Abstract

The performance of the fiber specklegram sensor (FSS) by use of the waveguide coupled-mode theory is analyzed. The analyses are based on the microbending effect on the sensing fiber, in which we have found that the sensitivity of the FSS is affected by the core diameter and the bending geometry. Experimental confirmations of the analyses are also provided in which we have shown that experimental data are consistent with the analyses.

© 1995 Optical Society of America

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References

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  1. S. Wu, S. Yin, F. T. S. Yu, “Sensing with fiber specklegrams,” Appl. Opt. 30, 4468–4470 (1991).
    [Crossref] [PubMed]
  2. S. Wu, S. Yin, S. Rajan, F. T. S. Yu, “Multichannel sensing with fiber specklegrams,” Appl. Opt. 31, 5975–5983 (1992).
    [Crossref] [PubMed]
  3. P. Zhang, K. D. Bennett, C. Indebetouw, “Correlation-based fiber sensor using a holographic matched filter,” J. Lightwave Technol. LT-8, 1123–1126 (1990).
    [Crossref]
  4. F. T. S. Yu, M. Wen, S. Yin, C-M. Uang, “Submicrometer displacement sensing using inner-product multimode fiber speckle fields,” Appl. Opt. 32, 4685–4689 (1993).
    [Crossref] [PubMed]
  5. F. T. S. Yu, S. Yin, J. Zhang, R. Guo, “Application of fiber speckle hologram to fiber sensing,” Appl. Opt. 33, 5202–5203 (1994).
    [Crossref] [PubMed]
  6. F. T. S. Yu, K. Pan, C-M. Uang, “Fiber specklegram sensing by means of an adaptive joint transform correlator,” Opt. Eng. 32, 2884–2889 (1993).
    [Crossref]
  7. P. K. Cheo, Fiber Optics and Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1990), Chap. 5, p. 73.
  8. R. A. Pappert, E. E. Gossard, I. J. Rothmuller, “An investigation of classical approximation used in VLF propagation,” Radio Sci. 2, 387–400 (1967).
  9. A. Yariv, Optical Electronics (Saunders College Publishing, Orlando, Fla., 1991), Chap. 13, p. 479.
  10. S. Yin, F. T. S. Yu, “Specially doped LiNbO3 crystal holography using a low-power laser diode,” IEEE Photogr. Tech. Lett. 5, 581–582 (1993).
    [Crossref]

1994 (1)

1993 (3)

F. T. S. Yu, M. Wen, S. Yin, C-M. Uang, “Submicrometer displacement sensing using inner-product multimode fiber speckle fields,” Appl. Opt. 32, 4685–4689 (1993).
[Crossref] [PubMed]

F. T. S. Yu, K. Pan, C-M. Uang, “Fiber specklegram sensing by means of an adaptive joint transform correlator,” Opt. Eng. 32, 2884–2889 (1993).
[Crossref]

S. Yin, F. T. S. Yu, “Specially doped LiNbO3 crystal holography using a low-power laser diode,” IEEE Photogr. Tech. Lett. 5, 581–582 (1993).
[Crossref]

1992 (1)

1991 (1)

1990 (1)

P. Zhang, K. D. Bennett, C. Indebetouw, “Correlation-based fiber sensor using a holographic matched filter,” J. Lightwave Technol. LT-8, 1123–1126 (1990).
[Crossref]

1967 (1)

R. A. Pappert, E. E. Gossard, I. J. Rothmuller, “An investigation of classical approximation used in VLF propagation,” Radio Sci. 2, 387–400 (1967).

Bennett, K. D.

P. Zhang, K. D. Bennett, C. Indebetouw, “Correlation-based fiber sensor using a holographic matched filter,” J. Lightwave Technol. LT-8, 1123–1126 (1990).
[Crossref]

Cheo, P. K.

P. K. Cheo, Fiber Optics and Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1990), Chap. 5, p. 73.

Gossard, E. E.

R. A. Pappert, E. E. Gossard, I. J. Rothmuller, “An investigation of classical approximation used in VLF propagation,” Radio Sci. 2, 387–400 (1967).

Guo, R.

Indebetouw, C.

P. Zhang, K. D. Bennett, C. Indebetouw, “Correlation-based fiber sensor using a holographic matched filter,” J. Lightwave Technol. LT-8, 1123–1126 (1990).
[Crossref]

Pan, K.

