Abstract

We have analyzed and calculated the temperature and strain sensitivities of a high-birefringence double-clad elliptical fiber. We propose a method to minimize these sensitivities without increasing the fiber size or weight; this is achieved by selecting suitable fiber parameters—core ellipticity, refractive index difference, and thickness of the inner cladding. In addition, we discuss the design of temperature- or strain-insensitive fibers which may be used in polarimetric strain or temperature sensors. This method may also be used to minimize or enhance other external effects.

© 1992 Optical Society of America

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References

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  1. J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” IEEE J. Lightwave Technol. LT-4, 1071–1089 (1986).
    [CrossRef]
  2. S. C. Rashleigh, “Fiber-optic sensors with reduced sensitivity to environmental perturbations,” Appl. Opt. 20, 1498–1499 (1981).
  3. S. C. Rashleigh, M. J. Marrone, “Polarization holding in elliptical-core birefringent fibers,” IEEE J. Quantum Electron. QE-18, 1515–1523 (1982).
    [CrossRef]
  4. A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical fiber sensors,” NATA ASI Ser. E 132, 18–19 (1987).
  5. Y. Kikuchi, R. Yamauchi, M. Akiyama, O. Fukuda, K. Inada, “Polarimetric strain and pressure sensors using temperature-independent polarization maintaining optical fiber,” in Second International Conference on Optical Fiber Sensors: OFS ’84, R. T. Kersten, R. Kist, eds., Proc. Soc. Photo-Opt. Instrum. Eng.514, 395–398 (1984).
    [CrossRef]
  6. G. F. Mcdearmon, “Theoretical analysis of the minimization of the temperature sensitivity of a coated optical fiber in a fiber-optic polarimeter,” IEEE J. Lightwave Technol. 8, 51–55 (1990).
    [CrossRef]
  7. R. M. Measure, “Fiber optic sensors—The key to smart structures,” in Fibre Optics ’89, P. McGeehin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1120, 161–174 (1989).
    [CrossRef]
  8. R. Davidson, D. H. Bowen, S. S. J. Roberts, “Composite materials monitoring through embedded fiber optics,” in Fibre Optics ’89, P. McGeehin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1120, 152–160 (1989).
    [CrossRef]
  9. F. Zhang, J. W. Y. Lit, “Polarization characteristics of double-clad elliptical fibers,” Appl. Opt. 29, 5336–5342 (1990).
    [CrossRef] [PubMed]
  10. D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10, 2252–2258 (1971).
    [CrossRef] [PubMed]
  11. L. E. Sutton, O. N. Stavroudis, “Fitting refrative index data by least squares,” J. Opt. Soc. Am. 51, 901–905 (1961).
    [CrossRef]

1990

G. F. Mcdearmon, “Theoretical analysis of the minimization of the temperature sensitivity of a coated optical fiber in a fiber-optic polarimeter,” IEEE J. Lightwave Technol. 8, 51–55 (1990).
[CrossRef]

F. Zhang, J. W. Y. Lit, “Polarization characteristics of double-clad elliptical fibers,” Appl. Opt. 29, 5336–5342 (1990).
[CrossRef] [PubMed]

1987

A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical fiber sensors,” NATA ASI Ser. E 132, 18–19 (1987).

1986

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” IEEE J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

1982

S. C. Rashleigh, M. J. Marrone, “Polarization holding in elliptical-core birefringent fibers,” IEEE J. Quantum Electron. QE-18, 1515–1523 (1982).
[CrossRef]

1981

1971

1961

Akiyama, M.

Y. Kikuchi, R. Yamauchi, M. Akiyama, O. Fukuda, K. Inada, “Polarimetric strain and pressure sensors using temperature-independent polarization maintaining optical fiber,” in Second International Conference on Optical Fiber Sensors: OFS ’84, R. T. Kersten, R. Kist, eds., Proc. Soc. Photo-Opt. Instrum. Eng.514, 395–398 (1984).
[CrossRef]

Bowen, D. H.

R. Davidson, D. H. Bowen, S. S. J. Roberts, “Composite materials monitoring through embedded fiber optics,” in Fibre Optics ’89, P. McGeehin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1120, 152–160 (1989).
[CrossRef]

Chester, A. N.

A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical fiber sensors,” NATA ASI Ser. E 132, 18–19 (1987).

Davidson, R.

R. Davidson, D. H. Bowen, S. S. J. Roberts, “Composite materials monitoring through embedded fiber optics,” in Fibre Optics ’89, P. McGeehin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1120, 152–160 (1989).
[CrossRef]

Fukuda, O.

Y. Kikuchi, R. Yamauchi, M. Akiyama, O. Fukuda, K. Inada, “Polarimetric strain and pressure sensors using temperature-independent polarization maintaining optical fiber,” in Second International Conference on Optical Fiber Sensors: OFS ’84, R. T. Kersten, R. Kist, eds., Proc. Soc. Photo-Opt. Instrum. Eng.514, 395–398 (1984).
[CrossRef]

Gloge, D.

Inada, K.

