Abstract

The numerical study of acoustic modal properties in w-shaped optical fibers with high-delta germanium-doped core and F-doped inner cladding (F-HDF) is demonstrated. The cutoff conditions of acoustic modes in the F-HDF show opposite behaviors in contrast with those of optical ones because F-doped inner cladding contributes differently to acoustic and optical waveguides. The acoustic dispersion characteristics vary to a great extent with respect to the location of the acoustic modes in the fiber’s core or in the fiber’s inner cladding. The resonance frequency spacing between neighboring acoustic modes is theoretically and experimentally found to have a quadratic relation to the core’s germanium concentration. We also investigate the critical conditions to move high-order acoustic modes into the F-doped inner cladding and validate the optimal feasibility of employing L 01 and L 03 acoustic modes to fiber-optic Brillouin-based discriminative sensing of strain and temperature.

© 2008 Optical Society of America

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References

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  1. A. Kobyakov, S. Kumar, D. Q. Chowdhury, A. B. Ruffin, M. Sauer, and S. R. Bickham, "Design concept for optical fibers with enhanced SBS threshold," Opt. Express 13, 5338-5346 (2005).
    [CrossRef] [PubMed]
  2. M. J. Li, S. Li and D. A. Nolan, "Nonlinear fibers for signal processing using Kerr effects," J. Lightwave Technol. 23, 3606-3614 (2005).
    [CrossRef]
  3. S. R. Bickham, X. Chen, M. J. Li, and D. T. Walton, "High SBS threshold optical fiber with fluorine dopant," U. S. Patent 7228039 (June 2007).
  4. I. Flammer, "Optical fiber with reduced stimulated Brillouin scattering," U. S. Patent application, 2007/0081779 (April 2007)
  5. M. Nikles, L. Thevenaz, P. A. Robert, "Simple distributed fiber sensor based on Brillouin gain spectrum analysis," Opt. Lett. 21, 738-740 (1996).
    [CrossRef]
  6. K. Hotate and M. Tanaka, "Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlationbased continuous-wave technique," IEEE Photon. Technol. Lett. 14, 179-181 (2002).
    [CrossRef]
  7. W. Zou, Z. He, M. Kishi, and K. Hotate, "Stimulated Brillouin scattering and its dependences on temperature and strain in a high-delta optical fiber with F-doped depressed inner cladding," Opt. Lett. 32, 600-602 (2007).
    [CrossRef] [PubMed]
  8. A. Yeniay, J. M. Delavaux, and J. Toulouse, "Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers," J. Lightwave Technol. 20, 1425-1432 (2002).
    [CrossRef]
  9. M. Monerie, "Propagation in doubly clad single-mode fibers," IEEE J. Quantum Electron. QE-18, 535-542 (1982).
    [CrossRef]
  10. B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, "The design and fabrication of monomode optical fiber," IEEE J. Quantum Electron. QE-18, 514-523 (1982).
    [CrossRef]
  11. 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]
  12. Y. Y. Huang, A. Sarkar, and P. C. Schultz, "Relationship between composition, density and refractive index for germania silica glasses," J. Non-Cryst. Solid. 27, 29-37 (1978).
    [CrossRef]
  13. Y. Park, K. Oh, U. C. Paek, D. Y. Kim, and C. R. Kurkjian, "Residual stresses in a doubly clad fiber with depressed inner cladding (DIC)," J. Lightwave Technol. 17, 1823-1834 (1999).
    [CrossRef]
  14. W. Zou, Z. He, A. D. Yablon, and K. Hotate, "Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains," IEEE Photon. Technol. Lett. 19, 1389-1391 (2007).
    [CrossRef]
  15. T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, "Refractive index and material dispersions of multi-component oxide glasses," J. Non-Cryst. Solid. 210, 155-162 (1997).
    [CrossRef]
  16. C. Su, "Eigenproblems of radially inhomogeneous optical fibers from the scalar formulation," IEEE J. Quantum Electron. QE-10, 1554-1557 (1985).
  17. E. Peral and A. Yariv, "Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to shift induced by stimulated Brillouin scattering," IEEE J. Quantum Electron. 35, 1185-1195 (1999).
    [CrossRef]
  18. W. Zou, Z. He, and K. Hotate, "Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers," IEEE Photon. Technol. Lett. 18, 2487-2489 (2006).
    [CrossRef]

