Abstract

The overall bandwidth of guided acoustic-wave Brillouin scattering has been measured in optical fibers with different fiber core diameters. The relative intensity of the light scattering produced by the different acoustic modes is compared with theory and shows good agreement when the optical fiber has its polymer jacket removed. The mode intensities and linewidths in a jacketed optical fiber are modified by the selective damping of individual guided acoustic modes.

© 1993 Optical Society of America

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  1. R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. Lett. 54, 939–942 (1985).
    [CrossRef] [PubMed]
  2. R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 31, 5244–5252 (1985).
    [CrossRef]
  3. M. D. Levenson, R. M. Shelby, A. Aspect, M. Reid, and D. F. Walls, Phys. Rev. A 32, 1550–1562 (1985).
    [CrossRef] [PubMed]
  4. R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, Phys. Rev. A 33, 4008–4025 (1986).
    [CrossRef] [PubMed]
  5. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, Phys. Rev. Lett. 57, 691–694 (1986).
    [CrossRef] [PubMed]
  6. M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153–156 (1991).
    [CrossRef] [PubMed]
  7. K. Bergman and H. A. Haus, Opt. Lett. 16, 663–665 (1991).
    [CrossRef] [PubMed]
  8. K. Bløtekjær, J. Lightwave Technol. 10, 36–41 (1992).
    [CrossRef]
  9. R. M. Shelby, P. D. Drummond, and S. J. Carter, Phys. Rev. A 42, 2966–2976 (1990).
    [CrossRef] [PubMed]
  10. E. K. Sittig and G. A. Coquin, J. Acoust. Soc. Am. 48, 1150–1159 (1970).
    [CrossRef]
  11. R. N. Thurston, J. Acoust. Soc. Am. 64, 1–37 (1978).
    [CrossRef]
  12. G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants (Longmans, Green, London, 1986).
  13. J. Sapriel, Acousto-Optics (Wiley Interscience, Chichester, 1979).
  14. J. Schroeder, J. Non-Cryst. Solids 40, 549–566 (1980).
    [CrossRef]
  15. D. Marcuse, Bell Syst. Tech. J. 56, 703–718 (1977).
    [CrossRef]
  16. A. J. Poustie, Opt. Lett. 17, 574–576 (1992).
    [CrossRef] [PubMed]
  17. D. Heiman, D. S. Hamilton, and R. W. Hellwarth, Phys. Rev. B 19, 6583–6592 (1979).
    [CrossRef]
  18. B. A. Auld, Acoustic Fields and Waues in Solids (Wiley, New York, 1973), Vol. 1.
  19. M. Ohashi, N. Shibata, and K. Shiraki, in Optical Fibre Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WK3.
  20. T. R. Meeker and A. H. Meitzler, in Physical Acoustics, W. P. Mason, ed. (Academic, New York, 1964), Vol. I, Part A.
  21. A. E. Armfnàkas, J. Acoust. Soc. Am. 47, 822–837 (1970).
    [CrossRef]
  22. J. Lai, E. H. Dowell, and T. R. Tauchert, J. Acoust. Soc. Am. 49, 220–228 (1971).
    [CrossRef]

1992 (2)

K. Bløtekjær, J. Lightwave Technol. 10, 36–41 (1992).
[CrossRef]

A. J. Poustie, Opt. Lett. 17, 574–576 (1992).
[CrossRef] [PubMed]

1991 (2)

M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153–156 (1991).
[CrossRef] [PubMed]

K. Bergman and H. A. Haus, Opt. Lett. 16, 663–665 (1991).
[CrossRef] [PubMed]

1990 (1)

R. M. Shelby, P. D. Drummond, and S. J. Carter, Phys. Rev. A 42, 2966–2976 (1990).
[CrossRef] [PubMed]

1986 (2)

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, Phys. Rev. A 33, 4008–4025 (1986).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, Phys. Rev. Lett. 57, 691–694 (1986).
[CrossRef] [PubMed]

1985 (3)

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. Lett. 54, 939–942 (1985).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 31, 5244–5252 (1985).
[CrossRef]

M. D. Levenson, R. M. Shelby, A. Aspect, M. Reid, and D. F. Walls, Phys. Rev. A 32, 1550–1562 (1985).
[CrossRef] [PubMed]

1980 (1)

J. Schroeder, J. Non-Cryst. Solids 40, 549–566 (1980).
[CrossRef]

1979 (1)