F. T. S. Yu, K. Pan, C-M. Uang, “Fiber specklegram sensing by means of an adaptive joint transform correlator,” Opt. Eng. 32, 2884–2889 (1993).
[Crossref]

Pappert, R. A.

R. A. Pappert, E. E. Gossard, I. J. Rothmuller, “An investigation of classical approximation used in VLF propagation,” Radio Sci. 2, 387–400 (1967).

Rajan, S.

Rothmuller, I. J.

R. A. Pappert, E. E. Gossard, I. J. Rothmuller, “An investigation of classical approximation used in VLF propagation,” Radio Sci. 2, 387–400 (1967).

Uang, C-M.

F. T. S. Yu, K. Pan, C-M. Uang, “Fiber specklegram sensing by means of an adaptive joint transform correlator,” Opt. Eng. 32, 2884–2889 (1993).
[Crossref]

F. T. S. Yu, M. Wen, S. Yin, C-M. Uang, “Submicrometer displacement sensing using inner-product multimode fiber speckle fields,” Appl. Opt. 32, 4685–4689 (1993).
[Crossref] [PubMed]

Wen, M.

Wu, S.

Yariv, A.

A. Yariv, Optical Electronics (Saunders College Publishing, Orlando, Fla., 1991), Chap. 13, p. 479.

Yin, S.

Yu, F. T. S.

Zhang, J.

Zhang, P.

P. Zhang, K. D. Bennett, C. Indebetouw, “Correlation-based fiber sensor using a holographic matched filter,” J. Lightwave Technol. LT-8, 1123–1126 (1990).
[Crossref]

Appl. Opt. (4)

IEEE Photogr. Tech. Lett. (1)

S. Yin, F. T. S. Yu, “Specially doped LiNbO3 crystal holography using a low-power laser diode,” IEEE Photogr. Tech. Lett. 5, 581–582 (1993).
[Crossref]

J. Lightwave Technol. (1)

P. Zhang, K. D. Bennett, C. Indebetouw, “Correlation-based fiber sensor using a holographic matched filter,” J. Lightwave Technol. LT-8, 1123–1126 (1990).
[Crossref]

Opt. Eng. (1)

F. T. S. Yu, K. Pan, C-M. Uang, “Fiber specklegram sensing by means of an adaptive joint transform correlator,” Opt. Eng. 32, 2884–2889 (1993).
[Crossref]

Radio Sci. (1)

R. A. Pappert, E. E. Gossard, I. J. Rothmuller, “An investigation of classical approximation used in VLF propagation,” Radio Sci. 2, 387–400 (1967).

Other (2)

A. Yariv, Optical Electronics (Saunders College Publishing, Orlando, Fla., 1991), Chap. 13, p. 479.

P. K. Cheo, Fiber Optics and Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1990), Chap. 5, p. 73.

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Figures (8)

Fig. 1
Fig. 1

Experimental setup of a PR FSS: M, mirrors; BS, beam splitter; L, lenses; L1, L3, fiber length.

Fig. 2
Fig. 2

(a) Geometry of a bending fiber; (b) equivalent geometry.A, input end; B, output end; R, bending radius; n1, n2, refractive indices.

Fig. 3
Fig. 3

Curvature of fiber bending.

Fig. 4
Fig. 4

Coupling coefficient kmn as a function of mode number N. Author:

Fig. 5
Fig. 5

NCPV as a function of transversal displacement for various bending curvatures.

Fig. 6
Fig. 6

NCPV as a function of transversal displacement for various core diameters.

Fig. 7
Fig. 7

NCPV as a function of transversal displacement for various NA's.

Fig. 8
Fig. 8

NCPV as a function of transversal displacement for calculated and experimental results.