2007 (2)

W. Zou, Z. He, A. D. Yablon, and K. Hotate, "Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains," IEEE Photon. Technol. Lett. 19, 1389-1391 (2007).
[CrossRef]

W. Zou, Z. He, M. Kishi, and K. Hotate, "Stimulated Brillouin scattering and its dependences on temperature and strain in a high-delta optical fiber with F-doped depressed inner cladding," Opt. Lett. 32, 600-602 (2007).
[CrossRef] [PubMed]

2006 (1)

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

2005 (2)

2004 (1)

2002 (2)

A. Yeniay, J. M. Delavaux, and J. Toulouse, "Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers," J. Lightwave Technol. 20, 1425-1432 (2002).
[CrossRef]

K. Hotate and M. Tanaka, "Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlationbased continuous-wave technique," IEEE Photon. Technol. Lett. 14, 179-181 (2002).
[CrossRef]

1999 (2)

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

Y. Park, K. Oh, U. C. Paek, D. Y. Kim, and C. R. Kurkjian, "Residual stresses in a doubly clad fiber with depressed inner cladding (DIC)," J. Lightwave Technol. 17, 1823-1834 (1999).
[CrossRef]

1997 (1)

T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, "Refractive index and material dispersions of multi-component oxide glasses," J. Non-Cryst. Solid. 210, 155-162 (1997).
[CrossRef]

1996 (1)

M. Nikles, L. Thevenaz, P. A. Robert, "Simple distributed fiber sensor based on Brillouin gain spectrum analysis," Opt. Lett. 21, 738-740 (1996).
[CrossRef]

1985 (1)

C. Su, "Eigenproblems of radially inhomogeneous optical fibers from the scalar formulation," IEEE J. Quantum Electron. QE-10, 1554-1557 (1985).

1982 (2)

M. Monerie, "Propagation in doubly clad single-mode fibers," IEEE J. Quantum Electron. QE-18, 535-542 (1982).
[CrossRef]

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, "The design and fabrication of monomode optical fiber," IEEE J. Quantum Electron. QE-18, 514-523 (1982).
[CrossRef]

1978 (1)

Y. Y. Huang, A. Sarkar, and P. C. Schultz, "Relationship between composition, density and refractive index for germania silica glasses," J. Non-Cryst. Solid. 27, 29-37 (1978).
[CrossRef]

Ainslie, B. J.

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, "The design and fabrication of monomode optical fiber," IEEE J. Quantum Electron. QE-18, 514-523 (1982).
[CrossRef]

Beales, K. J.

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, "The design and fabrication of monomode optical fiber," IEEE J. Quantum Electron. QE-18, 514-523 (1982).
[CrossRef]

Bickham, S. R.

Chowdhury, D. Q.

Chujo, W.

Day, C. R.

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, "The design and fabrication of monomode optical fiber," IEEE J. Quantum Electron. QE-18, 514-523 (1982).
[CrossRef]

Delavaux, J. M.

Fujino, S.

T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, "Refractive index and material dispersions of multi-component oxide glasses," J. Non-Cryst. Solid. 210, 155-162 (1997).
[CrossRef]

He, Z.

W. Zou, Z. He, A. D. Yablon, and K. Hotate, "Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains," IEEE Photon. Technol. Lett. 19, 1389-1391 (2007).
[CrossRef]

W. Zou, Z. He, M. Kishi, and K. Hotate, "Stimulated Brillouin scattering and its dependences on temperature and strain in a high-delta optical fiber with F-doped depressed inner cladding," Opt. Lett. 32, 600-602 (2007).
[CrossRef] [PubMed]

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

Hotate, K.

