(23), 1419–1420 (1988).
[CrossRef]

Gray, S.

Grüner-Nielsen, L.

Hansryd, J.

Harun, S. W.

R. Parvizi, H. Arof, N. M. Ali, H. Ahmad, and S. W. Harun, “0.16 nm spaced multi-wavelength Brillouin fiber laser in a figure-of-eight configuration,” Opt. Laser Technol.43(4), 866–869 (2011).
[CrossRef]

R. Parvizi, S. W. Harun, N. S. Shahabuddin, Z. Yusoff, and H. Ahmad, “Multi-wavelength bismuth-based erbium-doped fiber laser based on four-wave mixing effect in photonic crystal fiber,” Opt. Laser Technol.42(8), 1250–1252 (2010).
[CrossRef]

He, Z. Y.

R. K. Yamashita, W. W. Zou, Z. Y. He, and K. Hotate, “Measurement Range Elongation Based on Temporal Gating in Brillouin Optical Correlation Domain Distributed Simultaneous Sensing of Strain and Temperature,” IEEE Photon. Technol. Lett.24(12), 1006–1008 (2012).
[CrossRef]

W. W. Zou, Z. Y. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett.18(23), 2487–2489 (2006).
[CrossRef]

Headley, C.

Herstrøm, S.

Hotate, K.

R. K. Yamashita, W. W. Zou, Z. Y. He, and K. Hotate, “Measurement Range Elongation Based on Temporal Gating in Brillouin Optical Correlation Domain Distributed Simultaneous Sensing of Strain and Temperature,” IEEE Photon. Technol. Lett.24(12), 1006–1008 (2012).
[CrossRef]

W. W. Zou, Z. Y. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett.18(23), 2487–2489 (2006).
[CrossRef]

Ippen, E. P.

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett.21(11), 539–541 (1972).
[CrossRef]

Jen, C. K.

C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett.24(23), 1419–1420 (1988).
[CrossRef]

Joly, N.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecher, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys.2(6), 388–392 (2006).
[CrossRef]

Khelif, A.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecher, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys.2(6), 388–392 (2006).
[CrossRef]

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Photonic bandgap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B71(4), 045107 (2005).
[CrossRef]

Kibler, B.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Photonic bandgap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B71(4), 045107 (2005).
[CrossRef]

Kito, C.

Knight, J. C.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecher, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys.2(6), 388–392 (2006).
[CrossRef]

Knudsen, S. N.

Koch, T. L.

M. A. Duguay, Y. Kukubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multiplayer structures,” Appl. Phys. Lett.49(1), 13–15 (1986).
[CrossRef]

Koshiba, M.

I. Enomori, K. Saitoh, and M. Koshiba, “Fundamental characteristics of localized acoustic modes in photonic crystal fibers,”IEICE Trans. Electron,” E88-C(2), 876–882 (2005).

Kukubun, Y.

M. A. Duguay, Y. Kukubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multiplayer structures,” Appl. Phys. Lett.49(1), 13–15 (1986).
[CrossRef]

Kurashima, T.

Laude, V.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecher, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys.2(6), 388–392 (2006).
[CrossRef]

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Photonic bandgap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B71(4), 045107 (2005).
[CrossRef]

Lee, H.

Li, E. B.

Li, M. J.

Li, W.

Liao, M. S.

Litchinitser, N. M.

Liu, A.

Liu, S.

Luther-Davies, B.

Madden, S.

Maillotte, H.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Photonic bandgap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B71(4), 045107 (2005).
[CrossRef]

Martijnde Sterke, C.

Matsui, T.

Matsumoto, M.

McPhedran, R. C.

Misumi, T.

Mori, A.

Mungan, C. E.

Mussot, A.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Photonic bandgap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B71(4), 045107 (2005).
[CrossRef]

Ohashi, M.

K. Shiraki, M. Ohashi, and M. Tateda, “Performance of strain-free stimulated Brillouin scattering suppression fiber,” J. Lightwave Technol.14(4), 549–554 (1996).
[CrossRef]

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett.31(8), 668–669 (1995).
[CrossRef]

Ohishi, Y.

Okusaga, O.

Oliveira, J. E. B.

C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett.24(23), 1419–1420 (1988).
[CrossRef]

Pant, R.

Parvizi, R.

R. Parvizi, H. Arof, N. M. Ali, H. Ahmad, and S. W. Harun, “0.16 nm spaced multi-wavelength Brillouin fiber laser in a figure-of-eight configuration,” Opt. Laser Technol.43(4), 866–869 (2011).
[CrossRef]

R. Parvizi, S. W. Harun, N. S. Shahabuddin, Z. Yusoff, and H. Ahmad, “Multi-wavelength bismuth-based erbium-doped fiber laser based on four-wave mixing effect in photonic crystal fiber,” Opt. Laser Technol.42(8), 1250–1252 (2010).
[CrossRef]

Petropoulos, P.

Pfeiffer, L.

M. A. Duguay, Y. Kukubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multiplayer structures,” Appl. Phys. Lett.49(1), 13–15 (1986).
[CrossRef]

Poletti, F.

Poulton, C. G.

Pureza, P.

Qin, G. S.

Rakuljic, G.

Richardson, D. J.

Rowell, N. L.

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[CrossRef]

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K. Shiraki, M. Ohashi, and M. Tateda, “Performance of strain-free stimulated Brillouin scattering suppression fiber,” J. Lightwave Technol.14(4), 549–554 (1996).
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P. J. Thomas, N. L. Rowell, H. M. Vandriel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B19(10), 4986–4998 (1979).
[CrossRef]

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Vandriel, H. M.

