Abstract

The back-scattered pattern produced by a plane-polarized beam incident normally on a large uncladded optical fiber can be used to determine the refractive index and the radius of the fiber. The geometric-optics method is used to analyze the pattern. A new procedure to find the radius of the fiber is proposed. The procedure can make use of nearly the whole of the back-scattered pattern, without need to measure exactly the positions of all of the individual fringes. Special attention is given to the limits of accuracy.

© 1975 Optical Society of America

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References

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  1. W. J. Onions and B. Ellingham, Brit. J. Appl. Phys. 10, 328 (1959).
    [CrossRef]
  2. W. A. Farone and M. Kerker, J. Opt. Soc. Am. 56, 481 (1966).
    [CrossRef]
  3. K. C. Kao, T. W. Davies, and R. Worthington, Rad. Elect. Eng. 39, 105 (1970).
    [CrossRef]
  4. R. Horton and W. J. Williamson, J. Opt. Soc. Am. 63, 1204 (1973).
    [CrossRef]
  5. H. M. Presby, J. Opt. Soc. Am. 64, 280 (1974).
    [CrossRef]
  6. J. W. Y. Lit, Phys. in Canada 30, No. 3, 15 (1974).
  7. In Ref. 5, the plus signs in Eqs. (13) and (14), from which Eq. (18) is derived, should be replaced by minus signs.
  8. The author is grateful to H. M. Presby for sending an enlarged photo that corresponded to Fig. 6c in Ref. 5, which did not show the fine fringes, and also a suitably underexposed photo of the same back-scattered pattern, which showed clearly the fine structures.
  9. All of the scattered patterns presented in this article were calculated by assuming the amplitude of the incident ray to be unity, and by taking into account the Fresnel formulas for reflection and refraction.

1974 (2)

H. M. Presby, J. Opt. Soc. Am. 64, 280 (1974).
[CrossRef]

J. W. Y. Lit, Phys. in Canada 30, No. 3, 15 (1974).

1973 (1)

1970 (1)

K. C. Kao, T. W. Davies, and R. Worthington, Rad. Elect. Eng. 39, 105 (1970).
[CrossRef]

1966 (1)

1959 (1)

W. J. Onions and B. Ellingham, Brit. J. Appl. Phys. 10, 328 (1959).
[CrossRef]

Davies, T. W.

K. C. Kao, T. W. Davies, and R. Worthington, Rad. Elect. Eng. 39, 105 (1970).
[CrossRef]

Ellingham, B.

W. J. Onions and B. Ellingham, Brit. J. Appl. Phys. 10, 328 (1959).
[CrossRef]

Farone, W. A.

Horton, R.

Kao, K. C.

K. C. Kao, T. W. Davies, and R. Worthington, Rad. Elect. Eng. 39, 105 (1970).
[CrossRef]

Kerker, M.

Lit, J. W. Y.

J. W. Y. Lit, Phys. in Canada 30, No. 3, 15 (1974).

Onions, W. J.

W. J. Onions and B. Ellingham, Brit. J. Appl. Phys. 10, 328 (1959).
[CrossRef]

Presby, H. M.

Williamson, W. J.

Worthington, R.

K. C. Kao, T. W. Davies, and R. Worthington, Rad. Elect. Eng. 39, 105 (1970).
[CrossRef]

Brit. J. Appl. Phys. (1)

W. J. Onions and B. Ellingham, Brit. J. Appl. Phys. 10, 328 (1959).
[CrossRef]

J. Opt. Soc. Am. (3)

Phys. in Canada (1)

J. W. Y. Lit, Phys. in Canada 30, No. 3, 15 (1974).

Rad. Elect. Eng. (1)

K. C. Kao, T. W. Davies, and R. Worthington, Rad. Elect. Eng. 39, 105 (1970).
[CrossRef]

Other (3)

In Ref. 5, the plus signs in Eqs. (13) and (14), from which Eq. (18) is derived, should be replaced by minus signs.

The author is grateful to H. M. Presby for sending an enlarged photo that corresponded to Fig. 6c in Ref. 5, which did not show the fine fringes, and also a suitably underexposed photo of the same back-scattered pattern, which showed clearly the fine structures.

All of the scattered patterns presented in this article were calculated by assuming the amplitude of the incident ray to be unity, and by taking into account the Fresnel formulas for reflection and refraction.

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Figures (8)

FIG. 1
FIG. 1

Geometry of incident and scattered rays.

FIG. 2
FIG. 2

Amplitudes and back-scattering angles of rays back-scattered from an optical fiber with refractive index n = 1.5. Amplitude of incident wave is assumed to be unity. Waves are linearly polarized with E vector either parallel or perpendicular to the axis of the fiber.

FIG. 3
FIG. 3

Back-scattered patterns. Index of refraction of optical fiber = n = 1.5. Electric vector E of wave is parallel to the axis of the fiber. Curve A (dotted line), interference between rays i1 and i′. Curve B (broken line), interference between rays i2 and i′. Curve C (full line), results of rays i1, i2, and i′ interfering.

FIG. 4
FIG. 4

Same as in Fig. 3, but with the E vector perpendicular to the axis of the fiber.

FIG. 5
FIG. 5

Same as in Fig. 3, but with Φ close to Φm.

FIG. 6
FIG. 6

Same as in Fig. 4, but with Φ close to Φm.

FIG. 7
FIG. 7

Value of K as a function of i2. K = n−2(sini2 + sini′)−1. Refractive index = n = 1.5.

FIG. 8
FIG. 8

Mean values and standard deviations of K. The standard deviations are expressed as percentages of the mean values. K = n−2(sini2 + sini′)−1.

Equations (7)

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i = 2 sin - 1 ( sin i / n ) - i ,
i m = 2 sin - 1 ( 2 n 3 ( 1 - 1 4 n 2 ) 1 / 2 ) - sin - 1 ( 2 3 ( 1 - 1 4 n 2 ) 1 / 2 ) .
S = 4 a [ n ( 1 - sin 2 i n 2 ) 1 / 2 ( 1 + sin 2 i n 2 ) - sin 2 i cos i n 2 ]
a = 2 λ h 2 L ( Δ L ) ( 1 - 1 2 n ) ,
d Φ d S = - a - 1 ( sin i 2 + sin i ) - 1 .
K = n - 2 ( sin i 2 + sin i ) - 1 ,
K = ( sin i 2 + sin i ) - 1 / n 2 ,