W. Zou, Z. He, A. D. Yablon, and K. Hotate, "Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains," IEEE Photon. Technol. Lett. 19, 1389-1391 (2007).
[CrossRef]

W. Zou, Z. He, M. Kishi, and K. Hotate, "Stimulated Brillouin scattering and its dependences on temperature and strain in a high-delta optical fiber with F-doped depressed inner cladding," Opt. Lett. 32, 600-602 (2007).
[CrossRef] [PubMed]

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

K. Hotate and M. Tanaka, "Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlationbased continuous-wave technique," IEEE Photon. Technol. Lett. 14, 179-181 (2002).
[CrossRef]

Huang, Y. Y.

Y. Y. Huang, A. Sarkar, and P. C. Schultz, "Relationship between composition, density and refractive index for germania silica glasses," J. Non-Cryst. Solid. 27, 29-37 (1978).
[CrossRef]

Kim, D. Y.

Kishi, M.

Kobyakov, A.

Koyamada, Y.

Kumar, S.

Kurkjian, C. R.

Li, M. J.

Li, S.

Mito, T.

T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, "Refractive index and material dispersions of multi-component oxide glasses," J. Non-Cryst. Solid. 210, 155-162 (1997).
[CrossRef]

Monerie, M.

M. Monerie, "Propagation in doubly clad single-mode fibers," IEEE J. Quantum Electron. QE-18, 535-542 (1982).
[CrossRef]

Morinaga, K.

T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, "Refractive index and material dispersions of multi-component oxide glasses," J. Non-Cryst. Solid. 210, 155-162 (1997).
[CrossRef]

Nakamura, S.

Nikles, M.

M. Nikles, L. Thevenaz, P. A. Robert, "Simple distributed fiber sensor based on Brillouin gain spectrum analysis," Opt. Lett. 21, 738-740 (1996).
[CrossRef]

Nolan, D. A.

Oh, K.

Paek, U. C.

Park, Y.

Peral, E.

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

Robert, P. A.

M. Nikles, L. Thevenaz, P. A. Robert, "Simple distributed fiber sensor based on Brillouin gain spectrum analysis," Opt. Lett. 21, 738-740 (1996).
[CrossRef]

Ruffin, A. B.

Rush, J. D.

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, "The design and fabrication of monomode optical fiber," IEEE J. Quantum Electron. QE-18, 514-523 (1982).
[CrossRef]

Sakaguchi, S.

T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, "Refractive index and material dispersions of multi-component oxide glasses," J. Non-Cryst. Solid. 210, 155-162 (1997).
[CrossRef]

Sarkar, A.

Y. Y. Huang, A. Sarkar, and P. C. Schultz, "Relationship between composition, density and refractive index for germania silica glasses," J. Non-Cryst. Solid. 27, 29-37 (1978).
[CrossRef]

Sato, S.

Sauer, M.

Schultz, P. C.

Y. Y. Huang, A. Sarkar, and P. C. Schultz, "Relationship between composition, density and refractive index for germania silica glasses," J. Non-Cryst. Solid. 27, 29-37 (1978).
[CrossRef]

Sotobayashi, H.

Su, C.

C. Su, "Eigenproblems of radially inhomogeneous optical fibers from the scalar formulation," IEEE J. Quantum Electron. QE-10, 1554-1557 (1985).

Takeba, H.

T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, "Refractive index and material dispersions of multi-component oxide glasses," J. Non-Cryst. Solid. 210, 155-162 (1997).
[CrossRef]

Tanaka, M.

K. Hotate and M. Tanaka, "Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlationbased continuous-wave technique," IEEE Photon. Technol. Lett. 14, 179-181 (2002).
[CrossRef]

Thevenaz, L.