D. Heiman, D. S. Hamilton, and R. W. Hellwarth, Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

1978 (1)

R. N. Thurston, J. Acoust. Soc. Am. 64, 1–37 (1978).
[CrossRef]

1977 (1)

D. Marcuse, Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

1971 (1)

J. Lai, E. H. Dowell, and T. R. Tauchert, J. Acoust. Soc. Am. 49, 220–228 (1971).
[CrossRef]

1970 (2)

A. E. Armfnàkas, J. Acoust. Soc. Am. 47, 822–837 (1970).
[CrossRef]

E. K. Sittig and G. A. Coquin, J. Acoust. Soc. Am. 48, 1150–1159 (1970).
[CrossRef]

Armfnàkas, A. E.

A. E. Armfnàkas, J. Acoust. Soc. Am. 47, 822–837 (1970).
[CrossRef]

Aspect, A.

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, Phys. Rev. A 33, 4008–4025 (1986).
[CrossRef] [PubMed]

M. D. Levenson, R. M. Shelby, A. Aspect, M. Reid, and D. F. Walls, Phys. Rev. A 32, 1550–1562 (1985).
[CrossRef] [PubMed]

Auld, B. A.

B. A. Auld, Acoustic Fields and Waues in Solids (Wiley, New York, 1973), Vol. 1.

Bayer, P. W.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. Lett. 54, 939–942 (1985).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 31, 5244–5252 (1985).
[CrossRef]

Bergman, K.

Bløtekjær, K.

K. Bløtekjær, J. Lightwave Technol. 10, 36–41 (1992).
[CrossRef]

Carter, S. J.

R. M. Shelby, P. D. Drummond, and S. J. Carter, Phys. Rev. A 42, 2966–2976 (1990).
[CrossRef] [PubMed]

Coquin, G. A.

E. K. Sittig and G. A. Coquin, J. Acoust. Soc. Am. 48, 1150–1159 (1970).
[CrossRef]

DeVoe, R. G.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, Phys. Rev. Lett. 57, 691–694 (1986).
[CrossRef] [PubMed]

Dowell, E. H.

J. Lai, E. H. Dowell, and T. R. Tauchert, J. Acoust. Soc. Am. 49, 220–228 (1971).
[CrossRef]

Drummond, P. D.

R. M. Shelby, P. D. Drummond, and S. J. Carter, Phys. Rev. A 42, 2966–2976 (1990).
[CrossRef] [PubMed]

Hamilton, D. S.

D. Heiman, D. S. Hamilton, and R. W. Hellwarth, Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

Haus, H. A.

Heiman, D.

D. Heiman, D. S. Hamilton, and R. W. Hellwarth, Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

Hellwarth, R. W.

D. Heiman, D. S. Hamilton, and R. W. Hellwarth, Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

Kaye, G. W. C.

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants (Longmans, Green, London, 1986).

Laby, T. H.

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants (Longmans, Green, London, 1986).

Lai, J.

J. Lai, E. H. Dowell, and T. R. Tauchert, J. Acoust. Soc. Am. 49, 220–228 (1971).
[CrossRef]

Levenson, M. D.

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, Phys. Rev. A 33, 4008–4025 (1986).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, Phys. Rev. Lett. 57, 691–694 (1986).
[CrossRef] [PubMed]

M. D. Levenson, R. M. Shelby, A. Aspect, M. Reid, and D. F. Walls, Phys. Rev. A 32, 1550–1562 (1985).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. Lett. 54, 939–942 (1985).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 31, 5244–5252 (1985).
[CrossRef]

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

Meeker, T. R.

T. R. Meeker and A. H. Meitzler, in Physical Acoustics, W. P. Mason, ed. (Academic, New York, 1964), Vol. I, Part A.

Meitzler, A. H.

T. R. Meeker and A. H. Meitzler, in Physical Acoustics, W. P. Mason, ed. (Academic, New York, 1964), Vol. I, Part A.

Milburn, G. J.

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, Phys. Rev. A 33, 4008–4025 (1986).
[CrossRef] [PubMed]

Ohashi, M.

M. Ohashi, N. Shibata, and K. Shiraki, in Optical Fibre Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WK3.

Perlmutter, S. H.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, Phys. Rev. Lett. 57, 691–694 (1986).
[CrossRef] [PubMed]

Poustie, A. J.

Reid, M.