P. J. Thomas, N. L. Rowell, H. M. Vandriel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B19(10), 4986–4998 (1979).
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P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecher, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys.2(6), 388–392 (2006).
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V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Photonic bandgap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B71(4), 045107 (2005).
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R. Parvizi, S. W. Harun, N. S. Shahabuddin, Z. Yusoff, and H. Ahmad, “Multi-wavelength bismuth-based erbium-doped fiber laser based on four-wave mixing effect in photonic crystal fiber,” Opt. Laser Technol.42(8), 1250–1252 (2010).
[CrossRef]

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Zghal, M.

R. Cherif, M. Zghal, and L. Tartara, “Characterization of stimulated Brillouin scattering in small core microstructured chalcogenide fiber,” Opt. Commun.285(3), 341–346 (2012).
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Zou, L. F.

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R. K. Yamashita, W. W. Zou, Z. Y. He, and K. Hotate, “Measurement Range Elongation Based on Temporal Gating in Brillouin Optical Correlation Domain Distributed Simultaneous Sensing of Strain and Temperature,” IEEE Photon. Technol. Lett.24(12), 1006–1008 (2012).
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R. K. Yamashita, W. W. Zou, Z. Y. He, and K. Hotate, “Measurement Range Elongation Based on Temporal Gating in Brillouin Optical Correlation Domain Distributed Simultaneous Sensing of Strain and Temperature,” IEEE Photon. Technol. Lett.24(12), 1006–1008 (2012).
[CrossRef]

W. W. Zou, Z. Y. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett.18(23), 2487–2489 (2006).
[CrossRef]

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I. Enomori, K. Saitoh, and M. Koshiba, “Fundamental characteristics of localized acoustic modes in photonic crystal fibers,”IEICE Trans. Electron,” E88-C(2), 876–882 (2005).

J. Acoust. Soc. Am.

M. M. Sigalas, “Elastic wave band gaps and defect states in two-dimensional composites,” J. Acoust. Soc. Am.101(3), 1256–1261 (1997).
[CrossRef]

J. Lightwave Technol.

Nat. Phys.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecher, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys.2(6), 388–392 (2006).
[CrossRef]

Opt. Commun.

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M. J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno, “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express15(13), 8290–8299 (2007).
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R. Parvizi, S. W. Harun, N. S. Shahabuddin, Z. Yusoff, and H. Ahmad, “Multi-wavelength bismuth-based erbium-doped fiber laser based on four-wave mixing effect in photonic crystal fiber,” Opt. Laser Technol.42(8), 1250–1252 (2010).
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R. Parvizi, H. Arof, N. M. Ali, H. Ahmad, and S. W. Harun, “0.16 nm spaced multi-wavelength Brillouin fiber laser in a figure-of-eight configuration,” Opt. Laser Technol.43(4), 866–869 (2011).
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Phys. Rev. B

P. J. Thomas, N. L. Rowell, H. M. Vandriel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B19(10), 4986–4998 (1979).
[CrossRef]

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Photonic bandgap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B71(4), 045107 (2005).
[CrossRef]

Other

M. Takahashi, J. Hiroishi, M. Tadakuma, and T. Yagi, “Improvement of FWM conversion efficiency by SBS-suppressed highly nonlinear dispersion-decreasing fiber with a strain distribution,” in Proc. ECOC (2008).

P. D. Dragic, C. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” in Proc. CLEO (2005).

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Figures (9)

Fig. 1
Fig. 1

The cross-sectional structure of all-solid chalcogenide-tellurite PBGF.

Fig. 2
Fig. 2

The refractive index (a), and the velocity of the longitudinal acoustic wave (b) profile along the X axis of all-solid chalcogenide-tellurite PBGF.

Fig. 3
Fig. 3

The confinement loss of all-solid chalcogenide-tellurite PBGF.

Fig. 4
Fig. 4

BGS of all-solid chalcogenide-tellurite PBGF at λ = 1.55 μm.

Fig. 5
Fig. 5

BGS of air-hole tellurite PBGF at λ = 1.55 μm.

Fig. 6
Fig. 6

The fundamental optical mode (a), and the acoustic mode (b) of all-solid chalcogenide-tellurite PBGF at λ = 1.55 μm.

Fig. 7
Fig. 7

The fundamental optical mode (a), and the acoustic mode (b) of air-hole tellurite PBGF at λ = 1.55 μm.

Fig. 8
Fig. 8

BGS of all-solid chalcogenide-tellurite PBGF at λ = 1.65 μm.

Fig. 9
Fig. 9

The fundamental optical mode (a), and the acoustic mode (b) of all-solid chalcogenide-tellurite PBGF at λ = 1.65 μm.

Equations (11)

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

t 2 E+( 2π λ )( n 2 n eff )E=0
t 2 u+( ω a 2 v 2 β a 2 )u=0
f B,i = 2 n eff v i λ
S B,i (f)= Δ f 2 B 4 (f f B,i ) 2 +Δ f 2 B I i g B,i
I i = ( | E(x,y) | 2 u i * (x,y)dxdy ) 2 | E(x,y) | 4 dxdy | u i (x,y) | 2 dxdy
g B,i = 4π n eff 8 p 12 2 λ 3 ρc f B,i Δ f B
S B (f)= i S B,i (f)
P th K A eff α i G( v max ,L) I i
exp(ilx+ihziwt)=exp(ihziwt)× n= J n (lr)exp(inθ)
u x (x,y,z;t)=P (x,y) T u x cos(ωtkz) u y (x,y,z;t)=P (x,y) T u y cos(ωtkz) u z (x,y,z;t)=P (x,y) T u z sin(ωtkz) }
n 2 (λ)=1+ i=1 l A i λ 2 λ 2 L i 2

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