Abstract

It is shown that interferograms generated by passing light perpendicular to the axis of a fiber can be used to obtain the maximum refractive index difference and the index profile shape to better than ±10% accuracy in regions of the core where α is constant. This technique avoids the time consuming sample preparation required for the slab method, the propagation problems associated with the near-field technique, and the surface quality problem associated with the reflection technique.

© 1977 Optical Society of America

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References

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  1. D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).
  2. C. A. Burrus, R. D. Standley, Appl. Opt. 13, 2365 (1974).
    [CrossRef] [PubMed]
  3. B. C. Wonsiewicz, W. G. French, P. D. Lazay, J. R. Simpson, Appl. Opt. 15, 1048 (1976).
    [CrossRef] [PubMed]
  4. H. M. Presby, W. Mammel, R. M. Derosier, Rev. Sci. Instrum. 47, 348 (1976).
    [CrossRef]
  5. J. Stone, R. M. Derosier, Rev. Sci. Instrum. 47, 885 (1976).
    [CrossRef]
  6. R. F. Heitzenrater, E. J. Korda, S. J. Louisnathan, “Preparation of Optical Waveguide Fiber Thin Sections for Interference Microscope Measurements,” American Ceramic Society Fall Meeting, Bedford, Pa., 13–15 October 1976.
  7. F. M. E. Sladen, D. N. Payne, M. J. Adams, Appl. Phys. Lett. 28, 255 (1976).
    [CrossRef]
  8. M. Ikeda, M. Tateda, H. Yoshikiyo, Appl. Opt. 14, 814 (1975).
    [CrossRef] [PubMed]
  9. W. Eickhoff, E. Weidel, Opt. Quantum Electron. 7, 109 (1975).
    [CrossRef]
  10. J. Stone, H. E. Earl, Opt. Quantum Electron. 8, 459 (1976).
    [CrossRef]
  11. M. E. Marhic, P. S. Ho, M. Epstein, Appl. Phys. Lett. 26, 574 (1975).
    [CrossRef]
  12. W. Krug, J. Rienitz, G. Schulz, Contributions to Interference Microscopy (Hilger and Watts, London, 1964), p. 54.
  13. W. E. Martin, Appl. Opt. 13, 2112 (1974).
    [CrossRef] [PubMed]

1976 (5)

B. C. Wonsiewicz, W. G. French, P. D. Lazay, J. R. Simpson, Appl. Opt. 15, 1048 (1976).
[CrossRef] [PubMed]

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

J. Stone, R. M. Derosier, Rev. Sci. Instrum. 47, 885 (1976).
[CrossRef]

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

J. Stone, H. E. Earl, Opt. Quantum Electron. 8, 459 (1976).
[CrossRef]

1975 (3)

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]

W. Eickhoff, E. Weidel, Opt. Quantum Electron. 7, 109 (1975).
[CrossRef]

1974 (2)

1973 (1)

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

Adams, M. J.

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

Burrus, C. A.

Derosier, R. M.

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

J. Stone, R. M. Derosier, Rev. Sci. Instrum. 47, 885 (1976).
[CrossRef]

Earl, H. E.

J. Stone, H. E. Earl, Opt. Quantum Electron. 8, 459 (1976).
[CrossRef]

Eickhoff, W.

W. Eickhoff, E. Weidel, Opt. Quantum Electron. 7, 109 (1975).
[CrossRef]

Epstein, M.

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

French, W. G.

Gloge, D.

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

Heitzenrater, R. F.

R. F. Heitzenrater, E. J. Korda, S. J. Louisnathan, “Preparation of Optical Waveguide Fiber Thin Sections for Interference Microscope Measurements,” American Ceramic Society Fall Meeting, Bedford, Pa., 13–15 October 1976.

Ho, P. S.

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

Ikeda, M.

Korda, E. J.

R. F. Heitzenrater, E. J. Korda, S. J. Louisnathan, “Preparation of Optical Waveguide Fiber Thin Sections for Interference Microscope Measurements,” American Ceramic Society Fall Meeting, Bedford, Pa., 13–15 October 1976.

Krug, W.

