Abstract

This paper investigates experimentally the change of the refractive index, due to forces such as pulling and pure bending, in an optical fiber fabricated by the CVD technique. It is found that this phenomenon can be interpreted in terms of a simple model of the fiber, that is, a mechanically homogeneous circular rod. We compare the effect of the refractive-index change and that of a geometrical deformation of the fiber on transmission characteristics. A new method based on photoelasticity is also proposed to measure the curvature distribution of a fiber whose axis is deformed by external forces.

© 1978 Optical Society of America

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  1. W. B. Gardner, Bell Syst. Tech. J. 54, 457 (1975).
  2. D. B. Keck, Proc. IEEE 62, 649 (1974).
    [CrossRef]
  3. W. A. Gambling, D. N. Payne, H. Matsumura, Appl. Opt. 14, 1538 (1975).
    [CrossRef] [PubMed]
  4. R. Olshansky, Appl. Opt. 14, 20 (1975).
    [CrossRef] [PubMed]
  5. D. Gloge, Bell Syst. Tech. J. 54, 245 (1975).
  6. M. Ikeda, Y. Murakami, K. Kitayama, Appl. Opt. 16, 1045 (1977).
    [PubMed]
  7. J. Hanny, Electron. Lett. 12, 173 (1976).
    [CrossRef]
  8. O. G. Leminger, Electron. Lett. 13, 370 (1977).
    [CrossRef]
  9. Y. Namihira, M. Kudo, Y. Mushiake, Electron. Commun. Jpn. J60-c, 391 (1977).
  10. K. Brugger, Appl. Opt. 10, 437 (1971).
    [CrossRef] [PubMed]
  11. S. Kawakami, S. Nishida, IEEE J. Quantum Electron. QE-10, 879 (1974).
    [CrossRef]
  12. S. Kawakami, S. Nishida, M. Sumi, Proc. Inst. Electr. Eng. 123, 586 (1976).
    [CrossRef]
  13. E. B. Shand, Glass Engineering Handbook (McGraw-Hill, New York, 1958), p. 58.
  14. W. Primak, D. Post, J. Appl. Phys. 30, 779 (1959).
    [CrossRef]
  15. M. Heiblum, J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
    [CrossRef]
  16. S. Kawakami, M. Miyagi, S. Nishida, Appl. Opt. 14, 2588 (1975).
    [CrossRef] [PubMed]
  17. K. Inada, R. Yamauchi, S. Tanaka, in Digest of Topical Meeting on Optical Fiber Transmission 2 (Optical Society of America, Washington, D.C., 1977), post deadline paper PD-3.
  18. W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 12, 567 (1976).
    [CrossRef]
  19. R. A. Sammut, Electron. Lett. 13, 418 (1977).
    [CrossRef]
  20. S. Timoshenko, Strength of Materials: Part 1 (Van Nostrand, New York, 1955), Chap. 5.
  21. Ref. 20, Part 2, Chap. 2.

1977

M. Ikeda, Y. Murakami, K. Kitayama, Appl. Opt. 16, 1045 (1977).
[PubMed]

O. G. Leminger, Electron. Lett. 13, 370 (1977).
[CrossRef]

Y. Namihira, M. Kudo, Y. Mushiake, Electron. Commun. Jpn. J60-c, 391 (1977).

R. A. Sammut, Electron. Lett. 13, 418 (1977).
[CrossRef]

1976

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 12, 567 (1976).
[CrossRef]

S. Kawakami, S. Nishida, M. Sumi, Proc. Inst. Electr. Eng. 123, 586 (1976).
[CrossRef]

J. Hanny, Electron. Lett. 12, 173 (1976).
[CrossRef]

1975

W. B. Gardner, Bell Syst. Tech. J. 54, 457 (1975).

W. A. Gambling, D. N. Payne, H. Matsumura, Appl. Opt. 14, 1538 (1975).
[CrossRef] [PubMed]

R. Olshansky, Appl. Opt. 14, 20 (1975).
[CrossRef] [PubMed]

D. Gloge, Bell Syst. Tech. J. 54, 245 (1975).

M. Heiblum, J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

S. Kawakami, M. Miyagi, S. Nishida, Appl. Opt. 14, 2588 (1975).
[CrossRef] [PubMed]

1974

S. Kawakami, S. Nishida, IEEE J. Quantum Electron. QE-10, 879 (1974).
[CrossRef]

D. B. Keck, Proc. IEEE 62, 649 (1974).
[CrossRef]

1971

1959

W. Primak, D. Post, J. Appl. Phys. 30, 779 (1959).
[CrossRef]

Brugger, K.