Y. Kikuchi, R. Yamauchi, M. Akiyama, O. Fukuda, K. Inada, “Polarimetric strain and pressure sensors using temperature-independent polarization maintaining optical fiber,” in Second International Conference on Optical Fiber Sensors: OFS ’84, R. T. Kersten, R. Kist, eds., Proc. Soc. Photo-Opt. Instrum. Eng.514, 395–398 (1984).
[CrossRef]

Kikuchi, Y.

Y. Kikuchi, R. Yamauchi, M. Akiyama, O. Fukuda, K. Inada, “Polarimetric strain and pressure sensors using temperature-independent polarization maintaining optical fiber,” in Second International Conference on Optical Fiber Sensors: OFS ’84, R. T. Kersten, R. Kist, eds., Proc. Soc. Photo-Opt. Instrum. Eng.514, 395–398 (1984).
[CrossRef]

Lit, J. W. Y.

Marrone, M. J.

S. C. Rashleigh, M. J. Marrone, “Polarization holding in elliptical-core birefringent fibers,” IEEE J. Quantum Electron. QE-18, 1515–1523 (1982).
[CrossRef]

Martellucci, S.

A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical fiber sensors,” NATA ASI Ser. E 132, 18–19 (1987).

Mcdearmon, G. F.

G. F. Mcdearmon, “Theoretical analysis of the minimization of the temperature sensitivity of a coated optical fiber in a fiber-optic polarimeter,” IEEE J. Lightwave Technol. 8, 51–55 (1990).
[CrossRef]

Measure, R. M.

R. M. Measure, “Fiber optic sensors—The key to smart structures,” in Fibre Optics ’89, P. McGeehin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1120, 161–174 (1989).
[CrossRef]

Noda, J.

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” IEEE J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

Okamoto, K.

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” IEEE J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

Rashleigh, S. C.

S. C. Rashleigh, M. J. Marrone, “Polarization holding in elliptical-core birefringent fibers,” IEEE J. Quantum Electron. QE-18, 1515–1523 (1982).
[CrossRef]

S. C. Rashleigh, “Fiber-optic sensors with reduced sensitivity to environmental perturbations,” Appl. Opt. 20, 1498–1499 (1981).

Roberts, S. S. J.

R. Davidson, D. H. Bowen, S. S. J. Roberts, “Composite materials monitoring through embedded fiber optics,” in Fibre Optics ’89, P. McGeehin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1120, 152–160 (1989).
[CrossRef]

Sasaki, Y.

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” IEEE J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

Stavroudis, O. N.

Sutton, L. E.

Verga Scheggi, A. M.

A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical fiber sensors,” NATA ASI Ser. E 132, 18–19 (1987).

Yamauchi, R.

Y. Kikuchi, R. Yamauchi, M. Akiyama, O. Fukuda, K. Inada, “Polarimetric strain and pressure sensors using temperature-independent polarization maintaining optical fiber,” in Second International Conference on Optical Fiber Sensors: OFS ’84, R. T. Kersten, R. Kist, eds., Proc. Soc. Photo-Opt. Instrum. Eng.514, 395–398 (1984).
[CrossRef]

Zhang, F.

Appl. Opt.

IEEE J. Lightwave Technol.

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” IEEE J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

G. F. Mcdearmon, “Theoretical analysis of the minimization of the temperature sensitivity of a coated optical fiber in a fiber-optic polarimeter,” IEEE J. Lightwave Technol. 8, 51–55 (1990).
[CrossRef]

IEEE J. Quantum Electron.

S. C. Rashleigh, M. J. Marrone, “Polarization holding in elliptical-core birefringent fibers,” IEEE J. Quantum Electron. QE-18, 1515–1523 (1982).
[CrossRef]

J. Opt. Soc. Am.

NATA ASI Ser. E

A. N. Chester, S. Martellucci, A. M. Verga Scheggi, “Optical fiber sensors,” NATA ASI Ser. E 132, 18–19 (1987).

Other

Y. Kikuchi, R. Yamauchi, M. Akiyama, O. Fukuda, K. Inada, “Polarimetric strain and pressure sensors using temperature-independent polarization maintaining optical fiber,” in Second International Conference on Optical Fiber Sensors: OFS ’84, R. T. Kersten, R. Kist, eds., Proc. Soc. Photo-Opt. Instrum. Eng.514, 395–398 (1984).
[CrossRef]

R. M. Measure, “Fiber optic sensors—The key to smart structures,” in Fibre Optics ’89, P. McGeehin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1120, 161–174 (1989).
[CrossRef]

R. Davidson, D. H. Bowen, S. S. J. Roberts, “Composite materials monitoring through embedded fiber optics,” in Fibre Optics ’89, P. McGeehin, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1120, 152–160 (1989).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic diagram of a double-clad elliptical fiber with a depressed inner cladding. (b) Refractive-index distribution in the radial direction.

Fig. 2
Fig. 2

Sensitivities of temperature and strain as functions of the normalized frequency Vy for a1/b1 = 1.5, 2.0, and 2.5 with n0 = 1.49, Δ1 = 0.027, Δ2 = 0.01, and Rx = 1.154.

