Abstract

A set of successive approximation formulas for calculating the refractive index profile of optical fibers from their transverse interference patterns has been derived. The probing ray refraction due to the index gradient in the core is corrected for by these formulas, and the accuracy of index determination is improved. The error is confirmed to be less than 3 × 10−3% of the index difference by means of computer simulations. The index profiles of some optical fibers are practically determined with the help of these formulas.

© 1978 Optical Society of America

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References

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1977

1976

1975

K. Jürgensen, Appl. Opt. 14, 163 (1975).
[PubMed]

A. M. Hunter, P. W. Schreiber, Appl. Opt. 14, 643 (1975).
[CrossRef]

B. Shiraishi, G. Tanaka, S. Suzuki, S. Kurosaki, Nat. Conv. Rec. IECE Jpn. 891 (1975).

K. Nishizawa, M. Toyama, T. Fukushige, Conv. Rec. Jpn. Soc. Appl. Phys. 23a-G-1 (1975).

M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 575 (1975).
[CrossRef]

1973

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

1965

1952

F. D. Bennett, W. C. Carter, V. E. Bergdolt, J. Appl. Phys. 23, 453 (1952).
[CrossRef]

Bennett, F. D.

F. D. Bennett, W. C. Carter, V. E. Bergdolt, J. Appl. Phys. 23, 453 (1952).
[CrossRef]

Bergdolt, V. E.

F. D. Bennett, W. C. Carter, V. E. Bergdolt, J. Appl. Phys. 23, 453 (1952).
[CrossRef]

Carter, W. C.

F. D. Bennett, W. C. Carter, V. E. Bergdolt, J. Appl. Phys. 23, 453 (1952).
[CrossRef]

Epstein, M.

M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 575 (1975).
[CrossRef]

Fukushige, T.

K. Nishizawa, M. Toyama, T. Fukushige, Conv. Rec. Jpn. Soc. Appl. Phys. 23a-G-1 (1975).

Gardner, W. B.

Gloge, D.

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Ho, P. S.

M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 575 (1975).
[CrossRef]

Hunter, A. M.

Iga, K.

K. Iga, N. Yamamoto, Appl. Opt. 16, 1305 (1977).
[CrossRef] [PubMed]

K. Iga, Y. Kokubun, at 1977 International Conference on Integrated Optics and Optical Fiber Communication (1977), paper C2–4.

Jürgensen, K.

Kahl, G. D.

Keck, D. B.

Kokubun, Y.

K. Iga, Y. Kokubun, at 1977 International Conference on Integrated Optics and Optical Fiber Communication (1977), paper C2–4.

Kurosaki, S.

B. Shiraishi, G. Tanaka, S. Suzuki, S. Kurosaki, Nat. Conv. Rec. IECE Jpn. 891 (1975).

Marcatili, E. A. J.

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Marhic, M. E.

M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 575 (1975).
[CrossRef]

Mylin, D. C.

Nishizawa, K.

K. Nishizawa, M. Toyama, T. Fukushige, Conv. Rec. Jpn. Soc. Appl. Phys. 23a-G-1 (1975).

Olshansky, R.

Saunders, M. J.

Schreiber, P. W.

Shiraishi, B.

B. Shiraishi, G. Tanaka, S. Suzuki, S. Kurosaki, Nat. Conv. Rec. IECE Jpn. 891 (1975).

Stone, F. T.

Suzuki, S.

B. Shiraishi, G. Tanaka, S. Suzuki, S. Kurosaki, Nat. Conv. Rec. IECE Jpn. 891 (1975).

Tanaka, G.

B. Shiraishi, G. Tanaka, S. Suzuki, S. Kurosaki, Nat. Conv. Rec. IECE Jpn. 891 (1975).

Toyama, M.

K. Nishizawa, M. Toyama, T. Fukushige, Conv. Rec. Jpn. Soc. Appl. Phys. 23a-G-1 (1975).

Yamamoto, N.

1977 International Conference on Integrated Optics and Optical Fiber Communication

K. Iga, Y. Kokubun, at 1977 International Conference on Integrated Optics and Optical Fiber Communication (1977), paper C2–4.

Appl. Opt.

Appl. Phys. Lett.

M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 575 (1975).
[CrossRef]

Bell Syst. Tech. J.

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Conv. Rec. Jpn. Soc. Appl. Phys. 23a-G-1

K. Nishizawa, M. Toyama, T. Fukushige, Conv. Rec. Jpn. Soc. Appl. Phys. 23a-G-1 (1975).

J. Appl. Phys.

F. D. Bennett, W. C. Carter, V. E. Bergdolt, J. Appl. Phys. 23, 453 (1952).
[CrossRef]

J. Opt. Soc. Am.

Nat. Conv. Rec. IECE Jpn. 891

B. Shiraishi, G. Tanaka, S. Suzuki, S. Kurosaki, Nat. Conv. Rec. IECE Jpn. 891 (1975).

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Figures (4)

Fig. 1
Fig. 1

Ray trajectory in a fiber which has a cylindrically symmetric index profile. [The angle ψ(y) is on the order of 10−2 rad in magnitude.]

Fig. 2
Fig. 2

Principal errors obtained by computer simulations.

Fig. 3
Fig. 3

Principal errors as α takes various values.

Fig. 4
Fig. 4

(a) Transverse interference pattern of a graded index fiber made of compound glass. (b) Refractive index profile reduced from the pattern shown in (a) with the help of Eqs. (5)(7).

Equations (8)

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λ D · R ( y · sec ψ ) = P 0 P 1 n ( r ) d s 2 n 2 ( a 2 y 2 ) 1 / 2 n 2 y · tan ψ ,
P 0 P 1 n ( r ) d s = 2 n 2 ( a 2 y 2 ) 1 / 2 2 n 2 y u 2 [ d ln n ( u ) d u ] × u 2 d u ( u 2 n 2 2 y 2 ) 1 / 2
ψ ( y ) = 2 n 2 y n 2 y u 2 [ d ln n ( u ) d u ] d u ( u 2 n 2 2 y 2 ) 1 / 2 ,
n ( u ) = n 2 · exp { 1 π u / n 2 a [ λ D · d R ( y ) d y ] d u ( n 2 2 y 2 u 2 ) 1 / 2 } .
ψ 2 ( y ) = λ n 2 D · d R ( y ) d y .
F 2 ( y ) = λ D · R { y [ 1 + ψ 2 2 ( y ) 2 ] } + n 2 y 3 ψ 2 3 ( y ) ,
n ( u ) = n 2 · exp [ 1 π u / n 2 a d F 2 ( y ) d y d y ( n 2 2 y 2 u 2 ) 1 / 2 ] .
ε = n cal ( r ) n ( r ) n ( 0 ) ,

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