M. D. Levenson, R. M. Shelby, A. Aspect, M. Reid, and D. F. Walls, Phys. Rev. A 32, 1550–1562 (1985).
[CrossRef] [PubMed]

Rosenbluh, M.

M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153–156 (1991).
[CrossRef] [PubMed]

Sapriel, J.

J. Sapriel, Acousto-Optics (Wiley Interscience, Chichester, 1979).

Schroeder, J.

J. Schroeder, J. Non-Cryst. Solids 40, 549–566 (1980).
[CrossRef]

Shelby, R. M.

M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153–156 (1991).
[CrossRef] [PubMed]

R. M. Shelby, P. D. Drummond, and S. J. Carter, Phys. Rev. A 42, 2966–2976 (1990).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, Phys. Rev. Lett. 57, 691–694 (1986).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, Phys. Rev. A 33, 4008–4025 (1986).
[CrossRef] [PubMed]

M. D. Levenson, R. M. Shelby, A. Aspect, M. Reid, and D. F. Walls, Phys. Rev. A 32, 1550–1562 (1985).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. Lett. 54, 939–942 (1985).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 31, 5244–5252 (1985).
[CrossRef]

Shibata, N.

M. Ohashi, N. Shibata, and K. Shiraki, in Optical Fibre Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WK3.

Shiraki, K.

M. Ohashi, N. Shibata, and K. Shiraki, in Optical Fibre Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WK3.

Sittig, E. K.

E. K. Sittig and G. A. Coquin, J. Acoust. Soc. Am. 48, 1150–1159 (1970).
[CrossRef]

Tauchert, T. R.

J. Lai, E. H. Dowell, and T. R. Tauchert, J. Acoust. Soc. Am. 49, 220–228 (1971).
[CrossRef]

Thurston, R. N.

R. N. Thurston, J. Acoust. Soc. Am. 64, 1–37 (1978).
[CrossRef]

Walls, D. F.

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, Phys. Rev. A 33, 4008–4025 (1986).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, Phys. Rev. Lett. 57, 691–694 (1986).
[CrossRef] [PubMed]

M. D. Levenson, R. M. Shelby, A. Aspect, M. Reid, and D. F. Walls, Phys. Rev. A 32, 1550–1562 (1985).
[CrossRef] [PubMed]

Bell Syst. Tech. J. (1)

D. Marcuse, Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

J. Acoust. Soc. Am. (4)

E. K. Sittig and G. A. Coquin, J. Acoust. Soc. Am. 48, 1150–1159 (1970).
[CrossRef]

R. N. Thurston, J. Acoust. Soc. Am. 64, 1–37 (1978).
[CrossRef]

A. E. Armfnàkas, J. Acoust. Soc. Am. 47, 822–837 (1970).
[CrossRef]

J. Lai, E. H. Dowell, and T. R. Tauchert, J. Acoust. Soc. Am. 49, 220–228 (1971).
[CrossRef]

J. Lightwave Technol. (1)

K. Bløtekjær, J. Lightwave Technol. 10, 36–41 (1992).
[CrossRef]

J. Non-Cryst. Solids (1)

J. Schroeder, J. Non-Cryst. Solids 40, 549–566 (1980).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (3)

R. M. Shelby, P. D. Drummond, and S. J. Carter, Phys. Rev. A 42, 2966–2976 (1990).
[CrossRef] [PubMed]

M. D. Levenson, R. M. Shelby, A. Aspect, M. Reid, and D. F. Walls, Phys. Rev. A 32, 1550–1562 (1985).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, Phys. Rev. A 33, 4008–4025 (1986).
[CrossRef] [PubMed]

Phys. Rev. B (2)

D. Heiman, D. S. Hamilton, and R. W. Hellwarth, Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 31, 5244–5252 (1985).
[CrossRef]

Phys. Rev. Lett. (3)

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, Phys. Rev. Lett. 57, 691–694 (1986).
[CrossRef] [PubMed]

M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153–156 (1991).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. Lett. 54, 939–942 (1985).
[CrossRef] [PubMed]

Other (5)

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants (Longmans, Green, London, 1986).