Fig. 3
Fig. 3

Sensitivities of temperature and strain as functions of the refractive-index difference Δ1 for a1/b1 = 1.5, 2.0, and 2.5 with n0 = 1.49, Δ2 = 0.01, Rx = 1.154, and Vy = 1.5.

Fig. 4
Fig. 4

Sensitivities of temperature and strain as functions of the ratio of inner-cladding major axis to core major axis for a1/b1 = 1.5, 2.0, and 2.5 with n0 = 1.49, Δ1 = 0.027, Δ2 = 0.01, and Vy = 1.5.

Equations (33)

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n 2 ( ξ ) = n 0 2 [ 1 2 Δ 2 f ( ξ ) ] ,
f ( ξ ) = { 0 ξ < ξ 1 α h ( ξ ξ 1 ) ξ 1 ξ < ξ 2 h ( ξ ξ 2 ) ξ ξ 2 ,
h ( x ) = { 0 x < 0 1 x 0 , α = Δ 1 Δ 2 = n 0 2 n 1 2 n 0 2 n 2 2 ,
Δ 1 = n 0 2 n 1 2 2 n 0 2 , Δ 2 = n 0 2 n 2 2 2 n 0 2 .
V x = k a 1 n 0 ( 2 Δ 2 ) 1 / 2 , V y = k b 1 n 0 ( 2 Δ 2 ) 1 / 2 .
E x = Ψ ( x , y ) exp ( i β x z ) , E y = Ψ ( x , y ) exp ( i β y z ) .
Ψ ( x , y ) = exp [ 1 2 ( X 2 W x 2 + Y 2 W y 2 ) ] .
B = δβ k = 2 n 0 Δ 2 2 V y 4 [ 1 W y 4 1 ( a 1 / b 1 ) 4 W x 4 ] .
Δ τ = 1 c d ( δβ ) d k = 2 n 0 Δ 2 2 c d d V y { 1 V y 3 [ 1 W y 4 1 ( a 1 / b 1 ) 4 W x 4 ] } .
δ ϕ = δβ L .
d ( δ ϕ ) d ζ p = d ( δ β ) d ζ p L + d L d ζ p δ β .
d ( δ β ) d ζ p = ( δ β ) V d V d ζ p + ( δ β ) e d e d ζ p .
b ( V , e ) = ( β / k ) n 2 n 0 n 2 .
δβ = ( n 0 n 2 ) δ b ( V , e ) k .
d ( δ β ) d ζ p = 1 n 0 n 2 ( n 0 n 2 ) d ζ p + ( δ β ) V d V d ζ p + ( δ β ) e d e d ζ p ,
V d ( δ β ) d V = k ( δ β ) k [ 1 λ n 0 n 2 ( n 0 n 2 ) λ ] δ β ,
d V d ζ p = V b 1 b 1 ζ p + V n 0 2 n 2 2 ( n 0 n 0 ζ p n 2 n 2 ζ p ) .
d ( δβ ) d ζ p = k V V ζ p ( δβ ) k + ( δβ ) e d e d ζ p + [ 1 n 0 n 2 ( n 0 n 2 ) ζ p ( 1 λ n 0 n 2 ( n 0 n 2 ) λ ) 1 V V ζ p ] δβ .
d ( δ ϕ ) d ζ p = k V V ζ p ( δβ ) k L + ( δβ ) e d e d ζ p L + [ 1 n 0 n 2 ( n 0 n 2 ) ζ p ( 1 λ n 0 n 2 ( n 0 n 2 ) λ ) 1 V V ζ p + 1 L d L d ζ p ] δβ L .
d n i d λ = λ n i s = 1 3 A s λ s 2 ( λ 2 λ s 2 ) 2 ,
n i T = α n n p , i = 0 , 1 , 2 ,
b 1 T = α e b 1 , L T = α e L ,
1 V d V d T = α n + α e .
d e d T = 0
d ( δ ϕ ) L d T = k ( α n + α e ) [ ( δβ ) k + λ n 0 n 2 ( n 0 n 2 ) λ B ] .
d b 1 d ζ p = d b 1 d L = ν b 1 L ,
n i L = n i 3 2 L [ p 12 ν ( p 11 + p 12 ) ] , i = 0 , 1 , 2 ,
1 V d V d L ν L n 1 2 L [ p 12 ν ( p 11 + p 12 ) ] ,
1 n 0 n 2 ( n 0 n 2 ) L 2 n 0 2 L [ p 12 ν ( p 11 + p 12 ) ] .
d ( δ ϕ ) d L = k ( ν + C s t ) [ ( δβ ) d k + λ ( n 0 n 2 ) ( n 0 n 2 ) λ B ] + k ( 1 + ν C s t ) B ,
C s t = n 0 2 [ p 12 ν ( p 11 + p 12 ) ] .
( δβ ) d k + λ n 0 n 2 ( n 0 n 2 ) λ B = 0 .
d ( δ ϕ ) d L = k ( 1 + ν C s t ) B .

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