Gambling, W. A.

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 12, 567 (1976).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Appl. Opt. 14, 1538 (1975).
[CrossRef] [PubMed]

Gardner, W. B.

W. B. Gardner, Bell Syst. Tech. J. 54, 457 (1975).

Gloge, D.

D. Gloge, Bell Syst. Tech. J. 54, 245 (1975).

Hanny, J.

J. Hanny, Electron. Lett. 12, 173 (1976).
[CrossRef]

Harris, J. H.

M. Heiblum, J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

Heiblum, M.

M. Heiblum, J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

Ikeda, M.

Inada, K.

K. Inada, R. Yamauchi, S. Tanaka, in Digest of Topical Meeting on Optical Fiber Transmission 2 (Optical Society of America, Washington, D.C., 1977), post deadline paper PD-3.

Kawakami, S.

S. Kawakami, S. Nishida, M. Sumi, Proc. Inst. Electr. Eng. 123, 586 (1976).
[CrossRef]

S. Kawakami, M. Miyagi, S. Nishida, Appl. Opt. 14, 2588 (1975).
[CrossRef] [PubMed]

S. Kawakami, S. Nishida, IEEE J. Quantum Electron. QE-10, 879 (1974).
[CrossRef]

Keck, D. B.

D. B. Keck, Proc. IEEE 62, 649 (1974).
[CrossRef]

Kitayama, K.

Kudo, M.

Y. Namihira, M. Kudo, Y. Mushiake, Electron. Commun. Jpn. J60-c, 391 (1977).

Leminger, O. G.

O. G. Leminger, Electron. Lett. 13, 370 (1977).
[CrossRef]

Matsumura, H.

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 12, 567 (1976).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Appl. Opt. 14, 1538 (1975).
[CrossRef] [PubMed]

Miyagi, M.

Murakami, Y.

Mushiake, Y.

Y. Namihira, M. Kudo, Y. Mushiake, Electron. Commun. Jpn. J60-c, 391 (1977).

Namihira, Y.

Y. Namihira, M. Kudo, Y. Mushiake, Electron. Commun. Jpn. J60-c, 391 (1977).

Nishida, S.

S. Kawakami, S. Nishida, M. Sumi, Proc. Inst. Electr. Eng. 123, 586 (1976).
[CrossRef]

S. Kawakami, M. Miyagi, S. Nishida, Appl. Opt. 14, 2588 (1975).
[CrossRef] [PubMed]

S. Kawakami, S. Nishida, IEEE J. Quantum Electron. QE-10, 879 (1974).
[CrossRef]

Olshansky, R.

Payne, D. N.

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 12, 567 (1976).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Appl. Opt. 14, 1538 (1975).
[CrossRef] [PubMed]

Post, D.

W. Primak, D. Post, J. Appl. Phys. 30, 779 (1959).
[CrossRef]

Primak, W.

W. Primak, D. Post, J. Appl. Phys. 30, 779 (1959).
[CrossRef]

Sammut, R. A.

R. A. Sammut, Electron. Lett. 13, 418 (1977).
[CrossRef]

Shand, E. B.

E. B. Shand, Glass Engineering Handbook (McGraw-Hill, New York, 1958), p. 58.

Sumi, M.

S. Kawakami, S. Nishida, M. Sumi, Proc. Inst. Electr. Eng. 123, 586 (1976).
[CrossRef]

Tanaka, S.

K. Inada, R. Yamauchi, S. Tanaka, in Digest of Topical Meeting on Optical Fiber Transmission 2 (Optical Society of America, Washington, D.C., 1977), post deadline paper PD-3.

Timoshenko, S.

S. Timoshenko, Strength of Materials: Part 1 (Van Nostrand, New York, 1955), Chap. 5.

Yamauchi, R.

K. Inada, R. Yamauchi, S. Tanaka, in Digest of Topical Meeting on Optical Fiber Transmission 2 (Optical Society of America, Washington, D.C., 1977), post deadline paper PD-3.

Appl. Opt.

