Abstract

A new method to determine the refractive-index distributions of the cores of optical fibers is presented. The fiber is immersed in index matching oil to eliminate light refraction at the outer core boundary. Collimated light is passed transversely through the fiber core and is detected with a microscope focused just above the plane of the core boundary. The intensity distribution in the image plane is recorded with the aid of a computer-controlled video-analysis system. The refractive-index profile of the fiber core is then computed from this intensity distribution. In this paper we present error estimates and show how well the focusing method agrees with the interferometric slab method. The repeatability of the index measurement is approximately 2%, an error which is easily attributable to incident light level fluctuations.

© 1979 Optical Society of America

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  1. C. A. Burrus, R. D. Standley, Appl. Opt. 13, 2365 (1974).
    [CrossRef] [PubMed]
  2. H. M. Presby, W. Mammel, R. M. Derosier, Rev. Sci. Instrum. 47, 348 (1976).
    [CrossRef]
  3. H. M. Presby, I. P. Kaminow, Appl. Opt. 15, 3029 (1976).
    [CrossRef] [PubMed]
  4. H. M. Presby, D. Marcuse, H. W. Astle, Appl. Opt. 17, 2209 (1978).
    [CrossRef] [PubMed]
  5. M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 574 (1975).
    [CrossRef]
  6. M. J. Saunders, W. B. Gardner, Appl. Opt. 16, 2368 (1977).
    [CrossRef] [PubMed]
  7. L. Boggs, H. M. Presby, D. Marcuse, “Rapid Automatic Index Profiling of Whole-Fiber Samples: Part I”, to be published in Bell Syst. Tech. J.
  8. H. M. Presby, D. Marcuse, L. Boggs, H. W. Astle, “Rapid Automatic Index Profiling of Whole Fiber Samples: Part II”, to be published in Bell Syst. Tech. J.
  9. K. Iga, Y. Kokubun, Appl. Opt. 17, 1972 (1978).
    [CrossRef] [PubMed]
  10. M. Ikeda, M. Tateda, H. Yoshikiyo, Appl. Opt. 14, 814 (1975).
    [CrossRef] [PubMed]
  11. T. Okoshi, K. Hotate, Opt. Quantum Electron. 8, 78 (1976).
    [CrossRef]
  12. F. M. E. Sladen, D. N. Payne, M. J. Adams, Appl. Phys. Lett. 28, 255 (1976).
    [CrossRef]
  13. P. L. Chu, Electron. Lett. 24, Vol. 13736 (1977).
    [CrossRef]
  14. D. Marcuse, “Refractive Index Determination by the Focusing Method”, to be published in Appl. Opt.1Jan.1979.
    [CrossRef]
  15. H. M. Presby, “Axial Refractive Index Depression in Preforms and Fibers”, to be published in Fiber Integrated Opt.

1978 (2)

1977 (2)

1976 (4)

H. M. Presby, W. Mammel, R. M. Derosier, Rev. Sci. Instrum. 47, 348 (1976).
[CrossRef]

T. Okoshi, K. Hotate, Opt. Quantum Electron. 8, 78 (1976).
[CrossRef]

F. M. E. Sladen, D. N. Payne, M. J. Adams, Appl. Phys. Lett. 28, 255 (1976).
[CrossRef]

H. M. Presby, I. P. Kaminow, Appl. Opt. 15, 3029 (1976).
[CrossRef] [PubMed]

1975 (2)

M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 574 (1975).
[CrossRef]

M. Ikeda, M. Tateda, H. Yoshikiyo, Appl. Opt. 14, 814 (1975).
[CrossRef] [PubMed]

1974 (1)

Adams, M. J.

F. M. E. Sladen, D. N. Payne, M. J. Adams, Appl. Phys. Lett. 28, 255 (1976).
[CrossRef]

Astle, H. W.

H. M. Presby, D. Marcuse, H. W. Astle, Appl. Opt. 17, 2209 (1978).
[CrossRef] [PubMed]

H. M. Presby, D. Marcuse, L. Boggs, H. W. Astle, “Rapid Automatic Index Profiling of Whole Fiber Samples: Part II”, to be published in Bell Syst. Tech. J.

Boggs, L.

H. M. Presby, D. Marcuse, L. Boggs, H. W. Astle, “Rapid Automatic Index Profiling of Whole Fiber Samples: Part II”, to be published in Bell Syst. Tech. J.