M. Nikles, L. Thevenaz, P. A. Robert, "Simple distributed fiber sensor based on Brillouin gain spectrum analysis," Opt. Lett. 21, 738-740 (1996).
[CrossRef]

Todoroki, S.

T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, "Refractive index and material dispersions of multi-component oxide glasses," J. Non-Cryst. Solid. 210, 155-162 (1997).
[CrossRef]

Toulouse, J.

Yablon, A. D.

W. Zou, Z. He, A. D. Yablon, and K. Hotate, "Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains," IEEE Photon. Technol. Lett. 19, 1389-1391 (2007).
[CrossRef]

Yariv, A.

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

Yeniay, A.

Zou, W.

W. Zou, Z. He, A. D. Yablon, and K. Hotate, "Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains," IEEE Photon. Technol. Lett. 19, 1389-1391 (2007).
[CrossRef]

W. Zou, Z. He, M. Kishi, and K. Hotate, "Stimulated Brillouin scattering and its dependences on temperature and strain in a high-delta optical fiber with F-doped depressed inner cladding," Opt. Lett. 32, 600-602 (2007).
[CrossRef] [PubMed]

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

IEEE J. Quantum Electron. (4)

M. Monerie, "Propagation in doubly clad single-mode fibers," IEEE J. Quantum Electron. QE-18, 535-542 (1982).
[CrossRef]

B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, "The design and fabrication of monomode optical fiber," IEEE J. Quantum Electron. QE-18, 514-523 (1982).
[CrossRef]

C. Su, "Eigenproblems of radially inhomogeneous optical fibers from the scalar formulation," IEEE J. Quantum Electron. QE-10, 1554-1557 (1985).

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

IEEE Photon. Technol. Lett. (3)

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

W. Zou, Z. He, A. D. Yablon, and K. Hotate, "Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains," IEEE Photon. Technol. Lett. 19, 1389-1391 (2007).
[CrossRef]

K. Hotate and M. Tanaka, "Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlationbased continuous-wave technique," IEEE Photon. Technol. Lett. 14, 179-181 (2002).
[CrossRef]

J. Lightwave Technol. (4)

J. Non-Cryst. Solid. (2)

Y. Y. Huang, A. Sarkar, and P. C. Schultz, "Relationship between composition, density and refractive index for germania silica glasses," J. Non-Cryst. Solid. 27, 29-37 (1978).
[CrossRef]

T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, "Refractive index and material dispersions of multi-component oxide glasses," J. Non-Cryst. Solid. 210, 155-162 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (2)

S. R. Bickham, X. Chen, M. J. Li, and D. T. Walton, "High SBS threshold optical fiber with fluorine dopant," U. S. Patent 7228039 (June 2007).

I. Flammer, "Optical fiber with reduced stimulated Brillouin scattering," U. S. Patent application, 2007/0081779 (April 2007)

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Figures (10)

Fig. 1.
Fig. 1.

Schematic diagrams of transverse profiles of refractive index (ni ), longitudinal acoustic velocity (Vli ), and longitudinal acoustic index (Ni ) in an F-HDF. The subscripts i=1, 2, 0 correspond to the core, inner cladding and outer cladding, respectively.

Fig. 2.
Fig. 2.

Ratio of v ac /v op as a function of GeO2 concentration in the physical core (w 1, in unit of mol%).

Fig. 3.
Fig. 3.

(a) Optical cutoff v0op and (b) acoustic cutoff v0ac as functions of concentration ratio R for different radius ratio S.

Fig. 4.
Fig. 4.

Acoustic dispersion curves of Wac /S as functions of v ac for L 01, L 02 and L 03 modes, respectively, when w 1=10 mol%. (a) R=0.05; (b) R=0.10. The radius ratio S is 1.0, 2.0, 3.5 or 5.0 for the same-color cluster of curves from right to left. Al point (l=1, 2 or 3) depicts the crossing point of the based line with the dispersion curve of lth-order acoustic mode.

Fig. 5.
Fig. 5.