W. Krug, J. Rienitz, G. Schulz, Contributions to Interference Microscopy (Hilger and Watts, London, 1964), p. 54.

Lazay, P. D.

Louisnathan, S. J.

R. F. Heitzenrater, E. J. Korda, S. J. Louisnathan, “Preparation of Optical Waveguide Fiber Thin Sections for Interference Microscope Measurements,” American Ceramic Society Fall Meeting, Bedford, Pa., 13–15 October 1976.

Mammel, W.

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

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, 574 (1975).
[CrossRef]

Martin, W. E.

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

Rienitz, J.

W. Krug, J. Rienitz, G. Schulz, Contributions to Interference Microscopy (Hilger and Watts, London, 1964), p. 54.

Schulz, G.

W. Krug, J. Rienitz, G. Schulz, Contributions to Interference Microscopy (Hilger and Watts, London, 1964), p. 54.

Simpson, J. R.

Sladen, F. M. E.

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

Standley, R. D.

Stone, J.

J. Stone, R. M. Derosier, Rev. Sci. Instrum. 47, 885 (1976).
[CrossRef]

J. Stone, H. E. Earl, Opt. Quantum Electron. 8, 459 (1976).
[CrossRef]

Tateda, M.

Weidel, E.

W. Eickhoff, E. Weidel, Opt. Quantum Electron. 7, 109 (1975).
[CrossRef]

Wonsiewicz, B. C.

Yoshikiyo, H.

Appl. Opt. (4)

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]

Bell Syst. Tech. J. (1)

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

Opt. Quantum Electron. (2)

W. Eickhoff, E. Weidel, Opt. Quantum Electron. 7, 109 (1975).
[CrossRef]

J. Stone, H. E. Earl, Opt. Quantum Electron. 8, 459 (1976).
[CrossRef]

Rev. Sci. Instrum. (2)

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

J. Stone, R. M. Derosier, Rev. Sci. Instrum. 47, 885 (1976).
[CrossRef]

Other (2)

R. F. Heitzenrater, E. J. Korda, S. J. Louisnathan, “Preparation of Optical Waveguide Fiber Thin Sections for Interference Microscope Measurements,” American Ceramic Society Fall Meeting, Bedford, Pa., 13–15 October 1976.

W. Krug, J. Rienitz, G. Schulz, Contributions to Interference Microscopy (Hilger and Watts, London, 1964), p. 54.

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of Marhic fringes for a clad fiber: (a) (nf = ncl) and (b) (nfncl).

Fig. 2
Fig. 2

Marhic fringes for a clad fiber: (a) (nf = ncl) and (b) (nfncl).

Fig. 3
Fig. 3

Geometry for optical path difference for Marhic fringes.

Fig. 4
Fig. 4

Apparatus for rotating fiber about axis.

Fig. 5
Fig. 5

Marhic fringes: (a) (fiber stationary) and (b) (2-sec exposure of fiber rotating at 4 rps).]

Tables (1)

Tables Icon

Table I Comparison of Values of α and Δn Obtained by the Slab and Marhic Methods

Equations (9)

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n ( r ) = n ( 0 ) [ 1 - 2 Δ ( r / a ) α ] 1 / 2 , 0 r a ,
n ( r ) n ( 0 ) - Δ n ( r / a ) α .
n ( x ) = n ( 0 ) - Δ n a α [ ( x 2 + r p 2 ) 1 / 2 ] α .
4 [ 0 ( a 2 - r p 2 ) 1 / 2 n ( x ) d x - ( a 2 - r p 2 ) 1 / 2 n c l ] = N p λ ,
N p λ / 4 = Δ n ( a 2 - r p 2 ) 1 / 2 - Δ n a α 0 ( a 2 - r p 2 ) 1 / 2 ( x 2 + r p 2 ) α / 2 d x ,
n ( 0 ) = n c l + Δ n .
Δ n = ( α + 1 ) λ N * / 4 a α ,
N * = y max / Δ y ,             N p = y p / Δ y ,
σ Δ n Δ n = [ σ α 2 α 2 ( α + 1 ) 2 + σ a 2 a 2 ] 1 / 2 .

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