L. Boggs, H. M. Presby, D. Marcuse, “Rapid Automatic Index Profiling of Whole-Fiber Samples: Part I”, to be published in Bell Syst. Tech. J.

Burrus, C. A.

Chu, P. L.

P. L. Chu, Electron. Lett. 24, Vol. 13736 (1977).
[CrossRef]

Derosier, R. M.

H. M. Presby, W. Mammel, R. M. Derosier, Rev. Sci. Instrum. 47, 348 (1976).
[CrossRef]

Epstein, M.

M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 574 (1975).
[CrossRef]

Gardner, W. B.

Ho, P. S.

M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 574 (1975).
[CrossRef]

Hotate, K.

T. Okoshi, K. Hotate, Opt. Quantum Electron. 8, 78 (1976).
[CrossRef]

Iga, K.

Ikeda, M.

Kaminow, I. P.

Kokubun, Y.

Mammel, W.

H. M. Presby, W. Mammel, R. M. Derosier, Rev. Sci. Instrum. 47, 348 (1976).
[CrossRef]

Marcuse, D.

H. M. Presby, D. Marcuse, H. W. Astle, Appl. Opt. 17, 2209 (1978).
[CrossRef] [PubMed]

H. M. Presby, D. Marcuse, L. Boggs, H. W. Astle, “Rapid Automatic Index Profiling of Whole Fiber Samples: Part II”, to be published in Bell Syst. Tech. J.

D. Marcuse, “Refractive Index Determination by the Focusing Method”, to be published in Appl. Opt.1Jan.1979.
[CrossRef]

L. Boggs, H. M. Presby, D. Marcuse, “Rapid Automatic Index Profiling of Whole-Fiber Samples: Part I”, to be published in Bell Syst. Tech. J.

Marhic, M. E.

M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 574 (1975).
[CrossRef]

Okoshi, T.

T. Okoshi, K. Hotate, Opt. Quantum Electron. 8, 78 (1976).
[CrossRef]

Payne, D. N.

F. M. E. Sladen, D. N. Payne, M. J. Adams, Appl. Phys. Lett. 28, 255 (1976).
[CrossRef]

Presby, H. M.

H. M. Presby, D. Marcuse, H. W. Astle, Appl. Opt. 17, 2209 (1978).
[CrossRef] [PubMed]

H. M. Presby, I. P. Kaminow, Appl. Opt. 15, 3029 (1976).
[CrossRef] [PubMed]

H. M. Presby, W. Mammel, R. M. Derosier, Rev. Sci. Instrum. 47, 348 (1976).
[CrossRef]

H. M. Presby, “Axial Refractive Index Depression in Preforms and Fibers”, to be published in Fiber Integrated Opt.

L. Boggs, H. M. Presby, D. Marcuse, “Rapid Automatic Index Profiling of Whole-Fiber Samples: Part I”, to be published in Bell Syst. Tech. J.

H. M. Presby, D. Marcuse, L. Boggs, H. W. Astle, “Rapid Automatic Index Profiling of Whole Fiber Samples: Part II”, to be published in Bell Syst. Tech. J.

Saunders, M. J.

Sladen, F. M. E.

F. M. E. Sladen, D. N. Payne, M. J. Adams, Appl. Phys. Lett. 28, 255 (1976).
[CrossRef]

Standley, R. D.

Tateda, M.

Yoshikiyo, H.

Appl. Opt. (6)

Appl. Phys. Lett. (2)

M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 574 (1975).
[CrossRef]

F. M. E. Sladen, D. N. Payne, M. J. Adams, Appl. Phys. Lett. 28, 255 (1976).
[CrossRef]

Electron. Lett. 24 (1)

P. L. Chu, Electron. Lett. 24, Vol. 13736 (1977).
[CrossRef]

Opt. Quantum Electron. (1)

T. Okoshi, K. Hotate, Opt. Quantum Electron. 8, 78 (1976).
[CrossRef]

Rev. Sci. Instrum. (1)

H. M. Presby, W. Mammel, R. M. Derosier, Rev. Sci. Instrum. 47, 348 (1976).
[CrossRef]

Other (4)

L. Boggs, H. M. Presby, D. Marcuse, “Rapid Automatic Index Profiling of Whole-Fiber Samples: Part I”, to be published in Bell Syst. Tech. J.

H. M. Presby, D. Marcuse, L. Boggs, H. W. Astle, “Rapid Automatic Index Profiling of Whole Fiber Samples: Part II”, to be published in Bell Syst. Tech. J.

