Abstract

We propose a theoretical approach to analyze the pressure stress distribution in single mode fibers (SMFs) and achieve the analytical expression of stress function, from which we obtain the stress components with their patterns in the core and compute their induced birefringence. Then we perform a pressure vector sensing based on ~2 km SMF. Using Mueller matrix method we measure the birefringence vectors which are employed to compute the pressure magnitudes and their orientation. When rotating the pressure around the fiber, the corresponding birefringence vector rotates around a circle with double speed. Statistics show the average deviation of calculated pressure-magnitude to practical value is ~0.17 N and it is ~0.85° for orientation.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Chowdhury and D. Wilcox, "Comparison between optical fiber birefringence induced by stress anisotropy and geometric deformation," IEEE J. Sel. Topics Quantum Electron. 6, 227-232 (2000).
    [CrossRef]
  2. J. Sakai and T. Kimura, "Birefringence and polarization characteristics of single mode optical fibers under electric deformations," IEEE J. Quantum Electron. 17, 1041-1051 (1981).
    [CrossRef]
  3. Y. Park, U. C. Paek, and D.Y. Kim, "Determination of stress-induced intrinsic birefringence in a single-mode fiber by measurement of the two-dimensional stress profile," Opt. Lett. 27, 1291-1293 (2002).
    [CrossRef]
  4. K.S. Chang, "Pressure-induced birefringence in a coated highly birefringent optical fiber," J. Lightwave Technol. 8, 1850-1855 (1990).
    [CrossRef]
  5. S. M. Pietralunga, M. Ferrario, M. Tacca, and M. Martinelli, "Local Birefringence in Unidirectionally Spun Fibers," J. Lightwave Technol. 24, 4030-4038 (2006).
    [CrossRef]
  6. K. Saitoh, M. Koshiba, and Y. Tsuji, "Stress analysis method for elastically anisotropic material based optical waveguides and its application to strain-induced optical waveguides," J. Lightwave Technol. 17, 255-259 (1999).
    [CrossRef]
  7. S. Timoshenko and J. N. Goodier, Theory of elasticity (McGraw-Hill, 1970), Chap. 4.
  8. D.H. Yu, Mathematical theory of natural boundary element method (Science Press, Beijing, 1993), Chap. 3.
  9. A. J. Barlow and D. N. Payne, "The stress-optic effect in optical fibers," IEEE J. Quantum Electron. 19, 834-839 (1983).
    [CrossRef]
  10. S. Y. Lu and R. A. Chipman, "Interpretation of Mueller matrices based on polar decomposition," J. Opt. Soc. Am. A 13, 1106-1113 (1996).
    [CrossRef]

2006 (1)

2002 (1)

2000 (1)

D. Chowdhury and D. Wilcox, "Comparison between optical fiber birefringence induced by stress anisotropy and geometric deformation," IEEE J. Sel. Topics Quantum Electron. 6, 227-232 (2000).
[CrossRef]

1999 (1)

1996 (1)

1990 (1)

K.S. Chang, "Pressure-induced birefringence in a coated highly birefringent optical fiber," J. Lightwave Technol. 8, 1850-1855 (1990).
[CrossRef]

1983 (1)

A. J. Barlow and D. N. Payne, "The stress-optic effect in optical fibers," IEEE J. Quantum Electron. 19, 834-839 (1983).
[CrossRef]

1981 (1)

J. Sakai and T. Kimura, "Birefringence and polarization characteristics of single mode optical fibers under electric deformations," IEEE J. Quantum Electron. 17, 1041-1051 (1981).
[CrossRef]

Barlow, A. J.

A. J. Barlow and D. N. Payne, "The stress-optic effect in optical fibers," IEEE J. Quantum Electron. 19, 834-839 (1983).
[CrossRef]

Chang, K.S.

K.S. Chang, "Pressure-induced birefringence in a coated highly birefringent optical fiber," J. Lightwave Technol. 8, 1850-1855 (1990).
[CrossRef]

Chipman, R. A.

Chowdhury, D.

D. Chowdhury and D. Wilcox, "Comparison between optical fiber birefringence induced by stress anisotropy and geometric deformation," IEEE J. Sel. Topics Quantum Electron. 6, 227-232 (2000).
[CrossRef]

Ferrario, M.

Kim, D.Y.

Kimura, T.

J. Sakai and T. Kimura, "Birefringence and polarization characteristics of single mode optical fibers under electric deformations," IEEE J. Quantum Electron. 17, 1041-1051 (1981).
[CrossRef]

Koshiba, M.

Lu, S. Y.

Martinelli, M.

Paek, U. C.

Park, Y.

Payne, D. N.

A. J. Barlow and D. N. Payne, "The stress-optic effect in optical fibers," IEEE J. Quantum Electron. 19, 834-839 (1983).
[CrossRef]

Pietralunga, S. M.

Saitoh, K.

Sakai, J.

J. Sakai and T. Kimura, "Birefringence and polarization characteristics of single mode optical fibers under electric deformations," IEEE J. Quantum Electron. 17, 1041-1051 (1981).
[CrossRef]

Tacca, M.