Optical LP 01 and acoustic L 0l field distributions in the calculated core region when w 1=10 mol%, R=0.05 and S=1.5. (a) v ac =9.54>v(3) c-ac ; (b) v ac =8.12=v(3) c-ac ; (c) v ac =7.03<v(3) c-ac ; (d) v ac =6.53<v(3) c-ac . The dashed-dotted lines are used to separate the physical core and the physical inner cladding.

Fig. 6.
Fig. 6.

Acoustic critical v(l) c-ac of lth-order mode and acoustic cutoff v(l+1) 0ac of (l+1)thorder mode as functions of concentration ratio R for different radius ratio S when w 1=10 mol%. (a) l=2; (b) l=3.

Fig. 7.
Fig. 7.

Simulated BGS in an F-HDF demonstrated by Yeniay et al. [8]. A dashed line distinguishes the two groups of BGS in the GeO2-doped core and the F-doped inner cladding, respectively.

Fig. 8.
Fig. 8.

(a) Acoustic dispersion curves for w 1=3.65 mol% (curves with circle symbols) and w 1=10 mol% (curves without circle symbols) when the concentration ratio R=0.05 and the radius ratio S=3.5. (b) Measured BGS of a 3.65-mol% step-index SMF (solid curve) and of a 17.0-mol% high-delta fiber (dashed curve).

Fig. 9.
Fig. 9.

(a) Each resonance frequency change, and (b) gain ratio (g 1/g 2 and g 1/g 3, respectively) and optical effective area (Aeff ) as functions of optical v op for S=1.5, R=0.05 and w 1=10 mol%.

Fig. 10.
Fig. 10.

Simulated BGS in an optimally-designed fiber for application of L 01 and L 03 acoustic modes in discriminative sensing. Note that its optical effective area (Aeff =53 µm 2) is comparable to that of a standard SMF (~80 µm 2) and the Brillouin gain of L 03 acoustic mode is only ~-5 dB lower than that of L 01 mode.

Equations (16)

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

N i = V l 0 V li .
n i = n 0 ( 1 + 1.0 × 10 3 w 1 3.3 × 10 3 w 2 ) ,
N i = N 0 ( 1 + 7.2 × 10 3 w 1 + 2.7 × 10 2 w 2 ) ,
a 2 E i + ( v op 2 P op 2 W op 2 ) E i = 0 ,
v op = k 0 a 1 n 1 2 n 0 2 , P op = a 2 a 1 n i ( r ) 2 n 0 2 n 1 2 n 0 2 , W op = k 0 a 2 n eff 2 n 0 2 ,
n · a E i + W op · K 1 ( W op ) K 0 ( W op ) E i = 0 ,
2 u z + ( ω ac ( l ) V l 1 2 β ac 2 ) u z = 0 ,
a 2 u z + [ v ac 2 P ac 2 W ac 2 · N i ( r ) 2 ] u z = 0 ,
v ac = β ac a 1 N 1 2 N 0 2 , P ac = a 2 a 1 N i ( r ) 2 N 0 2 N 1 2 N 0 2 , W ac = β ac a 2 1 1 N eff 2 ,
v ac ( l ) = 2 V l 0 λ o n eff N eff ( l ) .
A eff ao ( l ) = [ < E i 2 > < u z ( l ) E i 2 > ] 2 < u z ( l ) 2 > ,
v ac v op = 2 n eff N 1 2 N 0 2 n 1 2 n 0 2 ,
n · a E i = 0 , n · a E i + E i = 0 ,
v ac ( l ) = 2 V l 0 λ o b ( n 1 2 n 0 2 ) + n 0 2 W ac ( l ) 2 S 2 4 k 0 2 a 1 2 ,
Δ v ac ( l ) 1 v ac ( l ) V l 0 2 λ 0 2 W ac ( l ) 2 S 2 W ac ( l + 1 ) 2 S 2 2 k 0 2 a 1 2 .
A eff = < E i 2 > 2 < E i 4 >

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