J. Sapriel, Acousto-Optics (Wiley Interscience, Chichester, 1979).

B. A. Auld, Acoustic Fields and Waues in Solids (Wiley, New York, 1973), Vol. 1.

M. Ohashi, N. Shibata, and K. Shiraki, in Optical Fibre Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WK3.

T. R. Meeker and A. H. Meitzler, in Physical Acoustics, W. P. Mason, ed. (Academic, New York, 1964), Vol. I, Part A.

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Figures (10)

Fig. 1
Fig. 1

Depolarized GAWBS rf spectrum for 110 mW in 3 m of unjacketed single-mode optical fiber (φ ≈ 105 μm, Δn = 0.0065, λcutoff = 900 nm). The detected power was 2.5 mW, and the electronic resolution bandwidth was 300 kHz. The theoretical points are calculated with α = 0.6261, φ = 106.20 μm, φcore = 6.5 μm, and Vd = 5968 ms−1.

Fig. 2
Fig. 2

Measured variation in depolarized GAWBS mode line-width with mode frequency in an unjacketed optical fiber.

Fig. 3
Fig. 3

Single depolarized GAWBS mode in detail, showing structure. The electronic resolution was 21.5 kHz, the optical power in 1.5 m of fiber was 110 mW and the detected power was 2.5 mW.

Fig. 4
Fig. 4

Comparison of the low-frequency region of the depolarized GAWBS spectrum in (a) an unjacketed optical fiber (L = 1.5 m, P = 110 mW) and in (b) a fiber with a polymer jacket (L = 900 m, P = 20 mW). The detected power in each case was 2.5 mW, and the electronic resolution was 300 kHz.

Fig. 5
Fig. 5

Theoretical calculation of the relative values of Ur at the fiber surface for the depolarized GAWBS modes.

Fig. 6
Fig. 6

Comparison of depolarized GAWBS spectrum in (a) 2 m of unjacketed optical fiber and (b) 2 m of optical fiber with 1.5 m in a set gelatin solution. The depolarized GAWBS mode numbers m that are selectively damped are circled and agree well with those predicted by the theory as shown in Fig. 5.

Fig. 7
Fig. 7

Theoretical calculation of the relative values of Ur at the fiber surface for the polarized GAWBS modes.

Fig. 8
Fig. 8

Measured overall bandwidth of the depolarized GAWBS modes for the fiber parameters: (a) φcore = 6 μm, φ= 105 μm, Δn = 0.0065, λcutoff = 900 nm, L = 900 m; (b) φcore = 4 μm, φ = 125 μm, Δn = 0.013, λcutoff = 1025 nm, L = 1 km; (c) φcore = 3 μm, φ = 125 μm, Δn = 0.025, λcutoff = 940 nm, L = 200 m.

Fig. 9
Fig. 9

Measured overall bandwidth of the polarized GAWBS modes for 3.25 mW in 900 m of optical fiber and a local oscillator power of 3.5 mW. The shot noise of the local oscillator was digitally subtracted from the rf spectrum. Fiber parameters as in Fig. 8(a).

Fig. 10
Fig. 10

Theoretical calculation of the variation in the GAWBS bandwidth with optical fiber core radius for a fixed fiber diameter of 125 μm. The bandwidth is defined as the frequency at which the scattering intensity is 10 dB below the maximum scattering intensity.

Equations (13)

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( 1 - α 2 ) J 0 ( y ) - α 2 J 2 ( y ) = 0 ,
ν m = V d y m / ( 2 π a ) ,
U r m ( r ) = C r m J 1 ( y m r / a ) ,
C r m = ( k B T 4 π 3 L ρ ν m 2 a 2 B r m ) 1 / 2 ,
B r m = 0 1 J 1 2 ( y m x ) x d x
Δ n ( r ) = ( n 3 / 2 ) ( P 11 + P 12 ) [ S r r ( r ) + S φ φ ( r ) ] ,
= ( 2 π ω L / c ) 0 a Δ n ( r ) E ( r ) r d r ,
E ( r ) ( 1 π w 2 ) exp [ - ( r / w ) 2 ] .
η 1 L ( 2 ) 2 ,
| [ ( 3 - y 2 / 2 ) J 2 ( α y ) ] [ ( 6 - y 2 / 2 ) J 2 ( y ) ] [ J 2 ( α y ) - α y J 3 ( α y ) ] [ ( 2 - y 2 / 2 ) J 2 ( y ) + y J 3 ( y ) | = 0 ,
U r ( r , φ ) = C T m u r ( r / a ) cos ( 2 φ ) U φ ( r , φ ) = C T m u φ ( r / a ) sin ( 2 φ ) .
T m = 0 1 { [ u r ( x ) ] 2 + [ u φ ( x ) ] 2 } x d x .
Δ n ( r ) = n 3 P 44 S r φ ( r ) ,

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