Abstract

We report theoretical and experimental analysis on Brillouin frequency shift in silica optical fibers with the double cladding structures that are comprised of GeO2-doped core, P2O5- and F-codoped inner cladding and silica outer cladding. The intrinsic Brillouin frequency shift was calculated for various fiber parameters utilizing boundary conditions for longitudinal acoustic waves. Optical fibers with different fiber parameters were fabricated and the Brillouin frequency shifts were measured in the wavelength region of 1.55μm. We confirmed that the inner cladding in an optical fiber could provide a new degree of freedom in controlling the Brillouin frequency shift.

© 2002 Optical Society of America

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References

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  1. S. J. Strutz, and K. J. Williams, �??Low-noise hybrid erbium/Brillouin amplifier,�?? Electron. Lett. 36, 1359-1360 (2000).
    [CrossRef]
  2. G. J. Cowle, D. Y. Stepanov, and Y. T. Chieng, �??Brillouin/Erbium Fiber Lasers,�?? J. Lightwave Technol. 15, 1198-1204 (1997).
    [CrossRef]
  3. B. Min, P. Kim, and N. Park, �??Flat amplitude equal spacing 798-channel Rayleigh-assited Brillouin/Raman multiwavelength comb generation in dispersion compensation fiber,�?? IEEE Photon. Technol. Lett. 13, 1352-1354 (2001).
    [CrossRef]
  4. H. H. Kee, G. P. Lees, and T. P. Newson, �??All-fiber system for simultaneous interrogation of distributed strain and temperature sensing by spontaneous Brillouin scattering,�?? Opt. Lett. 25, 1-3 (2000).
    [CrossRef]
  5. M. Nikles, L. Thevenaz, and P. A. Robert, �??Brillouin gain spectrum characterization in single-mode optical fibers,�?? J. Lightwave Technol. 15, 1842-1851 (1997).
    [CrossRef]
  6. K. Shiraki, M. Ohashi, and M. Tateda, �??Suppression of stimulated Brillouin scattering in a fiber by changing the core radius,�?? Electron. Lett. 31, 668-669 (1995).
    [CrossRef]
  7. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1950), Chap. 9.
  8. 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]
  9. B. A. Auld, Acoustic Fields and Waves in Solids (John Wiley-Sons, 1973).
  10. A. Safaai-Jazi, and R. O. Claus, �??Acoustic modes in optical fiberlike waveguides,�?? IEEE Trans. Ultrason., Ferroelec., Freq. Contr. 35, 619-627 (1988).
    [CrossRef]
  11. 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, 1823-1833 (1999).
    [CrossRef]
  12. S. P. Timoshenko, and J. N. Goodier, Theory of Elasticity (McGraw Hill, 1970).
  13. D. Cotter, �??Stimulated Brillouin scattering in monomode optical fiber,�?? J. Opt. Commun. 4, 10-19 (1983).
  14. G. W. McLellan, and E. B. Shand, Glass Engineering Handbook (McGraw Hill, 1984).

Electron. Lett.

S. J. Strutz, and K. J. Williams, �??Low-noise hybrid erbium/Brillouin amplifier,�?? Electron. Lett. 36, 1359-1360 (2000).
[CrossRef]

K. Shiraki, M. Ohashi, and M. Tateda, �??Suppression of stimulated Brillouin scattering in a fiber by changing the core radius,�?? Electron. Lett. 31, 668-669 (1995).
[CrossRef]

IEEE Photon. Technol. Lett.

B. Min, P. Kim, and N. Park, �??Flat amplitude equal spacing 798-channel Rayleigh-assited Brillouin/Raman multiwavelength comb generation in dispersion compensation fiber,�?? IEEE Photon. Technol. Lett. 13, 1352-1354 (2001).
[CrossRef]

IEEE Trans. Ultrason., Ferroelec., Freq.