D. Marcuse, “Refractive Index Determination by the Focusing Method”, to be published in Appl. Opt.1Jan.1979.
[CrossRef]

H. M. Presby, “Axial Refractive Index Depression in Preforms and Fibers”, to be published in Fiber Integrated Opt.

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Figures (14)

Fig. 1
Fig. 1

Experimental arrangement to measure the index profile of optical fibers by the focusing method.

Fig. 2
Fig. 2

Schematic of the experimental arrangement.

Fig. 3
Fig. 3

Monitor display showing graded-index fiber and associated light intensity distribution. The core diameter is approximately 60 μm.

Fig. 4
Fig. 4

Focusing effects used to locate center of fiber core: (a) microscope focused slightly below center; (b) microscope focused on center; and (c) microscope focused slightly above center.

Fig. 5
Fig. 5

This figure shows three intermediate functions that are used for the computation of the refractive index: the normalized light intensity distribution P(y) in the observation plane (L = 50 μm), t(y)/y, and [t(y) − y]/y.

Fig. 6
Fig. 6

Refractive-index profile computed from the functions shown in Fig. 2.

Fig. 7
Fig. 7

Comparison of the refractive-index profile of a fiber obtained by the focusing method (solid curve) and by the interferometric slab method (broken curve).

Fig. 8
Fig. 8

Same as Fig. 4 for a different fiber.

Fig. 9
Fig. 9

Same as Fig. 4 for a different fiber.

Fig. 10
Fig. 10

Comparison of focusing (solid curve) and interferometric slab method (broken curve) for a fiber with a deep boron dip near the core boundary.

Fig. 11
Fig. 11

Comparison of focusing and slab methods for a fiber that was slightly elliptical and happened to be placed in different orientations for both measurements.

Fig. 12
Fig. 12

This is the same fiber shown in Fig. 7, but the broken line was obtained by the interferometric whole fiber method, which resolves more detail near the core center.

Fig. 13
Fig. 13

The solid curve was obtained by the focusing method by placing the observation plane 16 μm from the core center but using L = 25 μm for the index computation. Placing the observation plane close to the fiber core brings out more of the fine structure of the index profile. The broken line was obtained by the interferometric whole fiber method.

Fig. 14
Fig. 14

Focusing effects of fiber exhibiting relatively large central index variations: (a) microscope focused on center; (b)–(f) microscope focused at L = 10 μm, 16 μm, 30 μm, 50 μm, and 100 μm, respectively.

Equations (19)

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t ( y ) = 0 y P ( y ) d y
n ( r ) - n c = n c π L r a t - y ( t ) ( t 2 - r 2 ) 1 / 2 d t .
n ( r ) - n c = Δ n
y ( t ) - y 0 ( t ) = Δ y ,
( Δ n - Δ n 0 ) 2 = ( n c π L ) 2 r a d t r a d t Δ y ( t ) Δ y ( t ) ( t 2 - r 2 ) 1 / 2 ( t 2 - r 2 ) 1 / 2 .
d y / d t = 1 / P
Δ y = ( Δ t ) / P 0 ,
Δ y ( t ) Δ y ( t ) = Δ t Δ t P 0 ( t ) P 0 ( t ) .
[ P ( y ) - P 0 ( y ) ] [ P ( y ) - P 0 ( y ) ] = [ P ( y ) - P 0 ( y ) ] 2 D δ ( y - y ) ,
Δ t Δ t = { D [ P ( y ) - P 0 ( y ) ] 2 y for y > y , D [ P ( y ) - P 0 ( y ) ] 2 y for y < y .
[ ( Δ n - Δ n 0 ) 2 ] 1 / 2 = n c π L { 2 D ( a - r ) [ P ( y ) - P 0 ( y ) ] 2 } 1 / 2 .
δ ( Δ n ) = n c π L r a δ y ( t 2 - r 2 ) 1 / 2 d t .
δ t = 0 y δ P ( y ) d y = y δ P ,
δ y = y [ ( δ P ) / P 0 ] .
δ ( Δ n ) = [ ( n c ) / ( π L ) ] ( a 2 - r 2 ) 1 / 2 δ P .
[ [ P ( y ) - P 0 ( y ) ] 2 ] 1 / 2 = 0.01.
[ ( Δ n - Δ n 0 ) 2 ] 1 / 2 = 7.6 × 10 - 4 .
[ ( Δ n - Δ n 0 ) 2 ] 1 / 2 10 - 4 .
δ ( Δ n ) = 0.46 δ P .

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