Bell Syst. Tech. J.

D. Gloge, Bell Syst. Tech. J. 54, 245 (1975).

W. B. Gardner, Bell Syst. Tech. J. 54, 457 (1975).

Electron. Commun. Jpn.

Y. Namihira, M. Kudo, Y. Mushiake, Electron. Commun. Jpn. J60-c, 391 (1977).

Electron. Lett.

J. Hanny, Electron. Lett. 12, 173 (1976).
[CrossRef]

O. G. Leminger, Electron. Lett. 13, 370 (1977).
[CrossRef]

W. A. Gambling, D. N. Payne, H. Matsumura, Electron. Lett. 12, 567 (1976).
[CrossRef]

R. A. Sammut, Electron. Lett. 13, 418 (1977).
[CrossRef]

IEEE J. Quantum Electron.

S. Kawakami, S. Nishida, IEEE J. Quantum Electron. QE-10, 879 (1974).
[CrossRef]

M. Heiblum, J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

J. Appl. Phys.

W. Primak, D. Post, J. Appl. Phys. 30, 779 (1959).
[CrossRef]

Proc. IEEE

D. B. Keck, Proc. IEEE 62, 649 (1974).
[CrossRef]

Proc. Inst. Electr. Eng.

S. Kawakami, S. Nishida, M. Sumi, Proc. Inst. Electr. Eng. 123, 586 (1976).
[CrossRef]

Other

E. B. Shand, Glass Engineering Handbook (McGraw-Hill, New York, 1958), p. 58.

S. Timoshenko, Strength of Materials: Part 1 (Van Nostrand, New York, 1955), Chap. 5.

Ref. 20, Part 2, Chap. 2.

K. Inada, R. Yamauchi, S. Tanaka, in Digest of Topical Meeting on Optical Fiber Transmission 2 (Optical Society of America, Washington, D.C., 1977), post deadline paper PD-3.

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Figures (10)

Fig. 1
Fig. 1

Experimental arrangement.

Fig. 2
Fig. 2

Schematic arrangements of the fiber, the polarizer P1, and the analyzer P2 when they are viewed from the detector.

Fig. 3
Fig. 3

Geometry and refractive-index profile of the W fiber.

Fig. 4
Fig. 4

Photomicrograph of the birefringence in the fiber due to the forces (a) under the action of a tensile force and (b) under the action of a pure bending force.

Fig. 5
Fig. 5

Relative output patterns P/P: (a) under the action of the tensile force; and (b) under the action of the pure bending force.

Fig. 6
Fig. 6

Geometry and refractive-index profile of curved and straight slab waveguides. The waveguide (a) can be transformed into equivalent structure (b).

Fig. 7
Fig. 7

(a) Schematic diagram of an apparatus for the experiment. (b) Photomicrograph of the birefringence in the fiber due to a concentrated load.

Fig. 8
Fig. 8

Schematic diagram of the stress distribution on the cross section of the fiber. Magnitude of the axial stress is shown by the shaded area.

Fig. 9
Fig. 9

Relative output patterns when the detector is scanned in the y direction. With respect to the right-hand side of the span, we obtained the same results.

Fig. 10
Fig. 10

Curvature distribution of the fiber as deduced by three different methods.

Equations (13)

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

σ = T / S ( for the tensile force ) ,
= E y / R ( for the pure bending force ) ,
n l = n 0 + C 1 σ , n t = n 0 + C 2 σ ,
δ ( y ) = Δ n k 2 a [ 1 ( y / a ) 2 ] 1 / 2 ,
sin 2 δ ( y ) 2 = P P .
sin 2 { C ( T / S ) k a [ 1 ( y / a ) 2 ] 1 / 2 } = P / P
sin 2 { C ( E y / R ) k a [ 1 ( y / a ) 2 ] 1 / 2 } = P / P
Δ n c Δ n t n 0 y / R C 2 E y / R 5 .
σ = T / S + E y / R
δ ( y , z ) = 2 k a C [ T / S + E y / R ( z ) ] [ 1 ( y / a ) 2 ] 1 / 2 .
P ̂ / P ̂ = 1 1 P P d ( y a ) ,
P ̂ / P ̂ = 1 1 sin 2 δ ( y , z ) 2 d ( y a ) .
1 / R ( z ) = 24 Y z l 3 ,

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