Equations (29)

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E 1 = n b n g n ( x , y ) ,
E 2 ( x , y ) = m c m g m ( x , y ) ,
c m = n b n T n m
E 2 ( x , y ) = n , m b n T n m g m ( x , y ) .
E 3 ( x , y ) = n , m b n T n m g m ( x , y ) exp ( j β m L 3 ) ,
CPV = E 3 ( x , y ) E 3 * ( x , y ) d x d y ,
CPV = s , t b s T s t g t ( x , y ) exp ( j β t , L 3 ) × n , m b n * T n m * g m * ( x , y ) exp ( j β m L 3 ) d x d y = s , t b s T s t exp ( j β t , L 3 ) n , m b n * T n m * × exp ( j β m L 3 ) g t ( x , y ) g m * ( x , y ) d x d y = s , t b s T s t exp ( j β t , L 3 ) × n , m b n * T n m * exp ( j β m L 3 ) δ t , m = n , m , s b s b n * T s t T n m * ,
b n = a n exp ( j ϕ n ) ,
CPV = n , m , s a s a n * T s m T n m * exp ( j ( ϕ s ϕ n ) .
CPV = n , m | a n | 2 T n m T n m * .
2 E ( r ) + k 2 n 2 ( r ) E ( r ) = 0 ,
n 2 ( r ) n 0 2 = 2 x R n 0 2 ,
R D 2 8 δ ,
E ( x , y , z ) = m H m ( z ) g m ( x , y ) exp ( j β m z ) ,
( 2 x 2 + 2 y 2 ) g m ( x , y ) + ( k 2 n 0 2 β m 2 ) g m ( x , y ) = 0
| 2 H m ( z ) z 2 | | β m H m ( z ) z | .
m j β m H m ( z ) ( z ) g m ( x , y ) exp ( j β m z ) = m k 2 x R n 0 2 H m ( z ) g m ( x , y ) exp ( j β m z ) .
β n H n ( z ) z exp ( j β n z ) = j m k 2 H m ( z ) K m n exp ( j β m z ) ,
K m n = k 2 β n g n * ( x , y ) x R n 0 2 g m ( x , y ) d x d y ,
g m ( x ) = { A m cos γ m x = ( α m 1 + α m d ) 1 / 2 cos γ m x , d x d , C m exp ( α m x ) = α m 1 / 2 exp ( α m d ) cos γ m d ( 1 + α m d ) 1 / 2 exp ( α m x ) , x > d , C m exp ( α m x ) = α m 1 / 2 exp ( α m d ) cos γ m d ( 1 + α m d ) 1 / 2 exp ( α m x ) , x < d ,
tan γ m d = α m γ m , α m 2 + γ m 2 = k 2 ( n 1 2 n 2 2 ) ,
g s ( x ) = { A s sin γ s x = ( α s 1 + α s d ) 1 / 2 sin γ s x , d x d , C s exp ( α s x ) = α s 1 / 2 exp ( α s d ) sin γ s d ( 1 + α s d ) 1 / 2 exp ( α s x ) , x > d , C s exp ( α s x ) = α s 1 / 2 exp ( α s d ) sin γ s d ( 1 + α s d ) 1 / 2 exp ( α s x ) , x < d ,
cot ( γ s d ) = α s γ s , α s + γ s 2 = k 2 ( n 1 2 n 2 2 ) .
K s m = k β s [ d C s exp ( α s x ) x R n 2 2 C m exp ( α m x ) d x + d C s exp ( α s x ) x R n 2 2 C m exp ( α m x ) d x + d d A s sin ( γ s x ) x R n 1 2 A m cos ( γ m x ) d x ]
= k n 1 2 β s R [ ( 1 α s + d ) ( 1 α m + d ) ] 1 / 2 × [ sin ( γ s + γ m ) d ( γ s + γ m ) 2 + sin ( γ s γ m ) d ( γ s γ m ) 2 d cos ( γ s + γ m ) d γ s + γ m d cos ( γ s γ m ) d γ s γ m ]
{ H s ( z ) z j k H m ( z ) K s m exp [ j ( β s β m ) z ] , H m ( z ) z j k H s ( z ) K m s exp [ j ( β s β m ) z ] .
H m ( z ) = exp [ j ( β s β m ) z / 2 ] { H m ( 0 ) [ cos ( w s m z ) + j ( β s β m ) 2 w s m sin ( w s m z ) ] j k 2 K m s w s m sin ( w s m z ) H s ( 0 ) } ,
T s m = H m ( L 2 ) exp ( j β m L 2 ) H s ( 0 ) H m ( 0 ) = 0 = exp [ j ( β s + β m ) L 2 / 2 ] [ j k K m s 2 w s m sin ( w s m L 2 ) ] ,
w s m = [ ( β s β m 2 ) 2 + k 2 K s m K m s ] 1 / 2 .

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