A. Safaai-Jazi, and R. O. Claus, �??Acoustic modes in optical fiberlike waveguides,�?? IEEE Trans. Ultrason., Ferroelec., Freq. Contr. 35, 619-627 (1988).
[CrossRef]

J. Lightwave Technol.

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, 1823-1833 (1999).
[CrossRef]

M. Nikles, L. Thevenaz, and P. A. Robert, �??Brillouin gain spectrum characterization in single-mode optical fibers,�?? J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

G. J. Cowle, D. Y. Stepanov, and Y. T. Chieng, �??Brillouin/Erbium Fiber Lasers,�?? J. Lightwave Technol. 15, 1198-1204 (1997).
[CrossRef]

J. Opt. Commun.

D. Cotter, �??Stimulated Brillouin scattering in monomode optical fiber,�?? J. Opt. Commun. 4, 10-19 (1983).

Opt. Lett.

Phys. Rev. B

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

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

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1950), Chap. 9.

G. W. McLellan, and E. B. Shand, Glass Engineering Handbook (McGraw Hill, 1984).

S. P. Timoshenko, and J. N. Goodier, Theory of Elasticity (McGraw Hill, 1970).

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Figures (7)

Fig. 1.
Fig. 1.

The schematics of refractive index profile of the optical fiber with the matched inner cladding. a , b , and c are the radii of core, inner cladding, and outer cladding, respectively.

Fig. 2.
Fig. 2.

The calculated thermal stress profile of optical fiber. σr , σθ , and σz are the radial, circumferential, and axial thermal stress, respectively. Core radius a =3 μm, outer radius of inner cladding b =6.32 μm, and outer radius of outer cladding c =62.5μm [11].

Fig. 3.
Fig. 3.

Corresponding density distribution. The density in the absence of volumetric stress is 2,220kg/m3 [14].

Fig. 4.
Fig. 4.

The effect of inner cladding radius, b , on Brillouin frequency shift: An optical fiber is assumed to be composed of GeO2-doped core, P2O5- and F-doped inner cladding, and pure silica outer cladding where acoustic frequencies are given by V L1 =5,691, V L2 =5,677, and V L3 =5,759m/s. Note that the acoustic velocity at the inner cladding is lower than that at the core.

Fig. 5.
Fig. 5.

The effect of acoustic velocity in inner cladding, V L2 , on the Brillouin frequency shift: Here we have assumed the inner cladding radius, b =6.32μm, the core acoustic velocity V L1 =5,691m/s, and outer cladding acoustic velocity V L3 =5,759m/s.

Fig. 6.
Fig. 6.

Measured Brillouin frequency shifts for three different core radii. Theoretical curve assumes the estimation of the inner cladding of b =6.35μm, the core acoustic velocity of V L1 =5,694m/s, the inner cladding acoustic velocity V L2 =5,676m/s and the outer cladding velocity V L3 =5,759m/s.

Fig. 7.
Fig. 7.

The Brillouin gain spectra of test fibers. The Brillouin frequency shift (νB ) and Brillouin bandwidth (∆νB ) are 10.7149GHz and 20.6164MHz for 4.053μm core radius, respectively. νB =10.7168GHz, ∆νB =22.2530MHz for 4.701mm core radius and νB =10.7194GHz, ∆νB =23.4422MHz for 5.182mm core radius.

Equations (7)

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V A = E ( 1 ν ) / ( 1 + ν ) ( 1 2 ν ) ρ
Φ ( 0 ) = { A n J n ( u 1 r ) , for r < a B n J n ( u 2 r ) + C n Y n ( u 2 r ) , for a < r < b D n K n ( w 3 r ) , for r > b
u i = 2 πf [ ( 1 V Li ) 2 ( 1 V ) 2 ] 1 / 2 , i = 1,2
w 3 = 2 πf [ ( 1 V ) 2 ( 1 V L 3 ) 2 ] 1 / 2
V = λ 2 n 1 f
{ u 2 J 1 ( u 2 a ) u 1 J 0 ( u 2 a ) } { w 3 J 0 ( u 1 a ) Y 0 ( u 2 b ) K 1 ( w 3 b ) u 2 J 1 ( u 1 a ) Y 1 ( u 2 b ) K 0 ( w 3 b ) }
{ u 2 Y 1 ( u 2 a ) u 1 Y 0 ( u 2 a ) } { w 3 J 0 ( u 1 a ) J 0 ( u 2 b ) K 1 ( w 3 b ) u 2 J 1 ( u 1 a ) J 1 ( u 2 b ) K 0 ( w 0 b ) } = 0

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