Abstract

When high-birefringent fibers are used in polarization-sensitive devices, one must ensure the proper alignment of the optical axes. One nondestructive alignment method involves squeezing the fiber and noting the change in the resultant birefringent axes. We use the finite-element method to determine the change in the principal stress direction, and, hence, the extrinsic birefringent axis orientation, as a function of the fiber coating eccentricity. Fiber eccentricity can shift the extrinsic birefringent axis by more than 1.5°, whch becomes important in high-performance device applications.

© 1992 Optical Society of America

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References

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  1. S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
    [CrossRef]
  2. M. Abebe, C. A. Villarruel, W. K. Burns, “Reproducible fabrication method for polarization preserving single-mode fiber couplers,” IEEE J. Lightwave Technol. 6, 1191–1198 (1988).
    [CrossRef]
  3. G. A. Olson, J. R. Onstott, “Polarization-maintaining optical fibers for coupler fabrication,” U.S. Patent4,906,068 (6March1990).
  4. W. Pleibel, R. H. Stolen, “Polarisation-preserving coupler with self aligning birefringent fibres,” Electron Lett. 19, 825–826 (1983).
    [CrossRef]
  5. J. Yokohama, M. Kawachi, K. Okamoto, J. Noda, “Polarisation maintaining fibre couplers with low excess loss,” Electron Lett. 22, 929–930 (1986).
    [CrossRef]
  6. M. Corke, B. M. Kale, M. Keur, P. M. Kopera, K. Shaklee, K. Sweeney, “Polarization maintaining single mode couplers,” in Fiber Optic Couplers, Connectors, and Splice Technology II, D. W. Stowe, ed., Proc. Soc. Photo-Opt. Instrum. Eng.574, 122–128 (1985).
  7. S. L. A. Carrara, B. Y. Kim, H. J. Shaw, “Elasto-optic alignment of birefringent axes in polarization maintaining optical fiber,” Opt. Lett. 11, 470–472 (1986).
    [CrossRef] [PubMed]
  8. J. W. Dally, W. F. Riley, Experimental Stress Analysis, 2nd ed. (McGraw-Hill, New York, 1978).
  9. S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1970).
  10. K. Okamota, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
    [CrossRef]
  11. C.-L. Chen, W. K. Burns, “Polarization characteristics of single-mode fiber couplers,” IEEE J. Quantum Electron QE-18, 1589–1600 (1982).
    [CrossRef]

1988

M. Abebe, C. A. Villarruel, W. K. Burns, “Reproducible fabrication method for polarization preserving single-mode fiber couplers,” IEEE J. Lightwave Technol. 6, 1191–1198 (1988).
[CrossRef]

1986

J. Yokohama, M. Kawachi, K. Okamoto, J. Noda, “Polarisation maintaining fibre couplers with low excess loss,” Electron Lett. 22, 929–930 (1986).
[CrossRef]

S. L. A. Carrara, B. Y. Kim, H. J. Shaw, “Elasto-optic alignment of birefringent axes in polarization maintaining optical fiber,” Opt. Lett. 11, 470–472 (1986).
[CrossRef] [PubMed]

1983

W. Pleibel, R. H. Stolen, “Polarisation-preserving coupler with self aligning birefringent fibres,” Electron Lett. 19, 825–826 (1983).
[CrossRef]

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

1982

C.-L. Chen, W. K. Burns, “Polarization characteristics of single-mode fiber couplers,” IEEE J. Quantum Electron QE-18, 1589–1600 (1982).
[CrossRef]

1981

K. Okamota, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
[CrossRef]

Abebe, M.

M. Abebe, C. A. Villarruel, W. K. Burns, “Reproducible fabrication method for polarization preserving single-mode fiber couplers,” IEEE J. Lightwave Technol. 6, 1191–1198 (1988).
[CrossRef]

Burns, W. K.

M. Abebe, C. A. Villarruel, W. K. Burns, “Reproducible fabrication method for polarization preserving single-mode fiber couplers,” IEEE J. Lightwave Technol. 6, 1191–1198 (1988).
[CrossRef]

C.-L. Chen, W. K. Burns, “Polarization characteristics of single-mode fiber couplers,” IEEE J. Quantum Electron QE-18, 1589–1600 (1982).
[CrossRef]

Carrara, S. L. A.