Tsuji, Y.

Wilcox, D.

D. Chowdhury and D. Wilcox, "Comparison between optical fiber birefringence induced by stress anisotropy and geometric deformation," IEEE J. Sel. Topics Quantum Electron. 6, 227-232 (2000).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. Sakai and T. Kimura, "Birefringence and polarization characteristics of single mode optical fibers under electric deformations," IEEE J. Quantum Electron. 17, 1041-1051 (1981).
[CrossRef]

A. J. Barlow and D. N. Payne, "The stress-optic effect in optical fibers," IEEE J. Quantum Electron. 19, 834-839 (1983).
[CrossRef]

IEEE J. Sel. Topics Quantum Electron. (1)

D. Chowdhury and D. Wilcox, "Comparison between optical fiber birefringence induced by stress anisotropy and geometric deformation," IEEE J. Sel. Topics Quantum Electron. 6, 227-232 (2000).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Other (2)

S. Timoshenko and J. N. Goodier, Theory of elasticity (McGraw-Hill, 1970), Chap. 4.

D.H. Yu, Mathematical theory of natural boundary element method (Science Press, Beijing, 1993), Chap. 3.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) The schematic graph and (b) enlarged cross section of SMF under lateral pressure.

Fig. 2.
Fig. 2.

Stress distributions (a): σx , (b): σy , and (c): τxy in the core of the fiber under lateral pressure.

Fig. 3.
Fig. 3.

Experimental setup for pressure vector measurement based on Mueller matrix method.

Fig. 4.
Fig. 4.

(a) Measurement and calculation of pressure magnitude, (b) birefringence vectors under different pressure orientations.

Fig. 5.
Fig. 5.

Comparison for calculated and practical azimuthes of lateral pressureure.

Equations (18)

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

( 2 r 2 + 1 r r + 1 r 2 2 θ 2 ) 2 A ( r , θ ) = 0 ,
σ r = 1 r A r + 1 r 2 2 A θ 2 , σ θ = 2 A r 2 , τ r θ = r ( 1 r A θ ) , σ z = τ rz = τ z θ = 0 .
A ( r , θ ) = 0 2 π [ R r cos ( θ φ ) 2 πR X μ ( φ ) R 2 r 2 4 πR v ( φ ) ] X d φ ,
X = ( R 2 r 2 ) [ R 2 + r 2 2 Rr cos ( θ φ ) ] ,
μ ( φ ) = { PR sin φ , 0 φ π 0 π φ 2 π , v ( φ ) = { P sin φ , 0 φ π 0 π φ 2 π .
A ( r , θ ) = P 4 πR [ 2 π Rr sin θ + 4 Rr sin θ tan 1 ( 2 Rr sin θ R 2 r 2 ) + 2 ( R 2 r 2 ) ] , ( 0 r < R ) .
σ r = σ ( 8 r ˜ 2 cos 2 θ 3 ) , σ θ = σ [ 4 ( cos 2 θ r ˜ 2 ) 3 ] , τ = 2 σ ( 1 r ˜ 2 ) sin ( 2 θ ) ,
σ = P ( πR ) 1 [ 1 4 r ˜ 2 cos ( 2 θ ) ] , ( r ~ = r R ) .
σ x = σ { 3 + 2 r ˜ 2 [ 1 + 3 cos ( 2 θ ) ] } , σ y = σ [ 1 + 4 r ˜ 2 cos θ cos ( 3 θ ) ] ,
τ xy = 4 σ r ˜ 2 sin ( 2 θ ) [ ( r ˜ 2 1 ) cos ( 2 θ ) + r ˜ 2 ] .
Δ ε ˜ = ( Δ ε r Δ ε Δ ε zr Δ ε Δ ε θ Δ ε θz Δ ε zr Δ ε θz Δ ε z ) ,
d dz ( A 1 A 2 ) = j ( α 11 α 12 α 21 α 22 ) ( A 1 A 2 ) , α mn = ω ε 0 s E m * · Δ ε ˜ E n ds s z ̂ · ( E m * × H m + E m × H m * ) ds ,
B = α 11 α 22 17 CP 2 [ 1 1.166 ( a R ) 2 ] .
θ = cos 1 ( B ̂ · B ̂ 0 ) 2 ,
P = 3.5984 B .
M B = MM D 1 , M D = m 11 ( 1 D T D m D ) , D = D D ̂ = D D D = m 11 1 ( m 12 , m 13 , m 14 ) T m D = 1 D 2 diag [ 1 , 1 , 1 ] + ( 1 1 D 2 ) D ̂ D T
B = B B ̂ = B ( s 1 , s 2 , s 3 ) T , B = B = cos 1 [ Tr ( M B ) 2 1 ] ,
s 1 = ( m 34 B m 43 B ) ( 2 sin B ) , s 2 = ( m 42 B m 24 B ) ( 2 sin B ) , s 3 = ( m 23 B m 32 B ) ( 2   sin B ) ,

Metrics