Chen, C.-L.

C.-L. Chen, W. K. Burns, “Polarization characteristics of single-mode fiber couplers,” IEEE J. Quantum Electron QE-18, 1589–1600 (1982).
[CrossRef]

Corke, M.

M. Corke, B. M. Kale, M. Keur, P. M. Kopera, K. Shaklee, K. Sweeney, “Polarization maintaining single mode couplers,” in Fiber Optic Couplers, Connectors, and Splice Technology II, D. W. Stowe, ed., Proc. Soc. Photo-Opt. Instrum. Eng.574, 122–128 (1985).

Dally, J. W.

J. W. Dally, W. F. Riley, Experimental Stress Analysis, 2nd ed. (McGraw-Hill, New York, 1978).

Edahiro, T.

K. Okamota, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
[CrossRef]

Goodier, J. N.

S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1970).

Hosaka, T.

K. Okamota, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
[CrossRef]

Kale, B. M.

M. Corke, B. M. Kale, M. Keur, P. M. Kopera, K. Shaklee, K. Sweeney, “Polarization maintaining single mode couplers,” in Fiber Optic Couplers, Connectors, and Splice Technology II, D. W. Stowe, ed., Proc. Soc. Photo-Opt. Instrum. Eng.574, 122–128 (1985).

Kawachi, M.

J. Yokohama, M. Kawachi, K. Okamoto, J. Noda, “Polarisation maintaining fibre couplers with low excess loss,” Electron Lett. 22, 929–930 (1986).
[CrossRef]

Keur, M.

M. Corke, B. M. Kale, M. Keur, P. M. Kopera, K. Shaklee, K. Sweeney, “Polarization maintaining single mode couplers,” in Fiber Optic Couplers, Connectors, and Splice Technology II, D. W. Stowe, ed., Proc. Soc. Photo-Opt. Instrum. Eng.574, 122–128 (1985).

Kim, B. Y.

Kopera, P. M.

M. Corke, B. M. Kale, M. Keur, P. M. Kopera, K. Shaklee, K. Sweeney, “Polarization maintaining single mode couplers,” in Fiber Optic Couplers, Connectors, and Splice Technology II, D. W. Stowe, ed., Proc. Soc. Photo-Opt. Instrum. Eng.574, 122–128 (1985).

Noda, J.

J. Yokohama, M. Kawachi, K. Okamoto, J. Noda, “Polarisation maintaining fibre couplers with low excess loss,” Electron Lett. 22, 929–930 (1986).
[CrossRef]

Okamota, K.

K. Okamota, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
[CrossRef]

Okamoto, K.

J. Yokohama, M. Kawachi, K. Okamoto, J. Noda, “Polarisation maintaining fibre couplers with low excess loss,” Electron Lett. 22, 929–930 (1986).
[CrossRef]

Olson, G. A.

G. A. Olson, J. R. Onstott, “Polarization-maintaining optical fibers for coupler fabrication,” U.S. Patent4,906,068 (6March1990).

Onstott, J. R.

G. A. Olson, J. R. Onstott, “Polarization-maintaining optical fibers for coupler fabrication,” U.S. Patent4,906,068 (6March1990).

Pleibel, W.

W. Pleibel, R. H. Stolen, “Polarisation-preserving coupler with self aligning birefringent fibres,” Electron Lett. 19, 825–826 (1983).
[CrossRef]

Rashleigh, S. C.

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

Riley, W. F.

J. W. Dally, W. F. Riley, Experimental Stress Analysis, 2nd ed. (McGraw-Hill, New York, 1978).

Shaklee, K.

M. Corke, B. M. Kale, M. Keur, P. M. Kopera, K. Shaklee, K. Sweeney, “Polarization maintaining single mode couplers,” in Fiber Optic Couplers, Connectors, and Splice Technology II, D. W. Stowe, ed., Proc. Soc. Photo-Opt. Instrum. Eng.574, 122–128 (1985).

Shaw, H. J.

Stolen, R. H.

W. Pleibel, R. H. Stolen, “Polarisation-preserving coupler with self aligning birefringent fibres,” Electron Lett. 19, 825–826 (1983).
[CrossRef]

Sweeney, K.

M. Corke, B. M. Kale, M. Keur, P. M. Kopera, K. Shaklee, K. Sweeney, “Polarization maintaining single mode couplers,” in Fiber Optic Couplers, Connectors, and Splice Technology II, D. W. Stowe, ed., Proc. Soc. Photo-Opt. Instrum. Eng.574, 122–128 (1985).

Timoshenko, S. P.

S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1970).

Villarruel, C. A.

M. Abebe, C. A. Villarruel, W. K. Burns, “Reproducible fabrication method for polarization preserving single-mode fiber couplers,” IEEE J. Lightwave Technol. 6, 1191–1198 (1988).
[CrossRef]

Yokohama, J.

J. Yokohama, M. Kawachi, K. Okamoto, J. Noda, “Polarisation maintaining fibre couplers with low excess loss,” Electron Lett. 22, 929–930 (1986).
[CrossRef]

Electron Lett.

W. Pleibel, R. H. Stolen, “Polarisation-preserving coupler with self aligning birefringent fibres,” Electron Lett. 19, 825–826 (1983).
[CrossRef]

J. Yokohama, M. Kawachi, K. Okamoto, J. Noda, “Polarisation maintaining fibre couplers with low excess loss,” Electron Lett. 22, 929–930 (1986).
[CrossRef]

IEEE J. Lightwave Technol.

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

M. Abebe, C. A. Villarruel, W. K. Burns, “Reproducible fabrication method for polarization preserving single-mode fiber couplers,” IEEE J. Lightwave Technol. 6, 1191–1198 (1988).
[CrossRef]

IEEE J. Quantum Electron

C.-L. Chen, W. K. Burns, “Polarization characteristics of single-mode fiber couplers,” IEEE J. Quantum Electron QE-18, 1589–1600 (1982).
[CrossRef]

IEEE J. Quantum Electron.

K. Okamota, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
[CrossRef]

Opt. Lett.

Other

J. W. Dally, W. F. Riley, Experimental Stress Analysis, 2nd ed. (McGraw-Hill, New York, 1978).

S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1970).

G. A. Olson, J. R. Onstott, “Polarization-maintaining optical fibers for coupler fabrication,” U.S. Patent4,906,068 (6March1990).

M. Corke, B. M. Kale, M. Keur, P. M. Kopera, K. Shaklee, K. Sweeney, “Polarization maintaining single mode couplers,” in Fiber Optic Couplers, Connectors, and Splice Technology II, D. W. Stowe, ed., Proc. Soc. Photo-Opt. Instrum. Eng.574, 122–128 (1985).

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Figures (5)

Fig. 1
Fig. 1

Eccentrically coated optical fiber and the definitions of various geometric variables used in the finite element analysis.

Fig. 2
Fig. 2

Theoretical and FEA stress results for a homogeneous cylinder of radius r.

Fig. 3
Fig. 3

Finite-element model of an eccentricially coated optical fiber showing the deformation induced by compressive loading. The dashed line is the original fiber shape.

Fig. 4
Fig. 4

FEA result summary of extrinsic birefringent angle α versus fiber eccentricity (ξ, Ө) δ = 10 μm.

Fig. 5
Fig. 5

FEA component stress results (ξ = 30 μm, δ = 10 μm).

Tables (1)

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Table I Finite-element Model Parametric Variable Definitions

Equations (4)

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B = ( 2 π / λ ) ( n 1 n 2 ) = C ( 2 π / λ ) ( σ 1 σ 2 ) ,
σ x = F π r [ 1 4 r 2 x 2 ( r 2 + x 2 ) 2 ] , σ y = F π r [ 1 4 r 2 ( r 2 + x 2 ) 2 ] .
( σ 1 , σ 2 ) = ( σ x + σ y 2 ) ± [ ( σ x σ y 2 ) 2 τ x y 2 ] 1 / 2 ,
tan 2 ϕ = 2 τ x y ( σ x σ y ) .

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